Strategy is Underrated

          I can't stress enough the importance of using the right strategy when playing in the casino.  Over the years, I've heard all sorts of excuses for why people abandon strategy, ranging from it doesn't matter in the short run to some anecdotal story about how someone they know threw strategy to the wind and it paid off massively.  Yeah, that's nice.  If you're a sports fan, you know the importance of having a good coach or manager.  There are reasons why Pat Riley, Joe Torre and Bill Parcells are in such high demand.  Yes, it is because they win.  And they win because the utilize the right strategies for their respective sports.  This doesn't mean that once in a while their strategies won't fall apart.  Nor does it mean that there won't be times that they'll execute their strategy perfectly, yet still the other team will win due to a bad bounce.  I doubt any of these coaches would abandon their strategy over a bad bounce or a single loss.

            The same is true when you walk into the casino.  The coach/manager of your 'team' is you.  You decide which game to play.  This is the first key step in your strategy.  In fact, this leaves you with more power than any of the aforementioned coaches.  I'm sure many of them wish that they could pick their opponent on any given day, but they don't get to.  You on the other hand can decided whether to play slots, video poker or a table game.  If you decide on video poker (always a good choice), you decide which variation and to some degree, which paytable.  You can choose the short-pay paytable or make sure you find the full-pay paytable for the game of your choice.   Joe Torre isn't going to hit the field with only 8 fielders, why should you play jacks or better video poker that pays only 8 for a Full House instead of the full 9?

            Once you decide on your game and paytable, the real nitty gritty part of the strategy begins.  There are 52-cards in the deck.  There are 2,598,960 ways you can be dealt 5 cards from a 52-card deck.  There are 32 ways to play each of these deals, ranging from discarding none of the cards to discarding them all.  You have to make a decision on each of these hands which ones you will keep and which ones you will discard.  Fortunately, in about 75% of the cases, it is fairly obvious which ones you want to keep.  The other 25% is the challenge.  Back to our baseball analogy.  Most of the time, there isn't a lot for the manager to do.  He doesn't really have to tell his leadoff batter to 'get on base' every time he comes up.  I think it is fairly obvious that's what he will be trying to do.

            Unlike the baseball manager who has to outguess the opposing manager and players, the video poker Player doesn't need to outguess anyone or anything.  Video Poker is a game of pure math.  For each of those 32 possible ways to discard, there is a finite number of ways the hand can be completed.  Using computers, we can determine the final hand rank of every one of those hands and determine, on average, how many units the Player can expect to have return to him.  It is true that we don't know exactly which cards will come up this time, but we do know that over time, the actual results will approximate our expected results.  Based on this, we learn that the best play for the Player is to play the hand whichever way results in the highest expected return of units.  We call this 'expected value' or EV for short.

            This concept is used for EVERY single decision made in the casino in every game with any strategy.  The decision to hit or stick in blackjack is decided by which of these two decisions results in the higher expected value.  We Fold on Q-6-3 in Three Card Poker and Play on Q-6-4 because in the case of the Q-6-4, Playing has a higher Expected Value than Folding.  The opposite is true for Q-6-3.

            You are in complete control of how to play these hands.  In the case of video poker, the decisions you make are ones that can result in the machine you are playing having a 100.5% payback or a 96% payback.  One payback means you will win in the long run and the other means you will lose (and lose a lot more) in the long run.

            Does playing the right strategy mean you will win every session?  Absolutely not.  It just means your chances of winning increases greatly.   In today's world, the manager that utilizes matchup charts that show how hitters have done against certain pitchers is likely to be far more successful than one who just feels that now is the right time for a certain pinch hitter - he's due to get a hit.    Utilizing the right strategy is important in a variety of situations.  I can't stress enough that the casino is most definitely one of these situations.

House Money Strategy

            A few weeks ago, I discussed a new game that was about to be released called House Money.  Just before the article went to print, I found out that due to a technical snafu, the game did NOT go live in the casino I mentioned in that article.  But, in the ensuing weeks, it has gone live in four casinos (Cannery in LV, Drift on Inn and Great American Casino in Washington and Pala Casino in California) for a total of eight tables.

            As a quick refresher, House Money is a sidebet for blackjack.  On the surface it seems very simplistic.  You make the optional sidebet wager before the hand is dealt.  If you are dealt a 2-Card Straight Flush, a Straight or a Pair, you win.  What makes House Money stand out is what happens next.  You can either just take you winnings and play your blackjack game as normal OR you can take all those winnings and add them to your base blackjack wager.  It then becomes a part of your wager just as if you made it before the hand was dealt.  If you double, you must match the entire wager (unless the casino allows doubling for less).  If you split the hand, you must match the entire wager and be prepared for additional splits and/or doubling.

            Some decisions are rather easy.  If you're dealt a suited K-A (or even an off-suit K-A), there is not much to think about.  You take your winnings and cap your base bet.  If the Dealer has blackjack, no big deal, it all pushes and it is as if you took your winnings in the first place.  If the Dealer DOESN'T have blackjack, then you'll win 3 to 2 for the ENTIRE wager!

            Other decisions will be almost as easy.  If you're dealt a Pair of 10's or Face Cards, you'll always cap your base blackjack bet.  The Dealer will check for blackjack first, so you don't have to worry about losing your sidebet winnings that way.   Sometimes, the decision NOT to cap your wager will be rather easy too.  If you're dealt a 6-7 looking into a 10, you'll gladly take your winnings and know that whatever happens in the base game, the hand can't be an overall loser.

            There are two strategy problems that you are going to come across.  The first are the hands in which the strategy is less obvious.  For example, it may be no surprise that we cap the wager with a 9-10 against a 2 through 8.  But, we also do it against a 9 through Ace.  Yes, you're going to lose some of the hands against a 10 with a 19 but the odds are still in your favor.  It may also be difficult for you to cap your base blackjack wager when you have a 4-5 against an 8.  Yes, you are likely to draw a 10, but there will be times you draw a 6 and are stuck with a 15 against that 8.  You'll have to have the courage to risk busting the hand even with a wager that might be 3-10 times larger than your normal wager!

            The second strategy issue is going to be the double down and even more so, the potential split hands.   If you are dealt a 5-6, you must be ready to cap your base wager and then double the entire amount in order to maximize the payback of the sidebet.   So, if you are a $5 player and you put $5 on the sidebet and are dealt a suited 5-6, you'll win $20 on the sidebet and have $25 to add to your base wager.  You're now a $30 blackjack Player and you have to be ready to put down another $30 in these cases.

            In similar fashion, if you are dealt a Pair of 8's, you cap your base wager against a 2 through 7, which is probably no surprise.  With the Pair of 8's, you'll win $15 on the sidebet and have $20 to add to the base wager, making you a $25 Player.  Now, you have to split those 8's and be ready for the possibility of being dealt a 2, 3 or 8 leaving you with $25 double downs or splits.  You can quickly have $100 on the table.

            But, as the guy who did the math for Shuffle Master for this game, I can tell you that if you want to have a shot at earning the 98.3% payback from the sidebet, you're going to have not only cap your bet at the right times, but once you do, you must play blackjack using standard strategy.  One of the incredible features of House Money is that while it has its own strategy, it does not change basic Blackjack Strategy one bit!

            If you are interested in learning the complete strategy for House Money, I have created a simple 8 1/2" x 11" tipsheet that shows you when to cap your wager and when to take the money.  It is valid for all shoe sizes.  Eventually, I hope to shrink it down to a pocket-sized strategy card that you can bring with you to the casino, but for now, this will have to do.  If you are interested in ordering it, please send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89134.

Quads are the Key

For those of you who read my column regularly, you are probably now well aware that a full-pay jacks or better video poker machine pays 99.5%.  Many people are still confused, however as to what this means.  It does NOT mean that if I start with $100 I will walk away with 99.5% or $99.50.  It means that in the long run, you could take the total amount you wager (NOT your bankroll) and multiply it by 0.5% (the 'loss' rate or 100% minus the payback) and this should be the amount you have lost over time.  So, if you play 10,000 hands over the course of a year (or a month or a decade) and you play max-coin $1 machines, you would have wagered $50,000 and can expect to lose about $250. 

            In video poker, however, 10,000 hands isn't really the long run.  Don't get me wrong, it is certainly approaching the long run.  But, given that a Royal Flush should occur about every 40,000+ hands, it would be hard to declare 10,000 hands to be the long run.  If you've hit at least one Royal, you would be ahead of the game.  If you haven't, it would be totally fair to say you are behind because you still have 30,000+ hands to go.  Royal Flushes account for about 2% of our payback.  So, if you were to NEVER hit one, you'd theoretically be playing only a 97.5% game.

            With a hand frequency of 1 in 40,000+, Royals sort of march to their own drummer.  You might hit 2 or 3 in 40,000 hands or you might go 100,000 hands without hitting one.  When you hit one, you're going to have a very good month and when you don't, well, it will be harder to even break even.

            Four of a Kinds, on the other hand, should occur about 1 in about 420 hands.  With the average Player playing hundreds of hands per hour and perhaps thousands in a session, this hand becomes critical to our chances of success over a session or two.  It accounts for 6% of our overall payback.  Relative to the other hands, this is not necessarily large, but it is a hand that is frequent enough that you expect to hit it over a session, but not frequent enough to be sure you'll hit your fair share over a few nights.   If you were to play 10,000 hands, you'd probably find that the frequency of High Pairs and Trips and Straights are very close to what they should be.  Royals will by very definition have to be either more frequent or less frequent than expected, but Quads can be just about anywhere over that period of time. 

            In theory, you should hit about 24 of them over that time.  The math says you very likely could hit only 12 or as many as 36.  If you hit 12, you're about 3% short in payback.  Assuming you haven't hit a Royal and you're now 5% short.  The odds of coming up a winner over that span is very unlikely as you'll be playing at 94.5% and hoping the other hands come up big - which simply isn't very likely.

            Conversely, if you've hit36 of them, you'll be at 100.5% EVEN if you haven't hit a Royal.  A winning session is not guaranteed but certainly more likely.  Over time, the frequency of the Quads will slowly head towards that 24 per 10,000 hands, but your results in the short or medium run is heavily dependent on hitting your four of a kinds.

            As with anything video poker, the number of Four of a Kinds you get is at least partially attributed to luck.  We've all played for hours and been dealt dozens of Three of a Kinds to watch NONE of them turn into Quads.  We've also all sat there and drawn 3 Kings to a single King.  Nothing that happens is truly out of the ordinary.  However, you can increase your chances by playing the right strategy.  If you hold a 4-Card Straight OVER a Low Pair, you are going to greatly reduce your chances of Quads.  If you hold 3 High Cards instead of just the 2 that are suited, you will lower your chances for getting Quads.  The reason why we hold only the 2 suited cards is both to give us a chance to hit the Royal AND to increase the chances of Quads.  Both of these hands are reduced to ZERO CHANCE if you hold 3 off-suit High Cards!

            Of course, if you choose to hold a Low Pair OVER a 4-Card Flush you may increase the frequencies of Four of a Kinds, but you'll do so at your own peril.  Quads are important, but not so important that you should be throwing the proper strategy out the window.

Playing with House Money

            Over the years, there have been numerous successful sidebets to blackjack.  Many people have wondered why blackjack Players would bother with a sidebet.  A good blackjack Player can play the game at 99.5%, so why would they want to play a sidebet that might pay anywhere from 75%-90%.  That would seem to defeat the purpose of playing a game with such a narrow house edge. 

            I think the success of blackjack sidebets lie in the volatility of them.  Blackjack is essentially a game of coin tosses.  You win one, you lose one.  You win two, you lose three, you win two more.   It is hard to make a real killing (or get killed) on anyone hand unless you have one of those cases where you split 8's, draw another 8 and then a bunch of 2's and 3's for Double Down situation.   The average wager at a blackjack table is a mere 1.15 (roughly) units.

            The sidebet on the other hand will frequently afford the Player the opportunity to win big on a single hand.  The more frequent payoffs might pay 4 to 1 or even 10 to 1.  The more rare winning hands might pay 100 to 1 or 1000 to 1.  A $5 wager can quickly (so to speak) become $500 or $5000.    The tradeoff for this opportunity is generally the lower paybacks associated with no strategy sidebets.  The casinos can't offer 97-98% paybacks for games with no strategy because they can't rely on human error to help drive the casino edge.

            A couple of months ago, Roger Snow, Chief Product Officer at Shuffle Master brought a game idea to me to analyze.  As is frequently the case when we work together, the game went through multiple iterations before we arrived at the final product.  After we 'ran the numbers', I think Roger liked it but didn't love it.  I, on the other hand, told him I thought we had just come up with a nearly perfect sidebet for blackjack.  It was given the name House Money for reasons which will soon become clear.

            As far as I know, it is the first and only blackjack sidebet that has strategy, yet somehow does not affect base blackjack strategy at all.  As a result, if a Player chooses not to play the sidebet, he gives up nothing to the house by sitting at a table that offers it. Also, the casinos are able to offer a sidebet with a payback in the 95+% range because there is the possibility of human error in the strategy.  With all this, the concept of the sidebet is quite simple.

The Player makes a wager before being dealt his blackjack hand.  The Dealer deals the cards as per normal blackjack rules.  If the Player is dealt a Pair, a Straight or a Straight Flush, he wins.  As always, there may be multiple paytables over time, but for now, this is the most common one for a 2, 6 or 8-deck game:

Hand	Pays (TO 1)*
Suited A-K	9
2-Card Straight Flush	4
Pair	3
2-Card Straight	1

            Those payouts may not look all that spectacular.  In all honesty, they are not.  If the game ended right here, the payback would only be about 75% and this would just be another 'nothing special' blackjack sidebet.  But, the game does not end here.  The Player now has two options:

·         Take his winnings and play out his blackjack end per usual

·         Add any/all of his winnings to his base blackjack wager and then play out his hand per usual

            There are NO restrictions on these rules.  If the Player is dealt a Suited A-K, he will be paid 9 to 1 for his sidebet and then can add the entire 10 units to his base Blackjack wager which has ZERO chance of losing.  And YES, the casino will pay 3 to 2 for this additional wagered amount if the Dealer does not also have a Blackjack.

            If the Player is dealt a Pair of Jacks, he will be paid 3 to 1 for the sidebet.  If the Dealer has a 6 up, he can add all 4 units to the blackjack wager.  If the Dealer has a 10 up, he can choose to do so too, but here's where the strategy part comes in.  Is this the right move?  In reality, it is the correct move.  I should add that if the Dealer has Blackjack, the Player NEVER risks his winnings from the sidebet.

            The real fun begins when the Player is dealt a 5-6 (or 5-6 suited) and wins even money (or 4 to 1) and has to decide whether to risk his winnings on his base blackjack wager.  If the Player chooses to do so, it becomes a part of his wager in every sense of the word.  If he decides to double down, he MUST match the ENTIRE wager.  The same applies if he is dealt a Pair and chooses to split.

            Imagine starting with a $5 wager on both the base wager and the sidebet and being dealt a Pair of 8's.  The Dealer pays you 3 to 1 on your sidebet and you now have to decide if you want to add the $20 to your base blackjack wager, making it a total of $25.  Assuming you do and you go ahead and follow standard strategy, you will now split those 8's and you'll have to put up an additional $25 of your own.  Now, you are dealt another 8 and you put up another $25.  Then you're dealt a '3' and you double down and play ANOTHER $25.  You started as a $5 Player and now you have $100 down on the table on essentially one hand!

            For the record, you would only let your sidebet winnings ride if the Dealer has a 2 through 7 as an upcard.  However, whether you cap your bet or take your winnings, you still follow basic blackjack strategy and split those 8's.  You double down on all 11's.

            So far, House Money has been very well received by the casinos that it has been demonstrated in.  It is expected to go live in the next couple of weeks in Reno at the Grand Siena Reno.  It should go live in other casinos shortly thereafter as regulatory approvals are granted.  In a few weeks, after the game has gone live, I'll review the complete strategy for the game.

           

Eyes Wide Open

            I finally discovered something that has a lower payback than slot machines – New Jersey Turnpike tolls!  As I write this, we’re back on the East Coast for personal business.  After landing at Newark, we had to drive up to the Boston area.  I couldn’t believe the toll from Newark airport to northern end of the Turnpike.  It was $3.60 to go about 20 miles.  Throw in the $12 toll to cross the George Washington Bridge to cross into New York and I was out more than $15 after only being on the road for 25 minutes!  It takes quite a bankroll to drive on these roads, and with NO chance of winning.  We had only left NJ less than a year ago and all these tolls had gone up considerably since we left!

            On a more serious note regarding slots, I received a very good question from a reader this past week.  He acknowledged what I had written several weeks ago that the average slot machines paid only 92-93% and that video poker generally paid 97-100+%.  He asked that given that casino gambling is just a form of entertainment, what is so bad about the idea of taking $100 of your bankroll to go for a huge jackpot on a slot machine, especially given that winning a similar amount at video poker would take a long time with smaller wins along the way.  I have to admit, that it took me a little while for me to come up with a response.

            I think the best I can come up with is that if you go in with your eyes open as to what you are doing then I can’t really say there is anything wrong with it.  Gambling is entertainment and if it brings you enjoyment to take part of your bankroll and put it into a low payback slot machine with a jumbo-sized jackpot, that is your choice.  If I have any issue with the concept it is that it is very hard, if not impossible to go into this with your eyes truly open.  Yes, you can know the size of the jackpot, but you don’t know the probability of actually hitting it. 

            The other issue is that it is standard practice in casino gaming that if the game has a huge jackpot (usually Progressive) then the payback of the game tends to be even lower.  This is true for both slot machines and even table game sidebets.  Outside the casino, this is even truer for things like Lotto.  Most state lotteries have paybacks in the 50-60% range.  Players are willing to play games with very low paybacks in hope of winning that life altering prize.   Again, however, in the case of Lotto, we are able to compute the probability of winning the top prize.  This is not the case for slots.

            While the low payback of regular slots is concerning, and the presumed even lower payback of a Progressive slot is even more concerning, the biggest concern still belongs to the notion that there is no way to know anything about a slot machine.  We don’t know the probability of the jackpot spin or any other result.  We have no way of knowing the overall payback of the machine by a simple glance at the glass.  In a place like Nevada, the payback can be no less than 75% so that is about all we really know.

            So, that all said, if you feel that you want to play a game that has a life-changing jackpot with a portion of your bankroll, I can understand the desire to try your hand at a slot machine.   It is probably the only chance you have for a multi-million dollar prize.  If you are looking for a gigantic jackpot, I would personally recommend a Pai Gow Poker sidebet or the Six-Card sidebet for Three Card Poker.  The prizes will only be in the few hundred thousand to $1 million, but you’ll still be playing games with higher paybacks.

            In the end, it is your money and you have to decide how you want to spend it and what provides you the most enjoyment.  If chasing a mega jackpot on a low paying machines with a portion of your bankroll is what brings you joy, I won’t stop you.

            

Player Friendly

            This past week, I met someone who was visiting Las Vegas from California.  I told him about my work with video poker and he asked me what is the best game to play.  My natural reaction to that is to just laugh.  How am I supposed to answer that?  Besides the fact that 'best' is a very subjective term.  Admittedly most people want me to answer which games are the best mathematically.  But, as this guy was stating on the strip, the odds (pardon the pun) that the best game is anywhere near is rather slim.  In fact, I'm a bit scared to tell him to play a particular type of machine in fear that he'll find it, but not at anything near full-pay.

            As the conversation continued, he told me that he likes to play Double Double Bonus Poker.  I was certainly not surprised to hear this.  It is a very popular game and he cited the biggest reason that it is - the extra chance to get a huge jackpot with the Four Aces and a kicker.  He also told me about the time that he was playing a ten-play Double Double Bonus machine and was dealt Four Aces plus the kicker on the initial deal.  Multiply that by 10 and it is a NICE payday even if you are playing a relatively small denomination or not max-coin.

            When you get dealt a hand like that, you might just be hooked for life.  It reminds me of the day I was playing golf with a friend.  Neither of us are all that good.  I still had a great time, but he wasn't happy with how poorly he played.  Well, until we got to about the 17th green and he rolled in about 30 foot putt.  Then he wanted to know when we could play next. 

            I suggested to the man that he try to find some Double Bonus machines, which at full-pay have a 100.1% payback.  Double Double Bonus has a payback of only 98.8%, also at full-pay.  I then told him that the best paying machines were variants of Deuces Wild, but only if he played proper strategy.  I really didn't know if he had a clue as to proper strategy for even Bonus games, yet alone Deuces Wild.  I figured that he would still be better off sticking to what he was familiar with than trying to play a game like Deuces without the benefit having attempted to learn the strategy.  While there are differences between Double and Double Double, at least he is still in the same general universe with those two.

            Of course, the real problem with answering his question is that he was going to be playing on the strip, which isn't exactly know nowadays for having too many full-pay machines.   Much to my surprise, I checked my source for video poker inventory - www.vpfree2.com - and found that the casino he was staying in (I won't name it), DOES have a some full-pay machines, but all at denomination of $1 or more.  It took me a second to fully comprehend this.  Usually casinos only put out full-pay machines for low denominations.  If you want to play at nickels they'll allow some winners.  Then it hit me,  NONE of their full-pay machines were over 100%.  If you want to play Double Double at full-pay, they'll be happy to let you at $5 per hand ($1 max-coin).  With a payback of 98.9%, the casino can expect to clear more than $30 an hour!  Of course, they may have some quarter machines to play, but those will be short-pay and you may find the same loss rate as a result. 

            I'm not naive.  I fully realize that most video poker machines have paybacks below 100% and that means that you will lose over the long run.  I have stated many times that gambling is just a form of entertainment for almost everyone.   But given the nature of gambling is that the cost is variable and that sometimes you can win money, your goal should be to minimize the losses and give yourself the best chance to win.

            To do this, you need to find games that have paybacks as close to 100% (or over) being played at a denomination that you feel comfortable with.  If you are okay with playing a $1 machine, that's great, but make sure you have enough bankroll for it.  Don't expect to walk over with $100 and play all night.   If you start with $100 don't be surprised if it is gone in a hurry and once your bankroll is gone, there is no coming back from it. 

            If you don't feel comfortable playing $1 machines or you don't have enough bankroll to do it, make sure that when you step down in denomination that the paytable doesn't take a big step down too.  Or, as I told this gentleman, if he really wants to find good video poker options, he might have to venture to one of the 'locals' casinos where the paytables are known to be a bit more Player friendly.

The Penalty Box

            In last week's column, I analyzed a particular hand that could be played multiple ways.  The hand was as follows:

J♠        8♦        Q♦       3♥        9♦

            From a quick glance, one might think to play the hand as a 4-Card Inside Straight with 2 High Cards, a 3-Card Double Inside Straight Flush with 1 High Card or simply as Two High Cards.  As always, the decision comes down to which of the hands has the highest Expected Value (EV).   In last week's column, instead of simply relying on the EV in a strategy table, I used a program that I created that allows me to put in the EXACT 5 cards and tell it which ones I'm holding and which ones I'm discarding.  It then gives me the exact EV of the hand in question.  Why do I do this instead of just using the value in the strategy table?

            The values in the strategy tables are averages of all hands of that particular type.  The accuracy is thus dependent on a few factors, ranging to the nature of the specific hand to the specificity of that hand.  For example, we list the Expected Value of a 4-Card Flush as 1.22.  In reality, there is not a single 4-Card Flush that has that EV.  While there is always the same number of possible ways to draw the Flush (9), the number of High Cards in the hand will impact the exact expected value because it changes the number of ways we can pick up a High Pair.  If we have 0 High Cards, the EV is 1.15.  With 1 High Card it is 1.21 and with 2 High Cards it is 1.28.   We could just as easily list these three hand separately on the strategy table, but it wouldn't change the strategy we would employ at all.  There are no other hands that have an EV between 1.15 and 1.28.  So, in this case we lump all the 4-Card Flushes together and show the average EV for all 85,512 possible 4-Card Flushes.

            In a similar fashion, we have a single entry on our Strategy table called the 4-Card Royal which has an expected value of 18.66.  but not all 4-Card Royals are created equal.  We might have 10-J-Q-K which allows for pulling the suited 9 and picking up a Straight Flush.  Or we can pick up an unsuited 9 for a Straight.  However, we also only have 9 ways to pick up a High Pair.  Thus the EV of this hand is rather different from that of J-Q-K-A which has no way to pick up a Straight Flush and also has only one way to pick up a Straight (both ends are NOT open).  But, we get 3 additional cards that will give us the High Pair.  

            But, there is another item that can affect the specific Expected Value.  What happens if we are dealt a Flush 3-J-Q-K-A.  The Flush has an EV of 6.00 while the 4-Card Royal has an EV of 18.66.  But, when we discard the 3, we lose one opportunity to draw the Flush.  This will certainly NOT drop the EV of the 4-Card Royal to below that of a Flush, but we should recognize the impact of the specific card we discard.  When we discard a card that could help improve the final hand, it is called a 'penalty card'.  In this particular case, there is no impact to our strategy as a result of discarding the 3, so we are safe to lump all 4-Card Royals together.

            However, as we go down further on our strategy table, we begin to break apart the hands into smaller groupings.  We don't have all the 4-Card Straights listed together the way we do the 4-Card Flushes.  Because a Straight only pays 4 and there are only 8 ways to complete them, the EV of Straights drops to the point where it is very close to many 3-Card Straight Flushes, 2-Card Royals and even High Card hands.  Many of these hands also tend to overlap a lot, as in the example at the beginning of this article.  The hand is 2 High Cards, a 3-Card Straight Flush and a 4-Card Inside Straight all at the same time.  Slight changes in the hand make up could make it other hands all at the same time.

            When a hand overlaps as this one does, there is usually at least some penalty card situations.  In this case, if we choose to play the hand as 2 High Cards, discarding the 8 and 9 create the penalty card situation.  We wouldn't want to draw an 8, 9 and 3, but we wouldn't mind drawing an 8, 9 and 10.  While this may not be the most common outcome, it is one that would complete the Straight and give us one of the highest possible payouts for the 2 High Cards.  So, discarding them may reduce the ACTUAL Expected Value slightly from the one we may find under 2 High Cards in the strategy table.

            Likewise, when we hold the 8, 9 and Q, we are discarding the Jack which is a penalty card.  It can be used to complete a Straight or we might pick up another Jack to make a High Pair.  So, I calculate the exact Expected Value in last week's column to make sure the result was 100% accurate.

            As I've said many times in my column, you don't need to memorize the Expected Value of any hand because the value itself is meaningless.  What matters is the relative value.  You need to know which hand has the higher EV.   Once in a while, a penalty card situation will cause a hand as it is shown on the strategy table to have an ACTUAL Expected Value that actually drops it to below that of another playable hand from that same 5-card draw.  This in essence creates an exception condition to how the hand should be played when using a strategy table.  The hand should STILL be played according to which has the higher Expected Value, but because we are using the 'average' shown on a strategy table, we don't actually do this.

            When my father, Lenny Frome, developed Expert Strategy, he was well aware of this situation.  He felt that the impact on the payback of these exceptions was too small to be concerned with relative to the idea of listing out what could be several to dozens more lines on the strategy table.  Learning Expert Strategy can be enough of a challenge.  He didn't want to complicate it further by trying to list out hands that might look something like this:

·         4-Card Straight with 2 High Cards, EXCEPT if there is a 3-Card Straight Flush, but ONLY if the 2 High Cards are part of the 3-Card Straight Flush

            I tend to agree with my father and learning these extra rules are only for diehards and even then, the risk of error might be more than the extra 0.001% it might yield in payback.

Rare Gems - Straight Flushes

            One of the ironies about video poker paytables is that they don't always reward hands more for being more rare.  If I were to ask you which occurs more often in video poker - a Flush, a Straight or a Full House, I'm guessing most of you would say a Straight, followed by a Flush and lastly a Full House.  It is really a trick question.  Without knowing what the paytable is, there is no way to answer the question accurately.  The only thing we know is that, in general, a Full House outranks a Flush, which outranks a Straight. 

            On a full-pay video poker machine, assuming you use Expert Strategy, you will actually hit more Full Houses than either of the other two.  A Straight will occur just slightly more often than a Flush.  Upon close inspection, we realize that this is by far a product of the payouts for each hand than it is a product of the hands themselves.   If we take a look at the game of All American Video Poker - which would appear to now be obsolete - we will see a very different pattern develop.  In All American, a Straight, Flush and Full House all pay 8.  With no reason to go for one or the others, the pure probabilities of hitting each hand begin to show up.  As a result, the frequency of Straights and Flushes increase dramatically, to the point where they occur nearly twice as often as a Full House.

            A similar phenomenon occurs with a Straight Flush.  Generally speaking, it occurs just about 4 times as frequently as a Royal Flush, while paying only 1/16th of the amount.  Or we can look at it the other way and say that it is more than 20 times as rare as a Four of a Kind while only paying twice as much.  When we throw in the Bonus Video Pokers, it only looks worse.  This far more rare hand might actually pay LESS than many of the Quads we can hit, which are far more common.

            Of course, I'm wondering how many of you have hit nearly as many Royal Flushes as you've hit Straight Flushes.  I doubt you remember your Straight Flushes as vividly.  Winning $62.50 on a max-coin quarter machine isn't quite as memorable as a cool $1000, but that isn't my point.  If you use Expert Strategy on a jacks or better machine, you should hit a Royal every 40,400 hands or so and a Straight Flush every 9200 hands.  The key phrase is "if you use Expert Strategy."  Since most Players, at best, use pieces of strategy, I'm guessing that the Straight Flush shows up far less often because the partial Straight Flush is frequently overlooked when the Play.

            If dealt the following, what's the right play?

J♠        8♦        Q♦       3♥        9♦

            Do you play the 4-Card Inside Straight with 2 High Cards, the 3-Card Double Inside Straight with 1 High Card or the 2 High Cards?  As always, there is just one way to determine the right play.  We go to the Expected Values of each.

            Calculating the Expected Value for the 4-Card Inside Straight is fairly easy.  We can draw the Straight with 4 cards and we can draw a High Pair with 6 more.  This will return 22 units to us.  Divide by 47 and we get a result of just below 0.47.  For the other two, I ran them through a program I have that calculates the exact Expected Value given the specific discards.   The Two High Cards have an Expected Value of just below 0.50 and the 3-Card Double Inside Straight Flush has an Expected Value of just below 0.53.  This is the proper play. 

            While the odds of hitting the Straight Flush are 1 in 1081, this is still far greater than hitting it with either of the other two hands (it is zero in these cases).  Ironically, it is not the tremendous payout of the Straight Flush that causes us to play the hand this way.  By holding a 3-Card Straight Flush, we give ourselves numerous chances to hit just Straights and Flushes - a combined 1 in 20 (roughly).  Throw in opportunities for Three of a Kind and Two Pairs and this hand simply beats the others.

            Now, no one expects you to calculate the Expected Value of even the 4-Card Inside Straight on the fly or to carry a small computer to run my program that calculates the exact Expected Value for each hand.  It is much easier to simply use a strategy table that lists out each playable hand.   If we look up the three hands in a strategy table, we find a 3-Card Double Inside Straight Flush has an Expected Value of 0.54, the Two High Cards have an Expected Value of 0.49 and the 4-Card Inside Straight with 2 High Cards doesn't even make it onto our strategy table because the Two High Cards always outranks it.  These values are the average of all hands of that type so they don't always equal the exact Expected Value taken into account the exact discards.

            In the end, the frequency of a hand occurring is a product of the paytable and following the right strategy.  If you want to get your share of Straight Flushes, you can't do a lot about the former, but the latter is fully in your control.

Boston 7 Invades Taj Mahal in Atlantic City

            Almost everyone is familiar with what a heavy Boston accent sounds like.  Or should I say Bah-stun?  I'll never forget a story I heard while a freshman in college.  A classmate had visited one of the Boston colleges the year before to check it out.  The student giving the tour told him that "Freshman are not allowed to have cars on campus."  What he heard was "cahs: and not "cars."   A bit confused he asked the student leading the tour - "why would a freshman want to have a cow on campus?"

            Less well known about Bostonians is that they have taken the word 'wicked' and turned it upside down.  Wicked doesn't mean evil in Boston.  It means 'very'.  A wicked bad headache is a very bad headache.  So, when I say that John Feola of New Vision Gaming has invented one wicked cool game, it means it is a game worth playing! 

            The new game is called Boston 7 Stud Poker and it just opened at the Trump Taj Mahal in Atlantic City.  It is a wicked simple game and if you're familiar with Mr. Feola's Boston 5 Stud, you'll notice some similarities.  Boston 7 Stud just takes advantage of the on-going popularity of the 7-card Poker games.

            To begin with, the Player makes 2 equal size wagers, called the Ante and the 1st Wager.  He then receives 3 cards.  The Player now has a choice to make.  He can either Fold, forfeiting his Ante and 1st Wager or he can make a 2nd Wager - equal in size to the other two wagers - and receive 4 additional cards.

            If the Player decides to make the 2nd Wager, his hand will go head-to-head against the Dealer's hand.  The Player will make his best 5-Card Poker hand from his 7 cards.  The Dealer is also dealt 7 cards to make his best 5-card Poker Hand.   If the Player's hand beats the Dealer's hand, his 1st and 2nd Wager will pay even money.  The Ante will push unless the Player's hand is a Three of a Kind or better, in which case it will pay an Ante Bonus according to the following paytable:

Hand	Pays
7 - Card Royal	$25,000
6 - Card Royal	$5,000
5 - Card Royal	250
Straight Flush	100
Four of a Kind	25
Full House	4
Flush	3
Straight	2
Three of a Kind	1

            Note that the top two hands actually consist of 6-card and 7-card hands, respectively and are fixed pays, not odds pays.

            If the Dealer's hand beats the Player's hand, all wagers are taken, BUT the Player will still be paid according to the above paytable if he has a Three of a Kind or better.  So, while he will still lose his Ante Wager itself, he will still be paid for the hand.  If the Player's hand and Dealer's hands tie, all wagers push, but the Player can still earn an Ante Bonus.

            There is also an optional 3-card Bonus Sidebet that the Player can make that is based on his first three cards.  The Player MUST show his first three cards to the Dealer if he has a Pair or better in order to claim his win.  The paytable for the 3-Card Bonus is as follows:

Hand	Pays*
Royal Flush	100
Straight Flush	40
Three of A Kind	30
Straight	6
Flush	3
Pair	1

* Pays are "TO 1"

            As I did the analysis on this game for the regulatory agencies, I'm quite familiar with the math.  The overall payback of the base game is 97.59% which is fine for a game with essentially no strategy.  While the Player has to make a decision, in theory, there really is no decision in reality.  The Player should NEVER Fold.  Even the worst possible 3-card starter hand can come back to beat the Dealer often enough to make it not worth Folding.  As a result, what we really have is a game in which the Player and Dealer will each win 50% of the time.  The House edge is created from the fact that the Ante Pushes unless the Player's hand is Three of a Kind or better.  The Player also gets the advantage of being paid even on losing hands of Trips or better.

            For the 3-Card Bonus Sidebet, the payback is 93.81%, which is in-line with many other 3-Card paytables that can be found, especially in Atlantic City.  The game was developed with numerous Ante Bonus and 3-Card Bonus paytables, so pay careful attention to the actual paytables before you sit down and play. 

            If you do make it down to Atlantic City and play Boston 7, I'm sure you're in for one wicked good time.  You can go to www.newvisiongaming.com and check out more of their games, including Imperial Pai Gow

What to Play

            Last week, I wrote about Four Card Poker and mentioned how I would cover it's 'crazy' cousin - Crazy 4 Poker in an upcoming column.  I started to work on this column this past week when I got to the point of discussing why a Player would choose to play one of the games over the other.  The overall paybacks are fairly similar.  The reality is, that I can't really suggest to Players to play one of these games instead of the other.  This is because casino games are (or at least should be) a form of entertainment and we can't overlook this factor in our choices.

            So much of what I write is all about the math.  Years ago, my father, Lenny Frome, described Expert Strategy as a three-legged stool, with each leg equally important.  After all, we know what happens if one leg of a stool is shorter than the other two!   These three legs were:

·         Know which game to play

·         Know how to play that game

·         Know what to expect

            The first of these legs essentially referred to the payback of the game.  Don't play short-pay machines when you can find full-pay machines.  On the surface, it might mean play only the game(s) with the absolute highest payback.  But, if that were the case, everyone should be clamoring for the one type of video poker machine in the casino with the highest payback - probably some Deuces Wild variant. 

            If this were what my father intended, why did he bother to write about all the other games in detail - not just video poker but all of the proprietary table games too?  This is why a few years back, I added a concept to my father's three-legged stool.  I called it the comfy cushion.  It means you have to ENJOY playing whatever game you choose as well.  There are two significant reasons why I added this explicity to Expert Strategy.

            The first reason is because, as I said earlier, gambling should be a form of entertainment.  By this definition, you should enjoy it your time doing it.  Yes, I fully understand that it is a somewhat unique form of entertainment in that you might walk away with more money than you started, but with rare exception, these are not life-altering amounts of money we are talking about.  I'm sure no one minds being miserable while they are winning thousands (or hundreds of thousands of dollars), but more often than not, your win will be far smaller than this and you will lose more often than you will win.  No one likes to lose, but if you're absolutely miserable while you are losing $20 over 3 hours, something is very wrong.   When you go to a movie theater, there is a good chance you'll spend $20 too.  You'll have no chance of getting that money back.  You probably won't mind if the movie was good.  If the movie was a rotten tomato, it might bother you a bit more.  This is the same attitude you should take with you to the casino.

            The second reason is that if you're not having any fun while playing, there's a pretty good chance you are going to forget all about the other two legs of the stool.  You may know how to play a game, but in your frustration you'll start doing things you shouldn't be doing.  You may know what to expect, but while you're not having fun, you'll start imagining the cards are all against you or that the casino must be cheating and again, you'll go away from the strategy that you are supposed to be using.  So, on a theoretical level, you might be playing a game with a higher payback, but if you don't adhere to the strategy you may find that on a reality level, you've lowered the payback to the point where you'd be better off playing a different game.

            Undoubtedly, some of you may take what I'm saying as carte blanche to now go off and play any game in the casino.  In the end, of course, it is your decision.  But, please don't take this as my endorsement of playing slots or sitting down at a Craps table and simply playing the Hardways bets for hours at a time.  The other two legs of Expert Strategy remain full in force, so I suggest you certainly know what to expect in these cases.  Your chances of a winning session is greatly reduced.  It is one thing to pick a 99.2% video poker machine over a 99.6% one.  It is quite another to play a 91% payback proposition bet for hours.  If this is the only thing you enjoy in the casino, it might be time to pick a new form of entertainment

Four Play

           

            Four Card Poker has a special place in my heart because it sort of launched my career as a gaming analyst.  Ironically, I didn't analyze it as it was being developed.  Rather, I wrote about it right here in Gaming Today way back in February 2004.  The column got noticed by the then President of Shuffle Master, who put me in touch with Roger Snow, the inventor of the game and at the time, the Manager of Table Games for Shuffle Master.  That introduction was the beginning of what has been a very successful collaboration which has included blockbuster games such as Ultimate Texas Hold'em and Mississippi Stud, along with countless sidebets for virtually every game in the casino.

            Four Card Poker was also an important game for the evolution of proprietary table games.  By the time Four Card Poker hit stride, there had been a bit of a lull in table game creation.  The casino floor had already changed a good deal with Let It Ride, Caribbean Stud Poker, Three Card Poker and Spanish 21, but those games were all already several years old.  Perhaps there were some other games in between that I am unaware of.  Admittedly, this lull I speak of, occurred after my father passed away and before I entered the field.

            The game itself didn't really break any new ground in terms of betting structure or rules.   The new ground was broken by Four Card Poker's 'crazy' cousin - Crazy 4 Poker, which introduced the Super Bonus wager - which is more commonly known as the Blind wager on more recent Shuffle Master games.  This wager will push if the Player wins with a poor or so-so hand and will win odds if the Player wins with a strong hand.  I'll cover more about Crazy 4 Poker in a few weeks.  Crazy 4 Poker has about 100 tables in the marketplace as compared to Four Card Poker which has about 250.

            Four Card Poker utilizes the same betting structure as Three Card Poker.  There are two separate wagers - Aces Up and Ante/Play.   The Aces Up pays on a pair of Aces or better and is not concerned with the Dealer's hand at all.   The Ante/Play is the wager where you are playing head to head against the Dealer's hand.  You make an Ante wager to begin play and you are dealt your hand which you can review.  Now you can either make a Play wager of 1x - 3x your Ante or Fold, forfeiting your Ante wager.  If you beat the Dealer's hand, you are paid even money.  If you don't you lose both wagers.   Also, similar to Three Card Poker are the Ante Bonuses.  These pay the Player whether he wins or loses against the Dealer - if the Player can achieve a Four of a Kind, Straight Flush or Three of a Kind.  They pay 25, 20 and 2, respectively.

            So, by this point, if you are not familiar with Four Card Poker already, you're probably guessing that the Player and Dealer each get 4 cards and you might be wondering what hand the Dealer needs to qualify.  WRONG!  The name comes from the size of the hand the Player makes.  He is dealt FIVE cards to make a FOUR card hand.  The Dealer is dealt SIX Cards to make a FOUR card hand.  Thanks to this little benefit, the Dealer does NOT need to qualify in Four Card Poker.  Every hand plays. 

            In Three Card Poker, many people follow a strategy to just do what the Dealer does - and play any hand that is Queen or better.  This is a little below perfect, but will not hurt your bankroll significantly.  If you want to play like an Expert, you go with Queen-6-4 as the lowest hand you Play.  So, with the Dealer qualifying on every hand in Four Card Poker, you have nothing to guide you at all.  Adding to the dilemma is when to Play 1x vs. Play 3x.  As is normally, the case, we NEVER bet 2x.  We either cut our losses (FOLD), hedge (Play 1x) or slam on the gas (Play 3x).

            When Four Card Poker was introduced, Shuffle Master supplied information cards that included a basic strategy on them.  This strategy produced a 98.41% payback and includes only 3 rules.  In my analysis of the game, I took that strategy a bit further and produced one with about 7 rules (admittedly, more complex rules too) that takes the payback up to 98.60%.  Even this strategy is not absolutely perfect as it does not take into account specific suit make up of the Player's hand nor go any further than the first 'kicker' in the Player's hand.  It is my expert opinion that to do so would only get the Player an additional 0.01 - 0.02% in payback, but it would also greatly increase the probability of errors by making the strategy that much more complex.

            Without further ado, I present the basic strategy which Shuffle Master initially developed and I have verified.

·         Fold with a Pair of 2's or Less

·         Bet 1X with a Pair of 3's thru 9's

·         Bet 3X with a Pair of 10's or Better

           

            It's that simple if you want to earn the 98.41% payback which is respectable.   Expect to Fold a good amount of the time - just under half.  Four Card Poker was designed to be quite a bit more volatile than Three Card Poker.   As Roger told me way back in 2004, "one of three things typically happens.  One, you double up.  Two, you get crushed.  Three, both one and two, and not necessarily in that order." 

            If you'd like to learn more about Four Card Poker, including the Expert Strategy, I highly recommend my Expert Strategy for Four Card Poker.  You can order it by sending $5.95 to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.  This price includes free shipping and handling.

For the Love of the Game

            Perseverance can be a positive trait when you are trying to invent a new table game.  Unfortunately, it can also be a negative one which can all but kill your chances of ever having a game reach the casino floor.  This translates to one simple thought - Don't fall in love with your game.

            Getting a game into a casino is not an easy thing.  Getting it stay in the casino if you manage to get it placed is even harder.  Perhaps 5% of all games that are conceived of make it to the floor.  Of those that do, maybe 5% that make it there stay for any length of time and continue to grow.  When you add it all up, about 1% of all games invented are some type of financial success for the inventor. 

            This past week I had a conversation with a newcomer to the industry and reminded him that only 1 out of a hundred games becomes a success.  His response was that he'll just have to make sure he comes up with 100 games so that one of them can be successful.  That type of perseverance is the type you want to have. 

            A few years ago, I got a call from an inventor who wanted me to tweak a game that my father had originally worked on for him.  I found the file.  My father had worked on the game 10 years earlier.  In the 10 years, the game had been given a trial or two in a casino and been pulled out relatively quickly.  This is not a time for tweaks.  It is a time to move on to the next idea.  This type of perseverance could be a killer. 

            Roger Snow, Executive VP of Shuffle Master, may very well be the most prolific table game inventor of them all, with games like UltimateTexas Hold'em, Four Card Poker and Crazy 4 Poker to his credit.  He likes to remind people that he has probably invented more flops than anyone in the industry as well.  This doesn't mean that you should take any idea you have and quickly try to get it into a casino, with the goal being to try as any games as you can and hope something sticks.  Unless you have a track record of success, casinos are going to give you only so many chances, so you do want to put your best foot forward.

            If you do manage to get your game into the casino for a trial, it is time to take off the rose-colored glasses.  Listen to the feedback the table games manager gives you.  If the game isn't fairing well, don't start blaming it all on the casino that was kind enough to give you the trial.  They are NOT setting you up for failure.  Even in a free trial, it costs the casino money to try out your game.  They need to train the dealers.  They need to make room for your game by removing some other game that might have been doing okay - in hopes that yours will do great.

            No one can predict the success or failure of a game with a high degree of certainty.  In the end, it must perform which means its success is at the whim of the Players.  I have been working directly with inventors for a decade and indirectly for three decades and there is no clear rhyme or reason as to what succeeds and what doesn't.   The only thing is certain is that if you bring it to the Players and the Players don't like it - it is NOT a success.  It does not matter that your brother, sister, mother and Aunt Tilly all love the game and think it is the greatest thing they've ever seen.  I don't know how to tell you this - but they are BIASED!  This is the same bunch that told you how much they love that new pair of glasses - you know, the ones that make you look like a 1970's version of Elton John.

            If you spend 10 or 15 years trying to get a single game into the casino, you will likely have overlooked many other good ideas that you might have had.  There is a 99% chance that any single game idea you have will fail.  Every game that is invented is, as they say, a slave to the math.  That same math should be telling you that after a certain number of setbacks, your chances of success are greater by moving on than by insisting that the reason your game failed was some flaw of anything but the game itself.  Putting it another way, the expected value of working on the next game is greater than continuing to beat the dead horse.  And by now, you all know that the right play is the one with the higher expected value.

Still Wild About Deuces Wild

            A few weeks ago, I wrote about full-pay deuces wild video poker and it's 100.6% payback.  It has gotten harder to find 100+% payback machines, but this one can still be found in many of the casinos that cater to the locals (i.e. OFF the strip!)  People are still amazed to find that such machines exist at all.  As I've written many times, the casinos don't mind leaving a few of these around in lower denominations.  This way they can say that they have positive payback machines, but they don't really have to worry about the professionals swarming on them.

            Even if you are an Expert Player who can play at 800 hands per hour, you're dropping $1000 in the machine every hour.  At 0.6% advantage, you can expect to win $6 per hour.  It certainly beats losing, but no one is getting rich at $6 per hour.  If you're willing to sit in a casino for 40 hours per week just as you would any other job, you might be able to clear $12,000 per year.  Of course, you won't be collecting a regular paycheck.  Some weeks you're going to lose and others you're going to hit the big payout.  But, at the end of the year, should be fairly close to that $12,000.  This will be your reward for playing roughly 1.6 million hands of video poker and putting into the machine a mere $2 million!

            I'm not going to recommend you quit your day job and try this.  In fact, I won't even recommend you give up looking for work, if you currently are, and become an professional video poker Player.  For almost everyone reading this column, you are a recreational player and video poker is a form of entertainment.  Some nights you win, some nights you lose.  Depending how long you play for per session, you'll lose roughly 2 out of every 3 times you play.  But, if you pick the right machines and learn the right strategy, your night out might cost you $20 and you can get some entertainment and a few drinks.

            With a 100.6% payback, you would definitely be picking the right machine with Deuces Wild.  So, the only other thing for you to do is to learn the right strategy.   At first glance, the strategy table for Deuces Wild might look daunting due to its size, but when you look closely, you'll see it is broken down by the number of Deuces.  If you make sure to learn it this way, you'll find it much easier to learn AND you'll be doing yourself a huge favor in terms of learning to play properly.  Deuces is not a hard game to learn.  It is just so vastly different from any other game, that people make lots of mistakes.

            One of the most important things to learn is when to hold just the Deuces when drawing.  it is so tempting to want to hold the best possible portion of a hand, but sometimes you simply box yourself into a corner by doing so.  For example, if you are dealt the following:

2          2          6D       7C       QD

            You may be very tempted to hold the 4-Card Straight figuring that there are so many possible cards to complete the Straight (a 3, 4, 5, 8, 9 or 10).  If you pick up a 6 or a 7, you'll have Quads.  This is clearly superior to going for the 4-card Flush, which would require one of the remaining 11 (or 10 if the 2 was a Diamond) diamonds to make a Flush or a 6 or Q to complete the Quads.

            The problem with either of these is that they completely eliminate the possibility of any of the bigger payouts while in essence targeting some of the lower paying hands.   Further, we the two Deuces, we can do no worse than wind up with Trips, so it is not like we are giving up a sure winner.  Proper strategy says that unless you have a Royal, Five of a Kind, Straight Flush, Four of a Kind or a 4-Card Royal, you hold ONLY the two Deuces.

            When we take a closer look at the strategy, we find that we ONLY go for a 4-Card Straight or 4-Card Flush IF we have NO Deuces.   Be very prepared when dealt Deuces in Deuces Wild to frequently play them 'bare' (hold only the Deuces).  Of the 2,598,960 possible 5-card initial deals, 48 will consist of 4 Deuces (obviously, you're done when this happens).  Three Deuces will occur 4,512.  About 90% of these will be played as just the three Deuces.  Two Deuces will happen 103,776 and nearly 75% of these will be played as just the two Deuces.  A single Deuce will be dealt 778,310 times.  About 45% of these will be played as the single Deuce.  This is the 3rd most common hand in Deuces, following a Pair and a Razgu. 

            If you want to learn to play Deuces Wild, we have three different products that can help you.  You can find the strategy tables for full-pay Deuces Wild in our book Expert Video Poker for Las Vegas ($5).  We have the strategy table for full-pay Deuces Wild plus a variety of variations of full-pay Deuces Wild in Winning Strategies for Video Poker ($5).  Lastly, we have our Deuces Wild Tipsheet ($2.95) which contains the strategy tables for 3 different Deuces paytables and has the most detailed information on the full-pay variety of any of our 3 sources.  You can order any or all of these directly from us.  Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133

Jackpot Power

            As we get deep into the political season, we're all going to be frequently reminded how it is possible to make numbers say just about anything we want them to.  Quite frankly, it is not just the arena of politics this happens in.  It can be done with all types of math - casino math, included.

            By now, many of you well know that a full-pay jacks or better machine pays about 99.5%, which is a very solid number for a casino game.  Many of you may even be aware that the Royal Flush contributes 2% of this amount.  But what does this really mean?  It means that if the machine was defective and NEVER dealt a Royal Flush, but dealt all the rest of the hands in the frequencies we would expect, the payback of the game would be closer to 97.5%.   This is about the same payback we would get from a short-pay (8/5) jacks or better machine so should we expect roughly the same experience?

            ABSOLUTELY NOT!  One of the measures I like to use is what I call a 'session simulator'.  This process simulates a session of play for a particular game.  For video poker, I use 3 hours of play at 700 hands per hour.  For this particular demonstration, I ran 1000 of these sessions under 2 conditions.  The first was a full-pay jacks or better machined that NEVER paid a Royal Flush.  To be clear, the only way this could ever really happen would be if the machine was broken or rigged.  As I don't believe the latter happens in any reputable casino, nor would a broken machine likely stay on the floor for this many hands - this is merely for illustration purposes and to prove a point.

            In this scenario, the Player still managed to walk away a winner about 28% of the sessions.  This compares to about 29% when a regular full-pay jacks or better is played.   Why is there such little impact to this?  Under normal circumstances, the Royal would hit only about every 20 cycles or so.  Some of these cycles would already be winners, so the Royal Flush doesn't change this.  It only changes the magnitude of the win.  In the cases where the session was about to be a loser, the Royal most likely flipped ONLY these into winners.  However, when we look at the long run, the overall payback of ALL the sessions put together was where we expected it to be - at about 97.5%

            When we put the 8-5 jacks or better machine (with the Royal occurring as it should), we find that the Player wins only 14% of his sessions.  His winning sessions are cut by half!  The overall payback of all the sessions is also what we would expect it to be at 97.5%.

            So, why do two different machines paying about the same amount create such different short-term results?  This goes to a concept of volatility.  There is a mathematical formula for volatility, but I'm afraid if I start explaining it at that level, you're all going to turn the page.  That is why I like to use the session simulator as a means of explaining what volatility does and is.  When a large amount of the payback is concentrated into a very infrequently occurring hand, there is a larger degree of volatility.  In the case of the full-pay jacks or better game without the Royals, I removed a large degree of the volatility.  This is why a game with a considerably lower payback that the original version can still have a not very different short-term result.

            So, what does this all mean for you?  There are two points I'd like you take away from this week's column.  The first is to realize how important the Royal Flush is to your long-term results in video poker.  If you are on a cold streak of Royals, your short-term results may not look all that different from 'normal', but you may find that your larger bankroll is suffering.  If you play for 3 hours at a time, you may find that you're still leaving the casino a winner 3 out of 10 times, but for some reason your wallet still seems a lot lighter than it should.  The good news is that in the long run, those Royals will show up as often as they should (assuming you are playing Expert Strategy).  Ironically, when the Royals are running hot, you'll still walk away a winner about 3 out of 10 sessions.  But, a few more of those sessions will be big winners.

            The second point I want everyone to think about is if a 'mere' 800 unit payout occurring roughly every 40,000 hands can make this type of impact to a game, imagine what happens on a slot machine that can pay hundreds of thousands or millions of dollars for a 'hand' even more infrequent.  The average payback on a slot machine is ONLY 92-93%.  If we consider that many of them will have a massive top pay that might occur only every few hundred thousand hands (or million hands), what % of the overall payback does this account for? 

            With these occurrences being so infrequent (and COMPLETELY unknown as to how frequent), the payback of the machine without the jackpot could easily be 80-90%.  I'd put this through my session simulator but as it is not possible to know the frequency of all the payouts, there is no way to do it.  Just for fun, I built an 82.5% video poker paytable and put it through the process and it showed that the Player will walk away a winner only 5% of the time.  As we've already shown, it would then be possible to create an infrequent, very high paying jackpot which will push the overall payback up, while barely changing the short-term results. 

            The end result is one that we know all too well for slots.  Very few people walk away a winner even in the short run, which pays for the handful of people who win the big jackpots.  I'll take video poker any day!

Deuces Gone Wild

            I love getting fan mail and/or e-mails from readers.  There are two reasons for this.  The first is that it is always nice to know that someone is actually reading my column.  It is especially gratifying when someone tells me that they ALWAYS read my column.  The second reason is that a question from a reader can frequently become the basis for a particular week's article.  There are times I sit down to write my column and I simply don't know what I want to write.  I think of a topic and realized I covered it at some point.  Of course, being that I have now been writing for Gaming Today for more than 8 years, it is possible that I last wrote about the topic in 2005 and by now there may be some new readers.

            This week, I received an e-mail from someone who was questioning some of the strategy for Full Pay Deuces Wild.   Full Pay Deuces can be found in several casinos in Las Vegas.  As is the case for most 100+% machines, you won't find them on the strip.  You're going to have to head to some of the local casinos (such as Station Casinos) if you want to find them.  My source (www.vpfree2.com) shows that there should be 100+ machines scattered about at a variety of denominations up to a quarter. 

            While I've never been a big fan of Deuces Wild, this is just a personal choice.  Any game that pays 100.6+% is hard to criticize and is a good game for the regular Player to learn and master.  The strategy table is rather long, but when you break it down by the number of wild cards, you realize that it is not really a hard strategy to learn.  With a paytable that begins paying at Three of a Kind, you don't have to worry about counting High Cards.  The one thing, I strongly advise the beginner to learn is how to recognize hands with lots of wild cards in them.  It can become very easy to not realize that 2 6D 9D 10D KH is a 4-Card Inside Straight Flush with 1 Wild Card. 

            The question I received this week was specifically about holding a 4-Card Inside Straight (presumably with no Wild Cards) versus throwing all 5 cards as a Razgu.  The strategy table tells us that we hold the 4-Card Inside Straight.  If you look at the strategy table in Winning Strategies for Video Poker, however, it lists both hands as having an expected value 0.3+ - although it does list the 4-Card Inside Straight higher meaning its "+" is greater than the Razgu "+".

            While I write extensively on Video Poker in Gaming Today, I spend most of my time analyzing table games.  Many years ago I did write my own video poker engine that allows me to analyze most video poker paytables.  One of the limitations is that it does NOT do wild card games.  Fortunately, I have both other resources available to me and the ability to quickly create a program to help determine exactly how much those "+" are worth.

            Calculating the expected value of the 4-card Inside Straight was very easy.  There are 8 ways to draw the Straight (4 Wild Cards plus 4 of the 'natural' way to complete the Straight).  Each pays 2 units so we have a total return of 16 units.  Divide this by 47 ways to draw and we have an expected value of 0.3404.

            The Razgu is a bit more complicated.  As I've written about in the past, the overall expected value as shown in a strategy table for a hand like a Razgu is the actually the AVERAGE of all the possible hands of that type.  Often, no single hand will actually have EXACTLY the expected value shown. 

            About 20% of all hands in Deuces Wild are classified as a Razgu, each with their own subtleties.  The exact make up of suits and ranks will have some impact on the exact expected value.  For each 10 through Aces that is in the hand, there will be less chances to make a Natural Royal.   The exact suit composition of the initial deal will impact the number of possible Flushes that can be made if we discard all five cards. 

            In this particular case, however, the reader was talking about a 4-Card Inside Straight, which does limit the possibilities.  In order to get a more exact expected value, I quickly set up a program that had the initial deal set to 3D 4C 5H 7S 8S.  I figured that by leaving in all of the High Cards I would leave the expected value about as High as it could go and we could see just how close of a decision this really is.

            The expected value of this specific Razgu came back at 0.3267.   So, it would be more accurate to say that a Razgu is about 0.33- and a 4-Card Inside Straight is 0.34+.  It is not exactly a canyon between the two expected value, but there is a clearly superior choice.

            To help me prove my work, I realized that we also sell a Deuces Wild tipsheet that my father created a long time ago.  It has more detailed numbers on it.  It actually lists the expected value to two decimal places.  It lists the 4-Card Inside Straight 0.34 and the Razgu at 0.32.  (When all the possible Razgus are considered, the average must wind up at below 0.325).   It was good to know that my quick and dirty program was able to produce accurate results!

            If you're interested in learning the strategy on Deuces Wild, we have the tipsheet for $2.95.  It includes the strategy tables for Deuces Wild, Double Pay Deuces Wild and Triple Pay Deuces Wild.  Or you can order Winning Strategies for Video Poker which includes these 3 paytables plus dozens more for only $5.  Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89128.

Sometimes, Is Less More?

            This week, I received an e-mail from a reader who was interested in a game called Triple Bonus Poker.   He enjoyed playing the one and only machine he could find of it in Las Vegas, but was unsure of the payback and strategy.  Not familiar with the game off the top of my head, I went to check my copy of Winning Strategies for Video Poker and found the game the reader was talking about.  He had actually found a Full-Pay version of the game and its payback was a very respectable 99.6%.

            What also quickly struck my eye was that the strategy table was much shorter than most others.  Then I noticed the top of the page which said "KINGS or BETTER".   Triple Bonus Poker doesn't pay on Jacks or Better, it only pays on Kings or Better.  Yes, the payback is still 99.6%.  It does this by paying well for Quads (240,125,75 - no kickers required) and VERY well for Full Houses and Flushes - 11 and 7 respectively.   It should be noted that it only pays 1 for a Two Pair, so this game is going to be VERY streaky.

            So, why play this wild game?  Well, that very short and easy to learn strategy table is what intrigues me.  I've often wondered what the error rate is for many Players given the intricacies of the standard jacks or better strategy table.  Keeping track of those High Cards makes for a long strategy table with subtle differences between 4-Card Straights and 3-Card Straight Flushes.   Looking at the strategy table for Triple Bonus and most of it is fairly intuitive.  Yes, it helps to know for sure that you throw a Full House if you have Three Aces and you dump Two Pair if you have a Pair of Aces, but these are easy things to remember. 

            The strange part is that despite having a respectable payback and a relatively easy strategy table, my source for games in Las Vegas tells me that NONE of these games exist.  As this source is user maintained, it is on occasion incorrect as it is in this guess.  There appears to be at least ONE table in Las Vegas.   Easier to find is a game called Triple Bonus Plus or Triple Play Plus. 

            One has to be very careful to not confuse these two games as their names have more in common than the actual games themselves do.   First of all, the latter game is a Jacks or Better game.  This means a full-length strategy table.  The Straight Flush is upped to 100 from 50, but the Quads pay of 75 is lowered to 50.  Most noticeable is that the payouts for Full House and Flush are the more pedestrian 9 and 5, respectively.   The end result is a payback of 99.8%.

            A game that pays 99.8% can actually be profitable for a Player when you include cashback and comps.  Or, at the very least, it can be a neutral game which you can play for very long periods of time with a relatively small bankroll.  I'm not one to dismiss this idea.  Also, while 99.8% and 99.6% might seem very similar, I am frequently the one to point out that you should at this from the other side.  One has a 0.2% house advantage and the other a 0.4%.  In other words, Triple Bonus Poker has TWICE the house advantage of Triple Bonus Plus.

            That all said, Triple Bonus Poker offers the Player a relatively easy game to learn without all of those pesky High Cards.  I have little doubt that for the average Player, the error rate will go down and the gap between the two games will be reduce to below the 0.2%.  If you are truly an expert Player, this will matter less to you.

            Of course, it would seem that the casinos have taken the choice away from the Players anyhow.  While there is perhaps a single machine of Triple Bonus Poker in all of Las Vegas, my source states that Triple Bonus Plus can be found in moderate abundance - at least in some casinos that target locals.  This part isn't a surprise because the best paying machines are generally found in the locals casinos.  What we don't know is whether the casinos removed the Triple Bonus games because Players didn't like the very streaky (and lower hit frequency) Triple Bonus or because the real paybacks were higher due to a lower error rate.  If this is what happened, it may have been a case where less was more for most Players.

AMERICA BEATS ITSELF INTO A LOTTERY FRENZY OVER MEGA MILLIONS

            As I'm writing this, the country is beating itself into a frenzy not over politics but over a lottery.  The Mega Millions Lotto has an estimated prize of $640 MILLION.  That would make it the largest jackpot in the world.  Lotteries tend to have paybacks of about 50-60% so they aren't exactly a wise wager.  Yet, as I have often written, people are more willing to wager in games with bad paybacks if the top prize is life altering.  I think more than half a billion dollars meets that requirement.  I have to admit that if Nevada participated in Mega Millions, I would've tried to get some tickets.  I was NOT motivated enough to drive to nearby California to get them, however.

            Even when your choice of game is something like a Lotto, I think you should go in with your eyes open.  The odds of winning the top prize is about 176 million to 1.  To put that into a casino perspective, that is a little higher than the odds of being dealt a sequential Royal (10-A or A-10) in SPADES on the deal in video poker!  Of course, even if you're playing a Reversible Royals video poker machine, you're only going to get paid maybe $40,000 for that hit, not $640 million.

            Unfortunately, unlike most casino games, it is a bit more difficult to determine the expected value of this week's drawing for one major reason.  The $640 million dollars will be SPLIT by each of the people who have a winning ticket.  The lottery has stated that $1.5 billion worth of tickets have been sold, but from reading further it would appear that this is the TOTAL number of tickets sold since the last time the jackpot was won.  This does NOT represent the number of tickets sold for this particular drawing which is all that matters.  If we actually knew how many tickets were sold for this drawing, we could determine a more accurate expected value. 

            Armed with this information - and $176 million, it might actually pay to buy every possible combination of numbers.  We would then actually be wagering on how many other people hit the same set of numbers.  If less than 3 others, we would actually make some money on the deal.  Well, BEFORE Uncle Same takes hit cut anyhow.  To really make money, we'd probably have to be the only one to have the winning ticket.  History tells us this is unlikely and even less so if you were to add in someone who bought EVERY ticket. 

            No one plays these types of lotteries believing it is a wise investment.  We all know that the odds are very long.  The payback of the lottery is normally around 50-60% and even when it grows this large, it is probably no more than 70-80% when we consider that we are likely going to have to share it should we get struck by lightning and actually win.  What I find most amusing about these situations is the comments we get from some people.

            Today, I was reading a rather whimsical article about just how much money the $1.5 billion that was spent on lottery tickets really is.  It talked about how many families it could feed and how many trips to the space station you could make with this type of money.  Sadly, it also explained how it was only 0.1% of the national debt.  The article then moved on to quote some people who chose to play and why.  Of all the things I read, the one that made me to a double take came from an accountant in Louisiana (I won't post his name here):

            The article stated that the gentleman had bought 55 tickets and that he knows buying that many tickets doesn't mathematically increase his odds, and that his $55 could have gone elsewhere. He spent it anyway.

            "Mathematically, it doesn't make a difference, and intellectually we know that. But for some reason buying more tickets makes you feel more lucky," the accountant said. "Even people who know better are apt to feel that way."

            Maybe, he bought 55 tickets all with the same numbers?  Mathematically, buying more tickets doesn't make a difference?  So, if I buy one ticket I have the same chance to win as someone who buys 2 tickets?  What about the guy who buys 10?  or 50?  or 55?  or 176 million?  As an accountant, I would think he would understand numbers a bit better.   If you buy 2 tickets your probability of winning doubles as compared to buying 1 ticket.  If you buy 10 tickets your probability of winning multiplies ten-fold.  This gentleman bought 55 tickets, so he brought his odds down to a mere 3.2 million to 1 of hitting the big jackpot.  

            Fortunately, playing the Lotto takes as much skill as playing slot machines.  But many of the same people walk into a casino armed with about the same level of knowledge of the games.   Yes, mathematically, we know in the long run that we are likely to lose, but that doesn't mean we should take prudent steps to keep our losses to a minimum and give ourselves the best chance to win in the short run.  Because, in the end, mathematically, it all makes a difference.

There is Such a Thing as a Free Breakfast!

             Last Friday morning, my wife and I went to see one of the first showings of The Hunger Games at the Red Rock Station.  She had read the book a couple of months ago and has been very excited about the movie coming out.  I can't remember the last time we went to see a movie on opening day.  Maybe on the Sunday of opening weekend, but at 9:30 a.m. show on Friday?  We got there by about 8:30 a.m. to make sure we got tickets.  Fortunately, the 6 people ahead of us didn't buy them all and try to scalp them!  So, by 8:31 a.m. we had our tickets and now had tome to go get some breakfast.

            We walked over to the buffet and found out that if you have one of their Boarding Pass frequent Player cards, they'll take $3 off the cost.  I didn't have mine on me, but I knew I had one, so we walked over to the Customer Service area, got a new card and saved our $6.  While we were getting our new cards, I noticed a promotion that they were running today.  If you earn 300 points, you get a free box of Girl Scout Cookies.  Limit 2 per person and they DON'T take any of your points for the box of cookies.  If we were looking for a place to play, this might have swayed us to stay - all other things being equal.  We usually buy Girl Scout Cookies every year.  They cost about $4 per box, so there is some real value to us.  If we were diabetic, or I found they only have the one variety of cookies we don't like, then the value of this promotion has to be discounted from the $4 price.

            I'm a firm believer in taking advantage of any/all promotions that the casinos want to throw at the Player.  But, you have to be smart about deciding the value that each has to you.  If your local supermarket runs a half-price sale on cold breakfast cereal, but you like oatmeal in the morning, the sale has little value to you.  If you're the type of person who is going to stock up anyhow - just in case - well, you're going to be doing the casino a big favor by chasing everything. 

            After the movie was over, we stopped at the Rampart Casino on our way home.  It is completely on the way to our place.  They are running a promotion that gives me $10 in free slot play - which of course, includes video poker as the casinos continue to erroneously equate the two.  The rule is you have to play the full $10, but you get to keep any of the return.  I sat down at a nickel Bonus Poker machine and played max-coin.  40 hands later, the machine said $12 and I left.  It took about 5-10 minutes.  Am I that hard up for $12?  Certainly not.  But for 5 minutes of my time, the Rampart picked up the tab for breakfast for me and my wife!  If I had sat down for an hour and played their short-pay machines and lost the $10 AND another $20, I would've played right into the casinos hands.

            These are the little benefits the casinos give to Players to try to bring them into the casino.  They'll give you a discount on meals.  They'll give you some free play.  It is no different than what the supermarkets do.  They put milk on sale and hope you'll pay full price for bread, pasta and cheese.  No one has ever complained about the supermarkets doing it, so no one should be surprised that the casinos do it as well.

            Just like the supermarkets, the casinos now give you points when you play.  I've heard some Players voice concern that the casinos use your Rewards card in less savory ways.   Some are worried that the casino will have you win less often if you use your card because they are in essence paying you to play.  From a computer perspective, this is certainly possible.   But, do people really believe that the casino will cheat (aka. break the law) to not give the 1/4% back to the Player that they are telling the Player they can have.  Caesar's Entertainment (formerly known as Bally's and Harrah's) has a market cap of over $1.5 BILLION.  I don't think they are going to risk that type of money so that they can cheat some Player out of his $5 cashback!

            The lesson for today is get the Rewards card.  Get everyone you can.  Keep a little box of them with you when you head out to the casinos.  When you play in a casino, ALWAYS use your card.  That said, be smart when determining the value of the rewards when you decide where to play.  Are you better off playing at a casino that gives 50% more rewards, but has lower paybacks?  If there is a promotion running that allows you to get a free meal at a steakhouse, but you're a vegetarian, it has no value.  If it is a steakhouse you love to eat at, then it is worth its face value. 

            Especially for video poker players who are (hopefully) playing at 99% paybacks and higher, taking that extra 1/4% - 1/2% from the casino can put you very close to an even game.  It will certainly cut the house advantage down considerably and your bankroll will certainly notice.

Back to Video Poker

            I've spent 3 out of the last 4 weeks discussing Soft Hands in the games of blackjack, Spanish 21 and Blackjack Switch.  I did this for two reasons.  The first is that it is nice to write about something other than video poker once in a while.  The second is that it is frequently easier to illustrate important concepts by using games with more straightforward differences.  If you read my column this past month, you probably can understand why you don't use the same strategy for Soft Hands for these different games.  While they may be all blackjack based games, the differences created by removing the 10's (Spanish 21) and by having a Dealer Bust of 22 (Blackjack Switch) pushing against Player hands change the math, which in turn changes our strategy.

            One thing that these games have in common, for the most part, is the payouts.  A win is a win and you get paid even money.  Spanish 21 has its bonus hands and its Charlie payouts (which also effects strategy), but you don't have to worry about looking for a paytable to know what to do.  You just have to know which game you are playing.  I must admit that a very, very long time ago, I sat down at a Spanish 21 table not realizing for about 30 minutes that I wasn't playing regular blackjack!  When it finally hit me, I'm sure I turned a nice shade of red, something I don't do very often.

            The bottom line is that from my little detour on blackjack we learn that rule changes can and will change our strategy.  What we have to learn directly from video poker is that paytable changes can do the same thing.  One could argue that there really are no rule variations across virtually all video poker machines.  You are dealt 5 cards.  You decide which ones you want to replace.  You draw that many cards.  Games like Multi-Strike and some of the attempts at a 7-Card Stud game do manage to cross the rule line, in my opinion.  In the gray area are the games that use Wild Cards (Jokers and/or Deuces).  Are these really rule changes or paytable changes?  It really doesn't matter once you realize that both can have the same impact to our strategy.

            If I pick up a copy of Winning Strategies for Video Poker, I will find 27 different paytables JUST for jacks or better.  Admittedly, some of these paytables are pretty tough to find these days, but these paytables were considered to be the 'full-pay' paytables in a number of jurisdictions when the book was revised 15 years ago.  It purposefully left out many of the short-pay machines that are some of the most common both then and today.  There are probably 50-60 paytables in use today just for jacks or better.  

            Of course, in an ideal world, none of you reading this column would actually play any of the inferior paytables if given an opportunity to play one of the better ones, but that is not likely the reality.  Also, in order for this to happen, each of you would have to know how to determine which are the better paytables to actually play.  I'll save that for another column.

            Today's column is about understanding how the strategy changes as a result of a paytable change.  With dozens of paytables out there, each game could potentially have its own strategy.  This doesn't mean that if you bring your strategy from one game to another that you'll be committing bankroll suicide, but  you won't be helping yourself either.  In some cases, you might add another 1-2% to the house advantage by using the wrong strategy for any particular paytable.

            So, what is a Player to do?  First, you can't try to master every paytable out there.  I'm guessing there are not a lot of Experts who play regular blackjack, Spanish 21 and Blackjack Switch on a regular basis.  It is too easy to get parts of the strategy confused and then you start making mistakes.  Very quickly, 3 games each with paybacks of 99%+ become not nearly as strong for the Player.  The same is true of video poker.  After a while you're going to forget which games a 3-Card Straight Flush with 1 High Card outranks a 4-Card Inside Straight with 2 High Cards. 

            The key is to target a single game.  It should be a full-pay machine with a strong paytable.  Then, go out and learn the strategy.  Read a book.  Buy some software.  Practice at your desk.  ONLY when you have mastered the strategy should you venture out to the casino and play using real money.  Before you jump to play a different game, repeat the entire process all over again.

            

Soft Hand "Swtich"eroo

I’ve spent the last few weeks discussing some blackjack strategy. Blackjack strategies are developed the same way video poker strategies are. Using computers, we evaluate every option the player has and decide which will make the most or lose the least, as the case may be.

As in video poker, many decisions in blackjack are fairly obvious. It is the other hands, which are less obvious, that separate the beginners from the Expert Players.

One group of hands that falls in this category is the soft hands, where an Ace counts as an 11. Players have the option to double down, hit or stick on many of these hands. If you sit at a table for awhile, you’ll quickly find very few players play these hands correctly.

In regular blackjack, many of these hands create double down situations. This is because of the ability to improve the player’s hand AND the Ddaler’s likelihood of busting.

Last week, I showed how the strategy changes dramatically in Spanish 21 with the 10’s missing, and the reduced likelihood of the dealer busting. This week, I’ll take a look at what happens in Blackjack Switch where a Dealer 22 is a push.

In Blackjack Switch, the player must play two blackjack hands with equal wagers. The player then has the option to switch the second cards dealt to each hand. So, if dealt a 5-10 and a 10-6, you can turn that into a 5-6 and a 10-10 and greatly strengthen the hands. If dealt a 5-10 and a 6-10, then switching will do nothing.

The price the player pays for this option is if the dealer busts with a 22, all player hands still in action (except natural blackjacks) are pushed. This means a LARGE number of dealer busts wind up as pushes. Since we double down looking for dealer busts, this will alter our strategy greatly.

The strategy for soft hands in Blackjack Switch is rather simple. There are only FOUR times we double down. We double down on a soft 17 or soft 18 against a dealer 5 or 6. If we have a soft 17 or less and can’t double down (3-plus cards) then we hit. We stick on all soft 19’s or higher. For a soft 18, when we can’t double, we stick against an 8 or less and hit against a 9, 10 or Ace.

 Given how much doubling on soft hands adds to our payback in regular blackjack, how is it that in Blackjack Switch we can give up this benefit and still have a game that pays in the mid 99% range? It is the nature of the ability to switch that creates a bit of a paradox. We double down in far fewer situations in Blackjack Switch than regular blackjack because the Dealer Bust on 22 rule.

However, our starting hands (after the switch) are far stronger in Blackjack Switch than in regular Blackjack. In the case of soft hands, we will frequently perform a switch that will convert it from an ordinary soft hand into a 21 or a 20, leaving the other hand frequently in no worse shape.

So, while we lose the opportunity to double down on some of these soft hands, we instead gain stronger hands we don’t double down on. A 20 (hard or soft) is far preferable to a soft 17 – especially in Blackjack Switch.

While Blackjack Switch simplifies our soft hand strategy, it also adds an entire new layer of strategy by needing to know when to switch. This part of the strategy is far more important to achieving the theoretical payback than is the altered hit/stick strategy. However, I would strongly suggest you learn both!

Just as in video poker, when you change the payouts or the rules of the game, the strategy changes with it. While many of the switch decisions will be obvious, many will leave you scratching your head as to what is the better play.

Undoubtedly, there will also be times when you do the right thing and it backfires or you do the wrong thing and it works out. However, this doesn’t change what the right mathematical answer is. As the saying goes, even a broken clock is right two times a day!

To help you learn the right strategy, I’m continuing to offer our Buy 1 Get 1 Free special. Buy Expert Strategy for Blackjack Switch for $6.95 and get Expert Strategy for Spanish 21 for free. Both come with pocket-sized multi-color strategy cards to bring into the casino with you. If you’d like to order, please send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.