How do you say "Soft Hand" in Spanish?

            A couple of weeks ago, I discussed the strategy regarding Soft Hands in blackjack.  Soft Hands are those that contain an Ace which is counted as an 11.  Many of these hands should be played as a double down because of both the ability to significantly improve the hand (to a 17-21) AND due to the high probability that the Dealer will bust - as we mostly double down against Dealer Upcards of 2 through 6.

            As is the case with video poker, however, we must remember that the strategy changes with every paytable change or rule change.  We find slight changes to our strategy if we go from the Dealer hitting Soft 17 to the Dealer Sticking on all 17's.  However, if we go to the Blackjack variants of Blackjack Switch or Spanish 21, everything changes.

            In Spanish 21, the 10's have been removed from the decks, so that we are playing with a shoe of 48-card decks.  As may of us know, 10's and Face cards are our friends when playing blackjack.  They enable us to make good solid hands like 20's.  They help us Double Down on 10's and 11's and get strong hands.  Most importantly, they bust any Dealer hand above an 11.  When you hear about card counters, they are keeping track of the percent of 10's/Faces in the deck.  When there are more than 'normal', the game tips more into the Player's favor.  So, taking 4 of them out of each deck is NOT to the Player's advantage.

            Spanish 21 offsets this by giving the Player a host of other advantages.  The Player can double down on any number of cards.  So, if you start with a 5-3 and hit a 3 for 11, you can still double down.  Player 21's beat Dealer 21's.  Player Blackjacks beat Dealer Blackjacks.  There are also several 'bonus' 21 hands thrown in for free.  Get three 7's and win a small bonus.  The house advantage for Spanish 21 is about 0.8% which makes it a little greater than regular blackjack, but ONLY if you learn the proper strategy.

            Some of the biggest changes occur in the Soft Hands.  Not much changes in terms of how your hand will turn out.  The biggest impact is to the Soft 17's and 18's which have less of a chance to draw a 10, but a slightly greater chance to draw the little card you need to improve the hand.  The problem is that the Dealer will Bust less often.  The Bust rate for a Dealer 6 goes from 44.6% in regular blackjack to 40.6% in Spanish 21.  The changes to the Bust rate is enough to get us to make radical changes to our Soft Hand strategy. 

            To begin with, we NEVER Double down on a Soft 13 through 15 in Spanish 21.  We simply hit these hands.  We Double Down on a Soft 16 only against a 6.  However, if we have 4 cards or more, we hit these hands (remember that you can Double on 3 cards in Spanish 21).  Since there are special payouts for 5, 6 or 7+ card 21's, the lure of these payouts is stronger than the ability to Double Down. 

            Soft 17's are Doubled Down against a Dealer 4, 5 or 6.  BUT, only if the Player has 2 cards against the 4, 3 (or less) cards against the 5 and 4 (or less) cards against the 6.  If he has more cards than the minimum, he hits the hand in search of the 5+ card 21.

            Soft 18's bring us the most opportunities to Double Down.  We stick against a 7, but will Double Down even against an 8 as long as we have 3 cards or less.  We also Double Down against a 6 (5 cards or less), a 5 (4 cards or less) or a 2 through 4 (3 cards or less).

            Essentially we throw out everything we know about Soft Hands in Blackjack if we are planning on learning how to play Spanish 21.

            Next week, I'll discuss Soft Hands in Blackjack Switch and the impact of the Push on Dealer 22 rule on our strategy.  For those that want to get a jump on learning, I'm offering a 2 for 1 deal.  Order Expert Strategy for Blackjack Switch for $6.95 and get Expert Strategy for Spanish 21 for free.  Both books include a multi-color pocket-sized strategy card.  Send check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.

            

Hot Streak or Cold Streak?

          I've written many columns in the past several years about how our minds can play tricks with us regarding odd results.  We have a tendency to remember what appears to be very rare events and all but forget the routine.  The end result is that we begin to think that all that occurs are those strange occurrences.  This eventually leads many to believe that a game is either broken (if we are winning) or rigged (if we are losing).  The most likely real answer is two-fold.  First, we're not correctly remembering what actually occurred and second, most people really aren't aware as to how rare or common some event actually is.

            How much does it matter if our memories are a little faulty?  In the grand scheme of things, perhaps not much.  But, from a math perspective, it can make a great deal of difference.  Several months ago, a friend of mine relayed to me his experiences while playing Let It Ride.  He claimed that in a five-hand span he was dealt a Four of a Kind, a Full House, a Straight and TWO Three of a Kinds.  He must have been able to read the expression on my face as he kept telling me that it "REALLY" happened.  I was a bit skeptical. 

            When I got to my computer I did some computations and discovered that the odds of being dealt those 5 hands in a row (in any order) was about 27 BILLION to 1.  Okay, I wouldn't call it impossible, but I wouldn't call it very likely.  But, what if his memory was a little flawed?  What if he was dealt those 5 hands in a block of 10 hands?  What if his memory just 'forgot' about the five losing hands?  In this case, the odds would drop to a 'mere' 492 MILLION to 1.  At least we're back down into Lotto territory.  So, did my friend get these 5 power hands in 5 deals?  10 deals?  20 deals?  I have no clue. 

            This past week, I had the opportunity to do my own research.  Family is visiting from out of town, which usually means I'm playing in the casino a bit more often.  On one evening, I sat down at a five-play machine.  In the first 31 hands, I was dealt 5 Three of a Kinds (on the first 5 cards).  I know these numbers to be true not because I sit there and count how many hands I've played, but rather I was able to see the point counter on the machine and specifically took notice of how many hands I had played after being dealt my 5th Trips. 

            This made me wonder about just how rare is it to be dealt 5 Three of a Kinds in 31 hands.  So, when I got home and went to work on the calculation.  Before you read any further, I'd like you think about this and come up with how often you think this happens?  1 in 100? 1 in 1000? 1 in a million?  This is one of the cases where I think many people would guess rather wrong if they don't know how to do the actual math.  Until I did the calculation, I didn't really know what to expect.  I knew it wasn't astronomical, but I figured it was a bit more rare than it turned out to be.  In the end, the number was 562.  The odds of having 5 Trips in 31 hands is in the same ballpark as the odds of being dealt a Flush on the deal.  It didn't seem like such an odd occurrence anymore, but at the time, I figured the machine was on fire.

            Of course, I didn't draw a single Four of a Kind out of any of these hands.  Five times I had five chances to get those Quads and I couldn't hit a single one.  So, maybe the machine was actually cold, not hot.  How cold was the machine that I couldn't hit a single Four of a Kind from my 5 Trips?  In reality, not at all.  I had an 80% chance of not hitting any Four of a Kinds from these trips.  So had I actually hit one (or more), it would've have been the more rare occurrence.

            There are many things to take away from this column.  One is that it is hard to rely on anecdotal stories.  If you didn't witness the event yourself, you don't even know if the story is true.  And, even if you did witness it yourself, we necessary learn a lot because once upon a time something rare happened.  We need to look at all the stories everywhere in order to learn what to expect.  This is best done by computer programs and computer simulations.  From this, we learn that virtually everything that happens when we play in a casino is just part of the normal ups and downs that happen 'randomly'.

What to Do When Your Hand Goes Soft

            I'm going to continue talking about blackjack this week.  No, I'm certainly not giving up on video poker!  Blackjack is very similar to video poker in that they both require learning rather complex strategies in order to achieve a strong payback.  However, blackjack has the advantage, in my opinion, in that it is a bit easier to learn the strategy.  Recognizing hands in video poker can sometimes be tricky for the beginners.  But, with blackjack a 16 is a 16.  Well, sort of.

            You can actually have 3 different types of 16's.  The first is a Pair of 8's.  For this, we use Pair Strategy.  The second is a Hard 16, where there is no Ace counting as an 11 involved in the hand.  For this, we use our Hard hand strategy.  Lastly, there is a Soft 16, where the hand contains an Ace being used as an 11.  This hand cannot bust by hitting one additional card, so the strategy is quite different from a Hard 16.  For these, we use our Soft hand strategies.

            It is these Soft hands that I would like to focus on today.  Hard strategies are pretty well known.  Don't hit anything above a 16.  Don't hit most Hard hands between 12 and 16 unless the Dealer has a 7 through Ace showing.  There are a few exceptions with 12 and 13, but if you just followed what I wrote, you'll do okay.  But, when it comes to Soft hands, people do all sorts of things - many of them quite wrong.  We've all even seen a few people try to stop on a Soft low hand.  Which card could you draw that will make your Soft 16 more likely to lose as compared to staying put?

            The reason why learning Soft Hand strategy is so important is because these hands afford us the most opportunities to Double Down.  We Double Down for two reasons.  The first is that we have a strong hand (i.e. 10's and 11's) that is likely to get stronger with a single card.  The second is that we have a good hand and the likelihood is strong that the Dealer will bust.   

            When we have a Soft Hand, we have usually have at least 5 chances to make the hand better to the point where it matters - that is to say, wind up with a hand between 17 and 21.  If you can only hit one card and you hit a 13 and it becomes a 15, you really haven't done anything for your hand - positive or negative.  Quite frankly if you hit a Soft 16 and it become a Hard 12, you haven't done anything negative to your hand either.  So, when we Double Down on a Soft hand, we have a hand that MIGHT improve and we look to do this when the Dealer is likely to Bust.

            That last part tells us the first critical part of Soft Hand strategy - we NEVER Double Down when the Dealer has a 7 through Ace up with a Soft Hand.  The likelihood of the Dealer busting is not strong enough to make it worth Doubling Down.

            Next, you need to understand that when you Double Down, you are actually REDUCING your chances of winning the hand, while INCREASING how much you will win when you do.  So, imagine if an identical opportunity came up 100 times.  If you don't Double Down, you will win 75% of the time.  If you do Double Down you will win only 65% of the time.  Which would you want to do?  Well, if you don't Double Down, you will wager 100 and win back 150 for a net win of 50.  If you do Double Down, you will wager 200 and win 260 for a net win of 60.  If you want to win more, you Double Down even though you will win less often.

            As is the case with video poker, you don't have to do any amazing calculations on the fly to figure out what the right strategy is.  Someone like myself, with the help of some computer programs has already done all the hard work.  That is, unless you consider memorizing the strategy tables to be the hard work!

            There are some slight variations in strategy depending on whether the Dealer hits or sticks on a Soft 17.  What is presented here is for the cases where the Dealer does NOT hit a Soft 17.

• ·         Double Down with a Soft 13 or Soft 14 against a Dealer 5 or 6 Upcard. 
• ·         Double Down with a Soft 15 or Soft 16 against a Dealer 4, 5, or 6 Upcard. 
• ·         Double Down with a Soft 17 or Soft 18 against a Dealer 3, 4, 5, or 6 Upcard.

            If you have a Soft Hand that is more than 2 cards so that you can no longer Double Down, you Hit ALL Soft 12 - Soft 17 and Hit a Soft 18 against a Dealer 9, 10 or Ace Upcard.

            Yes, there will be times you will turn a Soft 18 into a Hard 16 and begin to wonder if you made the right move.  But, in these cases, don't just look at YOUR hand, look at the Dealer's.  If he turns over a 10/Face to wind up with 19 or 20, staying put on your 18 would still result in losing.

            Next week, I'll explain a bit more why I like to use Blackjack as a sort of training tool as we see how the strategy I've covered today might change if you were playing a Blackjack variant, such as Spanish 21 or Blackjack Switch.

Surrender and Insurance

            As I’ve described many times, the concepts of Expert Strategy apply to more than just video poker.  Essentially, they apply to every game in the casino (except slots of course).  You should always know which games to play, what strategy to play them with and what to expect.  Most games in the casino do not require learning very significant strategies to play them properly.  Two that do – video poker and blackjack (and its variants Blackjack Switch and Spanish 21 – require some serious effort to learn them correctly.  The reward for doing so is a payback that is above 99.5%.

            In order to achieve the theoretical payback, you have to learn ALL of the strategy including the less well-known parts and even the parts we might find ‘offensive.’  For blackjack this would be the concepts of insurance and surrender.  The idea of ‘surrender’ is the one that you may find to be ‘offensive’, but there are times it is the right play.

            First let’s begin with the definition of the Insurance bet.  When the Dealer has an Ace up, he will offer everyone at the table the option to make an Insurance wager (which must be ½ of your base blackjack wager).  In reality, it is nothing more than a proposition bet.  If the Dealer has a blackjack, then you win 2 to 1.  If he doesn’t you lose your Insurance wager.  Assuming you have not been counting cards, then the odds of the Dealer having Blackjack is roughly 4 out of 13 (I’m ignoring his upcard ‘Ace’ and any of the cards you can see).  Paying 2 to 1, gets us back 12 out of every 13 units wagered for a payback of about 92.31%.  Obviously, you can do some light card counting and only make this wager when it is more in your favor, but it will take a lot of non-10s/Faces to turn the deck in your favor.

            Sometimes you will hear a Player who has a Blackjack to ask for ‘even money’ when the Dealer has a Blackjack.  This is really the equivalent of the Player making the Insurance wager.  If he makes it and the Dealer does NOT have Blackjack he will win 3 for 2 on his base wager, but would have lost 1/2 unit on Insurance leaving him having won even money.  If the Dealer DOES have blackjack, he pushes his blackjack wager and wins his Insurance wager, which will pay 2 to 1 of the INSURANCE wager which is equal to his base wager – in other words, even money on the base wager.  To keep things moving along, most casinos will just allow the Player to call “even money” and get paid 1 to 1 on his blackjack wager. 

            In reality, this is no better a decision than making the Insurance wager under any other situation.  However, from an emotional standpoint, many Players hate the idea of a total push when getting a Blackjack.  This would be the outcome if you don’t take the Insurance Wager AND the Dealer has Blackjack.  The proper play is to stay unemotional and never take even money.  This situation should only occur about 1 in 275 hands (approximately) which would mean once every 9 hours of play.  For some strange reason, I seem to get it about 3 times an hour?!

            Next up is the Surrender rule.  Many of you may never have heard of it.  The casinos don’t really advertise it much.  You have the right to Surrender your hand before you take any other action by forfeiting half of your initial wager.  Once you hit, split, double down, etc… you can no longer Surrender your hand.  There are two different variations of Surrenders.  The first called Early Surrender is rarely offered.  It allows you to Surrender BEFORE the Dealer checks for a Blackjack when he has a 10/Face or an Ace up.  Thus, even if the Dealer has a Blackjack, you would have forfeited only half of your wager.  This is a big advantage to the Player which explains its rarity.  The other variation is called Late Surrender.  This version has the Dealer checking for Blackjack and only after it is confirmed that he does NOT have one can the Player opt to Surrender.

            Unlike the Insurance Wager, this is not a proposition wager better left ignored.  If that were the case, the casino would have it on the felt in big bold letters “PLEASE SURRENDER!”  Instead it is an option you need to take on occasion and you almost have to ask the casino permission to do so.  From a mathematical perspective, the decision is easy.  If you are going to win less than 25% of the time with your starting two cards, you Surrender.  At a 25%, you would win back exactly half of your initial wager which is what you’ll have left after Surrendering.  Hence, that is why this is the decision point.  There are slightly different strategies depending on whether the Dealer hits or sticks on  Soft 17. 

            You should always Surrender a Hard 16 to a Dealer 9, 10 or Ace.  You should also always Surrender a Hard 15 to a Dealer 10.  If the Dealer hits a Soft 17, you also Surrender a Hard 15 to a Dealer Ace and a Hard 17 (yes, I said 17) to a Dealer Ace.  If the Dealer has a 6 underneath, he gets to keep going and is that much more likely to wind up beating you.   These rules apply to larger shoes of 4-8 decks. 

            The impact of properly Surrendering is that the payback is increased by 0.07%.  This may not sound like a lot, but looked at differently, it can cut the house edge by about 15%.

Is the Search for Perfection Overrated?

            

            One of the traits I inherited from my father, Lenny Frome, is that I am a perfectionist.  This is not to say that I am perfect (far from it).  The joke in our family was always that one of my sister's brought home a '99' on a test and my father, not missing a beat said "why not a 100?"  Fortunately, for me, by the time I came along, he learned to temper his ways a bit.  I try to focus most of my perfectionism inward.  Nobody takes it harder when I find a mistake in my work more than I do.

            At the same time, I try very hard to be practical about things too, where strategy is concerned.  Us mere mortals do have limitations to our ability to memorize dozens of video poker game strategies.  It is why I strongly recommend that you learn one or two different games and do your very best to 'perfect' the strategies to those games.  But, what are you to do if the games whose strategy you memorized are not available when you go to the casino or if you're just in the mood to try something different?

            In these cases, you just have to use some common sense.  If you try to bring your Jacks or Better strategy over to Joker Poker, you may find yourself in deep trouble.  But, what happens if you use your basic full-pay Jacks or Better strategy on a full-pay Bonus Poker machine?  What will this really cost you in theory?  Calculating this - with the help of some of my video poker analysis programs - is relatively easy.

            We simply run the numbers on a full-pay jacks or better machine using Expert Strategy for jacks or better.  From this program, we extract the frequencies of all of our winning hands.  We then use these frequencies against the Bonus Poker paytable to get a theoretical payback of Bonus Poker using jacks or better strategy.  We then run the numbers on Bonus Poker using Expert Strategy for Bonus Poker and compare the results.

            The theoretical payback for Bonus Poker using Expert Strategy for Bonus Poker is 99.16%.  The theoretical payback for Bonus Poker using Expert Strategy for jacks or better is 99.15%.  If you were to play all 2,598,960 possible 5-card deals using jacks or better strategy you would find that you cost yourself about 200 coins.

            In other words, while it is still preferable to learn the right strategy for Bonus Poker, if you use your jacks or better strategy, your bankroll will not take a big hit.  However, this should not give you free license to play jacks or better strategy on any game you want.  If you were take your jacks or better strategy to a DOUBLE Bonus Poker game, you would find that it will play at about 99.6%.  This might sound good (after all jacks or better itself plays at a bit less than this), but you have to remember that Double Bonus Poker is one of the few positive games out there.  If you play it using the proper strategy, it can afford you a 100.1% payback.

            So, what's the point?  Good question.  Nobody should expect perfection when they head to the casino.  The simple mathematical fact is that every deviation from perfection, however, will cost you.  It might be peanuts as in the case of playing Bonus Poker using jacks or better strategy.  If you play a hundred hours a year as a $1 max-coin Player, you'll cost yourself $30 per year.  We'd all rather have that $30, but we're not talking a significant amount of money.  Do the same on our Double Bonus scenario and we're talking about $1500 per year, which I dare say is QUITE significant.

            So, while we shouldn't shy away from video poker because we might make a few mistakes, we should still be prepared to learn the right strategy for each game and to do our very best to utilize it every time we play.  This is the very essence of Expert Strategy - Know which games to play, know what strategy to use and know what to expect.

            For those of you who want to learn the subtle differences between jacks or better strategy and Bonus Poker strategy, both strategies can be found in Expert Video Poker for Las Vegas and Winning Strategies for VideoPoker.

Get Up to SPEED - Let It Ride and Mississippi Stud

            

            Comparing Let It Ride to Mississippi Stud gives us a great opportunity to understand how a subtle difference in betting structure can greatly alter the strategy of the game and thus radically change a game that is otherwise rather similar.  The subtle difference in this case is that in Let It Ride the '1' and '2' wagers are completely optional (essentially, they can be 'checked') and in Mississippi Stud the choice is to Play or Fold.  No checking allowed.

            To best compare these games we need to realize that the idea that the you can take your wager down in Let It Ride doesn't change the game.  The rules of the game could have simply made the '1' and '2' wagers simple optional wagers.  You can either 'check' or you can make the wager. 

            Mississippi Stud also differs in that your first decision is after seeing only 2 cards instead of the 3 as in Let It Ride.  Mississippi Stud's paytable also goes down to a Pair of 6's, whereas Let It Ride goes to a Pair of 10's.   After 2 cards, the Mississippi Stud Player must decide whether to make at least an additional 1-unit wager or to Fold.  Mathematically, this is vastly different than the decision to check or Play.  When we have the decision to check or Play the question becomes one of whether or not the Player will win more than he loses on THAT specific wager.  Prior and future wagers play no part in the equation.  When the choice is to Play or Fold, the question becomes one of whether we can win back at least the amount we are about to wager when we consider ALL other wagers - both those already made and those we might make during the hand.  This is because if we choose NOT to Play, we are forfeiting all past wagers and the right to make all future wagers.

            The impact to this becomes most evident when we compare the '1' wager in Let It Ride to the 4th street Wager in Misssissippi Stud.  In this case, both hands consists of 3 cards and we are deciding whether to/how much to wager on the 4th card.  In Let It Ride, we find ourselves making the wager very infrequently.  We are willing to leave the wager in place only on sure winners (Pair 10's or Better or Trips), 3-Card Royals and 3-Card Straight Flushes (Open or Inside, NOT Double Inside).   We make this wager only 7% of the time.

            In Mississippi Stud, by the time we get to 3 cards, we have already wagered our Ante and at least 1 unit on the 3rd Street Wager.  If we Fold, we are forfeiting both of these  wagers.  We will also end our hand right then and there.  So, we also forfeit the right to potentially benefit from our next wager (5th Street).  The decision to Play 3x is similar to our Let It Ride decision.  Once you are going to win more than you are going to lose on a specific wager, you wager as much as the house lets you.  So, we find that we wager 3x on all sure winners, 3-Card Royals and a variety of 3-Card Straight Flushes.  We still go ahead and wager 1x on a whole lot of hands that sound like they're going to need some help to become winners.  This includes all Low Pairs, 3-Card Flushes and hands with the right combination of High and Medium cards.

            The net result is that we very rarely fold at this decision point.  The overall fold rate for Mississippi Stud is 44%.   31% (or nearly 75% of the total folds) occur after you see the first 2 cards.  Of the remaining 69% of hands that go to 3 cards, you will fold only 12% of the time.

            In Let It Ride, you will let the '2' wager stay up 16% of the time.  In Mississippi Stud, you will make a wager at 5th Street more than 90% of the hands that go that far.  This happens for two major reasons.  The weakest hands were folded very early on.  A hand that started as two Low Cards was dropped early, which makes weaker hands that much less frequent later on.  In Let It Ride, even the weakest hands have a chance to make it to the end of the hand.  The second reason is that when you have 3 units already wagered and you are compelled to either Fold or make another 1-unit wager, it does NOT take a high win frequency to make it worthwhile to make that additional 1-unit wager.   With just 1 High card and 2 Medium Cards or 2 High Cards in hand, it still pays to make this wager.

            With 2 High Cards, the Player still has 6 chances to draw a High Pair which will return 8 units the Player (each).  With 48 cards remaining in the deck this amounts to an expected value of exactly 1.0, which is the cutoff for determining whether or not to make the wager.  Throw in a Medium card as well and he gets 3 more chances to pick up 4 units and the expected value is now 1.25.  If this were a check or Play decision as in Let It Ride, the decision would clearly be to pull it back with these types of hands.

            There is a reason why I've coined Mississippi Stud to be Let It Ride on SPEED.  The games are very similar in how they play but vastly different in strategy and size of bankroll needed to sit and play.  I can't quite cover all the differences or all the strategy here, but for a limited time, I'm offering up a buy one get one special on my two booklets for these games.  Buy Expert Strategy for Mississippi Stud for $5.95 and get Expert Strategy for Let It Ride for free.  Just send check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133 and I'll get them both out to you ASAP.

Smackdown! Video Poker vs. Slot Machines

            

            This past week, I received an e-mail regarding last week's article about slots.  In that article I talk about how casinos can legally and do make sure that slot machines are created so that they produce a large number of near misses to make the Player feel like he almost won.   A reader wanted to know if the same is true of video poker.  He wrote:

             I'm always interested in the little things casinos do to try and influence how a player thinks.  Your article spells out an excellent example of how a slot machine display can create the illusion of coming close to a big win. I was wondering if the same thing applies to some extent to Video Poker.  If I'm holding 3 to a royal flush and my 2 new cards don't create a winning hand, but one of those 2 cards is one of the cards I need for the Royal, then I might be influenced to think that I was close to hitting a royal, even though the hand is as much of a winner as any losing hand.  Do you think that VP machines are set up this way as well?

            My answer depends on the definition of "set up".  Are video poker machines specifically programmed to have Player get more near misses than one would expect to occur randomly?  Absolutely not (in most jurisdictions).  In places like Nevada the law requires that any game that uses a real life object (like a deck of cards or die) in digital form must play as random as the real-life object.  In other words, if the game uses a deck of cards, every card must have exactly the same probability of being dealt as every other card. 

            Thus, the casino CANNOT program the video poker machine to have one of the two remaining cards for the Royal Flush be drawn just so it looks like the Player came close to winning - EVEN if it doesn't change the overall outcome of the hand.   So, if the Player is dealt a suited 10-J-Q and the two cards that are supposed to be dealt are the 8D and 5C, the machine cannot change the 8D to the suited King just so the Player comes closer, but still loses.

            What makes Video Poker so superior, in my opinion, to slots is that there is no need for the casinos (or the manufacturers) to do this.  One of the beautiful things about almost any game being played with a deck of cards is that the suspense is built into the game by the very fact that a deck of cards is being used.  True, once in a while a hand is so bad, there is no suspense, but this is infrequent.  How many times have you played a hand of video poker where the first 2 cards are a Pair or 2 cards of a Royal Flush?  Your heart skips a beat as you begin to be believe you're about to be dealt Four of a Kind or maybe a Royal.  That suspense turns to much when the final 3 cards are a mess and help your hand not at all. 

            Conversely, how many times have you been dealt very little (a single High Card) and you wind up being dealt a Flush, a Straight or even a Four of a Kind?  Nobody is forcing these hands to come out of the machine.  They occur because of the nature of the random deck of cards which generates are near misses for us.

            When we look at my reader's question about a 3-Card Royal being dealt one of the necessary cards, we find that it is not such an unusual occurrence.  For a simplistic way to approximate the likelihood of this, we simply have to know that we are going to be dealt 2 cards and we are looking for one of 2 cards to appear.  So, this is roughly equivalent to giving us 4 chances to be dealt 1 card from 47 cards in the deck.  This works out to be about 8+% of the time, hardly making it a rare occurrence.

            I think this leads to an interesting question.  Does it really matter if near misses are occurring because of the nature of a random deck of cards or if it is purposefully being programmed in by the manufacturers.  Quite frankly, by itself, I don't think so.  However, I believe what this tells us about video poker machines and slot machines is the critical part. 

            Everything about a video poker machine is the result of using a random deck of 52 cards.  So, while it is random, we also know all of the probabilities with 100% certainty and thus we can calculate a payback, determine a strategy and know what to expect over the long run.  We can look at the paytable and know everything there is to know about the machine.  We KNOW that if we see 2 machines with identical paytables, they have identical paybacks.

            With slot machines, we know NOTHING.  We can look at 2 slot machines standing side by side with identical paytables and still know absolutely nothing about either of them.  We have no idea how often winning hands will occur.  We have no idea which losing hands are programmed into it and how often it will 'tease' us with near misses.  A moment ago I gave a rough estimate of how often we can expect to get a near miss when drawing on a 3-Card Royal.  This can be calculated with absolute precision too (8.3256%).  You can't do this with a slot machine just by looking at it.

            I guess in the end it comes down to the difference between NFL Football and WWE wrestling.  I don't know who will be the next Champion, but I prefer the NFL version where it comes down to the best team and not the WWE where someone decides who should win and then puts on a good show to make it happen!

SCIENCE FICTION: BELIEVING YOU CAN WIN AT SLOTS

            When I tell people that I help develop new games for the casino industry by doing the math behind them, I'm invariably asked if I work mostly on slot machines.  Ironically, I've never worked on the math behind slot machines.  I try to explain that in my opinion slot math is amongst the easiest math in the casino. 

            Developing a casino game is really two parts.  The first is the creative half that determines the specifics of the game. The second part is the math behind the game, which can frequently cause some changes in the first part.  This dependency mostly evaporates with slot machines.  Virtually every slot machine is a clone of another game from a math perspective.

            I'm a big fan of science fiction.  So, if I wanted to invent a slot machines based on Star Trek, I merely need to come up with 20 to 30 symbols that are identified with the shows.  Maybe I use the characters (Captain Kirk, Mr. Spock, etc...) or I use the different shows (the original Star Trek and The Next Generation).  It really doesn't matter.  Most importantly, I simply have to decide what determines a winning hand.  I list out all the winning hands on a spreadsheet.  I add the amount each of these winning hands should pay.  I then determine the frequency that each of these hands occur.  I do a few simple computations and play with the numbers to get a payback to my liking and I'm done.

            Now I'd like to create a slot machine based on Star Wars.  I don't need to change any of the numbers.  I just simply need to swap out Mr. Spock for Hans Solo and Captain Kirk for Luke and I'm done.  In theory, every single slot machine could be based on a single spreadsheet of probabilities and payouts. 

            How can this be done?  because essentially, slot machines are rigged.  No, they don't know who's playing, so it's not like someone with a Player Card is going to lose and someone without one is going to win.  Nor can it tell the difference between a local and a tourist.  When I say it is 'rigged', I mean that nothing about a slot machine conforms to the notion of what you see is what you get.  When you spin the wheels, you may see more Captain Kirks than any other single symbol, but that doesn't mean the probability of lining them up is any higher. 

            In that little spreadsheet I mentioned earlier, I need to list out all the losing hands too.  The slot could simply be programmed to randomly pick a losing hand a certain percent of the time, but what fun would that be?  Instead it is programmed to give you Captain Kirk, Captain Kirk, Tribble more times than you can count.  Just for good measure there will be a Captain Kirk above or below that Tribble 50% of the time.  OH, you were SO CLOSE to winning!  In reality, you were just as far away as if the screen showed, Klingon, Romulan and Ferengi!

            To put it in more familiar terms, just because the screen showed you 7-7-orange with a 7 just below the orange doesn't mean you were any closer to winning than if it showed Orange-Plum-Banana.  If you kept drawing the fruit salad, you might get bored and leave.  But by showing you 7-7-orange, you get a false sense that you just missed.

            I would love to hear from those of you who are reading this column who continue to play slot machines.  Why do you do this?  The average slot machine in Las Vegas pays about 92.3% which makes it about the worse play in the casino.  I supposed it is fun to sit down and play a slot machine with your favorite tv show on it, but is it really worth all that you are losing?  Wouldn't it make more sense to learn to play video poker or blackjack and simply buy the complete series of your favorite show on Amazon with the money you're saving?

            Maybe Ballys and IGT should introduce video poker that is themed to tv shows and movies?  They just simply need to make the deck take on the theme of whatever show we are talking about.  Imagine Batman Joker Poker where the Joker is the actual Joker from the show.  Batman can be the King and Robin can be the Jack.  Batwoman can be the Queen!

            These characters won't change the game any, which is what happens in the slot versions too.  Maybe we can get more people to give up slots and become video poker Players if we simply put their favorite characters onto the cards? 

            As we head into 2012, I don't really care what gets you to break the slot habit, I simply implore you to do so.  In the end, I think you'll have a lot more fun and your wallet will definitely thank you!

The Details Behind the Advice

I’ve spent the last couple of weeks trying to get the beginners among you to make a relatively simple adjustment to your strategy. It involves four relatively common hands – high pair, 4-card flush, low pair and 4-card straight.

As I explained last week, they are played in this order because of their expected values. This week, I will walk through the calculation of the expected values for each of these hands.

HIGH PAIR

We start with the easy one first. It is easy because EVERY high pair has exactly the same Expected Value (EV). Since we already have a pair of jacks or better, we don’t have to worry about what are the specific cards discarded as they cannot help the hand nor interfere with other hands being formed.

When dealt a high pair, we will draw three cards. There are 16,215 combinations we can then draw from the remaining 47 cards in the deck (47 choose 3). Let’s look at the results of all of these draws:

45 will result in a four of a kind paying 25 each for a total of 1,125.

165 will result in a full house paying nine each for a total of 1,485.

1,854 will result in a three of a kind paying three each for a total of 5,562.

2,592 will result in a two pair paying two each for a total of 5,184.

11,559 will result in a high pair paying one each for a total of: 11,559.

The Grand Total is 24,915.

We divide the grand total by the number of combinations to arrive at the Expected Value of 1.5365. Every high pair has this exact EV. By itself, this number means relatively little in terms of our strategy.

Yes, it does tell us that we can expect to win about 1.5 units back when we have a high pair, on average, but it doesn’t tell us if we should play a 4-card flush or a high pair when we have both.

LOW PAIR

This will generate very similar results to our high pair. The only (and very BIG) difference is that all of those high pair hands at the end will now end up as low pairs and pay nothing. Thus, we will have a grand total of only 13,356, which when divided by 16,215 gives us an Expected Value of 0.8237.

4-CARD FLUSH / STRAIGHT

The 4-card flush and the 4-card straight each have 47 possible draws. The flush can result in nine flushes paying six each – for a total of 54.

The straight (NOT INSIDE) can result in eight possible straights paying four each for a total of 32. However, depending on how many high cards each has, it may be possible to wind up with a high pair as well.

For each high card that is in the 4-card flush or 4-card straight, three additional hands can wind up as a high pair instead of a losing hand. These additional three units when divided by 47 possible combinations means that each high card adds about 0.0638 to the Expected Value of our 4-card flush or 4-card straight.

So, a 4-card flush with zero high cards has an expected value of 1.15 (54 divided by 47). If there is one high card, we add .064 to this to get to about 1.21. With two high cards it climbs to about 1.28.

With three high cards – well, we would have a 3-card royal and that’s a whole different hand! So, a 4-card flush has an EV of somewhere between 1.15 and 1.28.

Since no other hand has an EV in between these two, we don’t bother separating these hands out on our strategy chart. Instead, we take the average of ALL 4-card flushes and say that its Expected Value is 1.22.

With regard to a 4-card straight, the Expected Value with zero high cards is a paltry 0.68. With one high card it goes up to 0.74. With two high cards it goes 0.81 and with three high cards to 0.87. Technically, a 4-card straight with 4-high cards is an inside straight (only one way to complete it) so its EV is much lower.

Because numerous other hands, including our low pair have an Expected Value in this same range, our strategy table shows each of these hands separated out.

So, when we look at all of these hands and rank them from high to low in terms of their Expected Values, we come up with the following:

High Pair: 1.54

4-Card Flush: 1.22

4-Card Straight with three high cards: 0.87

Low Pair: 0.82

4-Card Straight with two high cards: 0.81

4-Card Straight with one high card: 0.74

4-Card Straight with zero high cards: 0.68

It is based on these Expected Values that our strategy is derived. I’d like to raise two final important points. First, note that the 4-card straight with three high cards actually outranks the low pair – which is in conflict with the simple rule I gave two weeks ago.

While you should play this 4-card straight OVER the low pair, this particular combination is so rare that ignoring it while you work on learning the strategy will not cost you much. The ONLY way this hand can occur is 10-10-J-Q-K.

This leads to the second important point. For the purposes of this part of the strategy, ALL of our 4-card straights are outside – meaning they can be completed on either end. The other type of straight is an "inside," which has a gap in the middle or has an ace on one end or the other.

These can be completed only one way and have a much lower Expected Value. In Jacks or Better, most inside straights are not even playable.

I’d like to take this opportunity to wish everyone a Happy and healthy New Year and remind everyone to make their resolution to break the slot habit in 2012!

Clarity on a Little Advice

Last week’s column gave some simplistic advice to beginners who are not yet ready to sit down and really learn the strategy for video poker. It discussed the relative rankings of four of the most common hands – high pair, four-card flush, low pair and four-card straight.

While I gave the expected values for each of these hands, along with some explanations as to why the rankings are what they are, this week I want to stress that these explanations are not the critical part of the process.

The strategy for video poker is based on one thing – math.

We don’t keep a high pair over a 4-card flush because the high pair is a sure winner. If this were the case, we’d keep a high pair over a four-card straight flush, too (but we don’t!). The fact that the high pair is a sure winner explains why its expected value is as strong as it is, but it is the actual value of this expected value that puts the high pair where it does.

So what is this "expected value" I keep talking about?

It is the average amount of coins we expect to win over the long run from that hand.

How is it calculated?

It is calculated by looking at EVERY possible draw given the 5-cards already dealt.

Say what?

There are 2,598,960 ways to deal five cards from a 52-card deck. For each of these ways, there are 32 different ways to play each – ranging from discarding all the cards to discarding none of them. For each of these 32 ways to play a hand, there is a varying number of possible draws.

If we discard one card, then there are 47 possible draws (each of the 47 remaining cards). If we discard three cards, then there are 16,215 possible draws (choosing three cards from 47). A computer program goes through every possible draw and tallies up the winning hands for each of the 32 ways to play a hand.

It then computes the average number of coins returned for that way. This is the expected value for that particular way of drawing. It compares the expected values for each of the 32 ways and whichever has the highest one is the proper play for that deal and is deemed the expected value for that deal.

An example usually helps to shed some light on this process. Assume you are dealt: 4 of clubs, 5 of hearts, 5 of clubs, 5 of spades, 7 of diamonds.

We recognize the three-of-a-kind (5’s), the EV of which is calculated as follows:

Drawing two cards from the 47 remaining in the deck will create 46 four-of-a-kind winners (a five combined with each of 46 remaining cards). Sixty-six draws will end as full houses (six pairs in all ranks but 4, 5, and 7; 3 pairs of 4 and 7) while the remaining 969 draws do not improve the hand but instead leave it as a three-of-a-kind.

In summary we have:

46 4-of-a-Kind paying 25 each,

66 Full Houses paying 9 each,

969 3-of-a-Kind paying 3 each,

We calculate the total payout as 4,651, which is an average of 4.30 for each of the 1,081 possible draws. Therefore, the expected value of this deal/draw combination is 4.30.

As should be fairly obvious, if we try to play this hand in any of the other 31 ways, the expected value will NOT be any higher than 4.30 and thus this is also the expected value of this deal.

As all three-of-a-kinds have exactly the same expected value, this is ALSO the expected value of all. We will find this value on our strategy table.

Next week, I’ll walk through the four hands (high pair, low pair, four-card flush and four-card straight) I used in last week’s column. This will explain why the strategy I described last week doesn’t just make some sort of logical sense but is the right play mathematically.

I’d like to take this opportunity to wish everyone a happy holiday and a very happy and healthy 2012!

A Little Advice

            Last week's column was a gambling related philosophical debate about perfect vs. good enough.  This week, I'm going to the other end of the spectrum.  It is nearly impossible to define a 'bad' strategy as there really is no end to how bad a Player can play most games.  Playing every hand in Three Card Poker would probably meet the definition of a bad strategy, but is it worse than Folding every hand below a Pair?  Probably not, and I'm not going to waste my time to try to find out.

            This is not to say that every strategy that isn't perfect or as per last week's column 'good enough' would necessarily meet the definition of 'bad'.  I don't consider playing Three Card Poker with the strategy of Play any hand with a Queen to be good enough, but I can't really call it a bad strategy either.  With a game like Three Card Poker, there isn't really much to learn so you draw your line in the sand where you do and that's how you play it.

            A game like video poker is far different.  For anyone that doesn't use Expert Strategy, you might be hard pressed to find two people who used identical strategies.  In reality, they may be TRYING to use Expert Strategy (or some other particular strategy) but due to its complexity, they make a variety of errors along the way.  Then there are the multitudes of Players who just play by the seat of their pants, pretty much oblivious to the math that should be guiding them.  To these Players, getting them to even good enough will be quite a challenge.

            But, no matter what level they play at, if they just learn a few simple strategy points that might help them get a little closer to Expert Strategy then at least it is a step in the right direction.  So, today's column is for these Players.  I would like you all to consider learning just this small part of the strategy and trying to implement it.  You may still be a long ways away from playing Expertly, but hopefully, we can save you just a few bucks along the way and add to your enjoyment too.

            Here goes:

            1)  High Pair

            2)  4-Card Flush

            3)  Low Pair

            4)  4-Card Straight

            This strategy only means something on the hands that are either a 4-Card Straight or a 4-Card Flush and are also a Pair.  Approximately 25% of all 4-Card Straights and Flushes fall into this category, so these hands are fairly common.  This is why it is imperative that these hands be played correctly.  Let's take a closer look at why you should play the hands as described above and learn how these are NOT close calls.

            The High Pair is the only sure winner in the bunch, but this is NOT the reason it is at the top of the chart.  The determining factor is always the expected value of the hand, which is the average amount we expect to win with that hand over the long run.  Sometimes, the sure winner is not the right answer, but in this case it is.  The expected value of our High Pair is 1.54 which reflects the opportunities to turn this into Two Pair, Trips, Full House and Quads. 

            Next up is the 4-Card Flush which will win for us in the long run.  This is NOT to say that we will have more winning hands than losing hands.  With 9 opportunities to complete a Flush and perhaps a few more to complete a High Pair (depending on the exact makeup of the 4-Card Flush), we can expect to win with this hand only 20-30% of the time.  But since many of these will win with a Flush, the wins will be significant.  The expected value of a 4-Card Flush is 1.22.  It will be a smidge higher if you have 1 or 2 High cards and a bit lower if you have none.  If you have 3 High Cards, you have a 3-Card Royal and that takes precedence over the 4-Card Flush, but not the High Pair.

            While the Low Pair has the exact same probabilities as the High Pair of winding up as Two Pair, Trips, Full House or Quads, the fact that it starts as a losing hand is enough to bring its expected value all the way down to 0.82.  That means in the long run, this is a losing hand.  It is the second strongest losing hand (behind the relatively rare 10-J-Q-K Straight, which is also the ONLY exception to the rule I'm presenting here as you hold this 4-Card Straight over a Low Pair, which can only happen with a Pair of 10's).  The Low Pair is also BY FAR the most common hand in video poker, accounting for nearly 30% of all hands.

            Lastly, we have the 4-Card Straights.  While a 4-Card Straight with 2 High Cards ranks only slightly below the Low Pair with an expected value 0.81, it is still below it.  It only gets worse with 4-Card Straights with 1 High Card or 0 High Cards with expected value of 0.74 and 0.68, respectively.  These may not seem like big differences, but they will eat at your bankroll over time.

            It would still be far better for anyone reading this to become a truly Expert Player, but any improvements in your strategy are still better than none.  To help you on your way, we continue with our holiday special.  We are offering Winning Strategies for Video Poker, Video Poker: America's National Game of Chance and Expert Video Poker for Las Vegas for $5 each, which includes postage and handling.  Feel free to order as many as you'd like as they make great stocking stuffers!  Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.  We'll do our best to get them to you before the holidays.

            

Perfection is the Enemy of Good Enough

            Recently, while my teenage son and I were debating something, he responded with "perfection is the enemy of good enough."  My initial response was to shoot back "good enough is the enemy of perfection."  Since this highly philosophical discussion, I've given both of these phrases a lot of thought.

            I'm very well aware that I am a perfectionist who was raised by a perfectionist.  If you brought home a 99 on a test, my father wanted to know why you didn't get a 100.  If there is such a thing, however, as a realistic perfectionist, I think both by dad and I would qualify.  We strive for perfection, but also realize that it is often not realistic to truly attain it all the time.  I think this is why I found the aforementioned quotes to be both interesting and a little befuddling.

            My initial reaction that good enough is the enemy of perfection goes to my basic notion that we should always strive to be perfect.  Over the years, I've been asked many times regarding the strategy for Three Card Poker and if it really matters if you go with Q-6-4 or just Q-High.  The impact to payback is barely noticeable.  You might play for hours before getting a hand that Plays under one strategy but not the other.  Yet, the notion of settling for the easier Q-High frustrates me so.  Clearly the strategy is 'good enough.'  But, is remembering Q-6-4 SO hard that you one needs to go with Q-High?  To me, this is a case where good enough became the enemy of perfection.

            There were times my father's work on video poker was criticized (mildly) by other analysts for being less than perfect.  On one hand, my father was not prone to doing things less than perfectly - especially math work.  On the other hand, he taught himself how to program a computer at age 60, so this was not totally his comfort zone.  In a nod to that realistic perfectionism I mentioned earlier, my father's strategies for video poker were not designed to be 100% perfect.  They were designed to be played by humans.  And, not a bunch of rocket scientists, but the masses.

            The process that my father used to analyze video poker was rather similar to the same one I use, which is most likely not all that different from the ones created by anyone else.  We all have different degrees of shortcuts we use to speed up the process but the basic idea is the same.  We look at each of the 2,598,960 possible initial 5-card deals from a 52-card deck.  We then analyze each of the 32 possible ways to discard and review each of the myriad ways to draw to each of these 32.  Whichever of these 32 ways results in the highest expected value is the proper way to play the hand. 

            The calculation to do the above is absolute and assuming no error in the process will be 100% accurate.  In other words, it will be PERFECT.  So, in a perfect world, a Player could sit down at a video poker machine, press the Deal button and then enter the five cards he was dealt into an APP on his phone, which would run the process I just mentioned and tell him exactly which cards to discard.

            Unfortunately, the casinos are not too keen on this idea.  In fact, I was recently sitting at a Blackjack table and pulled out my phone to check e-mails while the Dealer was shuffling and got reprimanded.  I knew you couldn't use such devices at the table, but I assumed this meant while the game was in progress, not while waiting for the shuffle!  So, sitting at a video poker machine with your tablet in your hand will probably not be allowed.

            Because of this, the next best thing is that the results of analyzing all of these hands need to be summarized a bit.  This is what we call a strategy table that lists the rankings of all the hands in order of their expected value.  Certain hands become essentially 'exceptions to rules' when we try to summarize the hands.  These exceptions could be listed as their own rows on the strategy table, but what would the impact be if the strategy table grew to be 50 or 60 rows instead of the usual 35 or so?   By ignoring these exceptions we cost ourselves MAYBE 0.01% or 0.02% of payback, but we greatly simplify the strategy table, thus reducing the probability of errors.

            In this case, my son was right as perfection could be the enemy of good enough.  My father could have put together a perfect strategy table, but if learning it became that much harder so that the likelihood of errors increased to the point where an average person would lose more in errors than he would gain in playing 'perfectly' - would this still really be 'perfect'?

            At the end of the debate, it would appear that my father had already resolved the issue for us - and we were both right!

            As we are approaching the holiday season, Gambatria would like to offer to all of our readers a deal that may not be perfect, but is certainly better than good enough.  We are offering Winning Strategies for Video Poker, Video Poker: America's National Game of Chance and Expert Video Poker for Las Vegas for $5 each, which includes postage and handling.  Feel free to order as many as you'd like as they make great stocking stuffers!  Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.  They'll ship 1st class mail (or priority mail in some cases) so you can get them in time for the holidays.

Vintage Lenny Frome - Video Poker is NOT Slots!

This article was first published in about 1992 by my father Lenny Frome.  Keep that in mind as you read through some of his comments and realize just how much has changed in the nearly 20 years since!

Video Poker is NOT Slots!

by Lenny Frome

            Every time we write a column for a new publication, we do so with a great deal of uneasy feeling.  After all, the readers who pick up this journal after a session at the poker tables or in the Bingo parlors look at Video Poker players with disdain.  No matter how special we consider our machines, they look at them as "just slots".

            In 1988 Las Vegas had a poker room paper called of all things, POKER ROOM. Within days of accepting our very first Video Poker article, the publication closed its doors. Imagine our guilt feelings as we contemplated that just planning to put Video Poker into print could cause a gambling paper to close. Maybe they were "just slots" then.

            In the four short years since , Video Poker has come of age.  From just a handful of game versions, there are at least 50 unique versions, which with their various pay-tables, create literally hundreds of different games.  Today, the term "Video Poker" doesn't hardly give a clue as to what kind of game we're referring to.

            The public by and large has learned to respect this family of games for several reasons. Most analysts attribute its popularity to the man-machine interaction--the decision making by the player which affects the outcome.  Others claim the players enjoy their privacy and are never intimidated.  Those reasons don't satisfy me because for a long time Video Poker languished in Las Vegas.  When the machines paid on on two-pair or better, they were a drug on the market.  Nobody knew how to play them and even when they did approach expert play, the payback of 90% disenchanted the public.

            When the pay-table was revised to pay on Jacks or Better, the public flocked to them.  Nobody, including the casinos really could explain this phenomenon because it took quite a while before the 99.6% payback on expert play was proven.  Meanwhile, the public could sense that they won much more often and played longer.  In the long run, players still left money in the machines but they enjoyed the time on them.  Today, one-third of casino revenue is derived from Video Poker.

            Outside of Las Vegas the payback is necessary lower which makes it even more important for players to learn how to play correctly.  To become a good player is easy once becomes be aware of several key factors:

          ELEMENTS OF EXPERT VIDEO POKER PLAY

(A)  The game is governed purely by known mathematical probability;  if you don't believe that, you cannot become a good player.

(B)  Once the deck is defined and a pay-schedule displayed, the optimum strategy for hold/discards on every hand is known, along with the payback percentage and the average number of each level of winners.

(C)  Unlike reel-slots, which can have their payback altered almost at the whim of the casino with absolutely no warning to the players, Video Poker payback is not variable unless the posted rules and/or pay table is revised.  Stated another way, all machines which play the same game and have the same pay table, must have the same payback.

(D)  It follows that players can tell which machines are the most liberal and can learn the strategy to optimize the payback.

  

(E)  The essence of Video Poker strategy is that every hand must be played (cards held) in the way that the hand has the maximum win-potential.

(F) The win-potential of a hand is indicated by a numerical value known as EXPECTED VALUE (EV). Players do not have to remember exactly how EV is derived  or even what the EV of any hand is, but they have to know the proper way to hold/discard so that the EV is highest.

(G)  Once the deck and paytable are defined, a ranking table is available in Video Poker books which shows the way to play every hand that can be dealt and played in that version.

            Learning the ranking tables is a lot easier than you might imagine since most hands are playable in only one way, which is obvious.

            We'll continue this treatise soon; in the meantime, practice on the kitchen table by dealing out 10 cards, five down and five up on top of them. That's how the machines do it. Rember that the caveat "Play With Your Head" translates into "Learn How First".

Giving Thanks

            I apologize to those of you who have been looking for my column the past couple of weeks and couldn't find it.  As some of you may have heard by now, my mother (and wife of Lenny Frome), passed away two weeks ago.  After the funeral, my brother recounted a story to me that I had never heard before.

            When my father passed away in 1998, my brother was the first one who headed out to Las Vegas to be with our mom.  It took a day or two before all the arrangements were made for them to come back East for my dad's funeral.  Yet, of course, they still had to eat.  My brother asked my mom where she wanted to go to dinner and she responded with Hugo's Cellar at the Four Queens.  My family had already made that a regular dinner spot when anyone came to town - and it is a tradition that carries through until today. 

            As they walked through the casino from the parking garage to the restaurant, they passed by two women playing video poker.  They were each holding a copy of one of my dad's books.  My brother said he could not have staged it any better if he tried.  This was clearly a sign.  My father's impact to the industry would continue long after he was gone.

            My father was informally called "the Godfather of Video Poker" by many in the industry.  To be sure, he played NO part in the invention of the game.  At the same time, no one can deny the impact he had on popularizing it.  Even if you are not a video poker expert or even a regular, I can't help but imagine that your play isn't just a tiny bit better from having read his articles - or any of the numerous writers who came after him - including me!  Would video poker have had the staying power if there wasn't someone telling the early Players how to play it?  Would video poker have eaten up as large a percentage of the casino floor as it does today?

            Of course, my father could just have easily been called "the Godfather of Proprietary Table Games".  He had a hand in the development of Let It Ride, Three Card Poker, Spanish 21 and Caribbean Stud Poker.  At their respective peaks, there must have been a combined 2500-3000 of these tables.  As I consider myself an extension of my father's work, we can add on Ultimate Texas Hold'em, Mississippi Stud and a host of smaller games to the total.  This brings the total to perhaps as high as 4000 proprietary tables that my father directly or indirectly had a hand in.  Imagine the casino floor without any of these games.

            While my father was the public face of everything that went on, everyone that knew them (both personally and professionally) knew that my parents were always together.  My dad brought my mom to business meetings to size up the potential client.  My mother was the proofreader for all of my dad's books and booklets.  She was responsible for shipping orders and for the accounting.  In fact, it was my mother who was always listed as the "President" of their company. 

            With the help of Catherine Jaeger, the editor of Midwest Gaming and Travel, we have launched a campaign to get my father into the American Gaming Association's (AGA) Gaming Hall of Fame in 2012.  No disrespect to Blue Man Group (one of the inductees for this past year), but I truly believe Lenny Frome's impact on the industry has been far greater.  To this end, we are asking people to write to the AGA and urge them to induct my father into the Hall of Fame in 2012.

            There are a number of ways to make your voice heard.  You can copy the sentence below or use your own experience to explain why you believe the time has come for Lenny Frome to be inducted into the Gaming Hall of Fame. "Because of his many significant contributions to casino gaming, I respectfully request your consideration of Lenny Frome for induction into the Gaming Hall of Fame."

Mail it to:
American Gaming Association
Frank J. Fahrenkopf, Jr., President/CEO
1299 Pennsylvania Avenue, NW, Suite 1175
Washington, DC 20004

Online:
E-mail to:
Brian Lehman/Communications Manager-AGA
blehman@americangaming.org
Facebook: www.facebook.com/AmericanGaming

            Over this Thanksgiving weekend, my family and I one again dined at Hugo's Cellar.  This time, for the first time we toasted the memory of both my father and my mother.  My dad may have been the "Godfather of Video Poker", but most importantly, they were the "Father/Mother and Grandfather/Grandmother of the Frome family."  Once again, they are "always together."

Beating the Casino

            

            A couple of weeks ago, I discussed how a blogger lamented how the last good table game invented was blackjack because none of the games invented since gave the Player a chance to beat it.  I would argue that blackjack is hardly 'beatable'.  It requires an incredible amount of discipline and knowledge of card-counting schemes in order to eke out even the slightest edge.  With the continuous shufflers and regrettably 6 to 5 payouts on blackjack, even with the most sophisticated counting scheme, beating the game is almost impossible.

            There is only one game on the casino floor (barring the occasional game that accidentally makes it to the floor) that is readily beatable.  That is video poker.  There are games all are over Las Vegas with paybacks of over 100%.  If you learn the proper strategy you can earn these paybacks.  I will not, however, promise that you will become filthy rich off them.  Unlike card-counting schemes which would allow you to bet $5 when the count is against you and perhaps $5000 or more when it is in your favor, video poker machines essentially have a constant wager and there are no known counts for you to track.  Each hand is completely random and no matter how many hands you have won or lost in a row, the next hand is still random.

            Over the years the casinos have caught on to this idea and this is why many are still willing to put machines on their floor with paybacks over 100%.  They simply don't put them on the floor with high denominations.   If you are willing to play video poker 40 hours per week (like a job), are able to play 700 hands per hour, you would play 1,456,000 hands per year (approximately).  If you played a quarter machine, you would wager the staggering sum of $1.82 Million per year.  If you can play the entire time on a full-pay Deuces Wild machine paying 100.76%, you'll earn about $13,800 per year.  This doesn't account for any taxes and doesn't account for any cash back and/or comps.  

            Of course, some of you will just suggest playing a higher denomination.  Even playing dollars, the annual 'salary' will get to only $55,000 or so.  This is certainly not a bad income.  Of course, this most certainly doesn't mean you can count on any sort of regular 'paycheck'.  There are going to be weeks you lose and there are going to be weeks you win far more than average.  And, as I said earlier - the casinos have caught on to this.  According to my research, there are no $1 machines playing full-pay Deuces Wild in the Las Vegas area.  So, the casinos are willing to let the resourceful Player make some money, but not enough to really entice large numbers of Players to do them harm. 

            This is also further proof that video poker machines are not slot machines.  Casinos would NEVER allow banks of 100+% slot machines to exist.  Slot machines require no strategy.  Thus, as long as the slot machine were to be played for 40 hours per week the casino would be paying out the $13,800.  To the casino it doesn't matter if this is one person, 10 people, 100 people or 1000 people who wind up winning this money.

            Video poker requires that the Player learn the proper strategy to earn this money.  So, if 52 people took turns playing for 1 week and played using Expert Strategy, then the casino would still be paying out the $13,800.  But the casinos know this is highly unlikely.  Despite strategies for virtually every imaginable game being available for 10-20 years, the overwhelming percent of Players simply choose to ignore the proper strategy.  The reality is that 50% of the Players probably know of no real strategy and just muddle along - playing a Deuces Wild game at no better than a 95% payback.  Perhaps another 25% play using some rudimentary strategy that they learned somewhere and play at 97%.  Another 15-20% have made real attempts to learn strategy but haven't really mastered it and can play at 99%.  The final 5-10% have learned the proper strategy and make a significant attempt to play properly.  Perhaps half of this group truly attains a payback of 100.5% or better.

            The result for the casino is that their machine probably pays out at no more than 96.5% in total.  A number that they can definitely live with.  However, just as the casino doesn't care if it is 1 or 1000 Players that win the $13,800, you do not have to be concerned with how any other Players do.  The casino is very happy with that machine that pays back 96.5% and will net them more than $65000 per year - EVEN if it means one of the Players made a few hundred or thousand over the course of the year.

            But, if you want to be this Player, you have to learn how to play video poker using the proper strategy.  To help you along the way, we're offering up our two full-length books for just $5 each (which includes postage and handling).  Winning Strategies for Video Poker includes strategy tables for 61 of the most common games found anywhere.  America's National Game of Chance: Video Poker is 200 pages of Lenny Frome's best articles, stories and quizzes and is an excellent way to learn how to play video poker in an easy to understand way.

            Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133 and you'll be on your way to becoming an Expert Video Poker Player.

The Godfather of Video Poker

The November issue of Midwest Gaming and Travel is a tribute to my father, Lenny Frome.

I'd like to thank Catherine Jaeger (the editor) for coming up with this idea and using it as a means of launching a campaign to have my father inducted into the American Gaming Association's Gaming Hall of Fame.  Here is a little bit more about this campaign - Make 2012 Lenny's year!

My father changed the landscape of every casino in the world by helping to make video poker as popular as it is.  He also provided the original analysis for games like Let It Ride, Three Card Poker, Caribbean Stud Poker and Spanish 21.  Imagine the casino floor without any of these games.

Below is a link to the article I wrote for Midwest Gaming and Travel about my dad.

The Godfather of Video Poker

Video Poker Progressives

            A couple of weeks ago, I described in detail how the math behind Progressives work.  In that column, I mentioned how video poker progressives works just a little different.  There are still two paybacks to be concerned with - the long term theoretical that the casino is concerned with and the specific payback at any point in time that should be the attention of the Player.  The majority of the calculation is still the same in that we multiply the payout of a winning hands by the frequency of the winning hands  and sum up these values.

            What is different about video poker is that the frequencies of the different winning hands can vary as the amount on the meter changes.  For those of you who are video poker Players, this should be no surprise.  For years, I've been telling you that a single unit change in the payout of a hand not only changes the payback but can change the strategy.  Each time you change the strategy you potentially increase the frequency of some hands at the expense of others.

            As a very simple example of this, imagine how the strategy changes as we go from a standard full-pay jacks or better machine to a Double Double Bonus machine.   Because the payout for Four Aces is so high, we actually find that the Player should discard Two Pair in favor of a single Pair of Aces.  This will obviously reduce greatly the frequency of Two Pairs and Full Houses and increase the frequency of Three of a Kinds and Four of a Kinds. 

            So, it should be no surprise that as the jackpot for a Royal increases above 800 that the strategy will begin to shift.  Hands with the potential to be a Royal will have their expected values increase.  This will lead to more Straights, Flushes and of course Royals and the expense of Pairs, Trips and Quads.  Of course, we will also throw away a variety of partial Straights or Flushes to go for the Royal, so this will work against the Straights and Flushes and might increase the number of High Pairs. 

            Thus, pinpointing the exact frequencies can be a bit tricky.  Fortunately, the far easier of the paybacks to determine is the payback at any point in time.  This is because at any point in time, we can know the exact amount of the Progressive jackpot and use this number to determine the exact strategy and in turn the exact frequency of each hand.

            The most common video poker Progressive is an 8-5 machine, meaning it pays about 97.3% when the jackpot is reset to 800 (per unit wagered).  At this level, the frequency of the Royal is about 1 in 40,200 hands.  If the jackpot were to climb to 1600 (per unit wagered) then the payback of the game will go up to about 99.5% and the frequency of the Royal goes up to 1 in 32,700 hands.

            Of course it is rather unlikely that you're going to see a Progressive for a Royal get this high.  With only 1% of the amount wagered (at most) going to the meter, the average amount that will be added to the Progressive Jackpot is somewhere between $327 and $402 (1% of the previously mentioned frequencies).  Of course, something that can occur 1 in 40,000 hands or so can easily occur every 10,000 hand or 80,000 hands.  So, it is not impossible to see the progressive meter go to 1600.  It would have to go to about 1800 for the game to become positive (payback over 100%).  This is not impossible, but not very likely.

            As the payback goes up, the strategy changes and the frequency of the Royal increases, making it harder and harder for the jackpot to keep increasing as the likelihood that it gets hit goes up.  Because of this, it is a bit harder to calculate easily the long term theoretical payback.  It is reasonable, however to approximate it using the same process used for regular progressives.

            In this case, I would take the frequency of each hand using the reset value of the jackpot and multiply each by the payout of the hand and sum these up.  Lastly we would add the percent of each wager going to the jackpot to the total.  This means that the long term theoretical payback of a Royal paying 8-5 with an 800 unit reset amount is about 98.3%.

            I have to admit, if I were designing a paytable for a video poker progressive, I would probably make the likelihood of the game going over 100% a bit more common.  I think it would be a lot of fun to the frenzy that would/should occur each time the payback at any point in time goes over 100%.

            

Vintage Lenny Frome - A's and 8's

When I have time I'm going to try and post up some of my father's (Lenny Frome) articles here as well.  The following article is about a rarely found (but I'm told there are still a few 50-cent machines at Circus Circus) version of video poker - Aces and Eights.  Its payback is about 100.25%.  This article is probably 15-20 years old, so some of the information may be dated:

Aces and 8's--From Green Felt to Video  

             Long, long ago before the world played Video Poker, the story of Aces and Eights, the dead man's hand was abroad in the land. It always conjured up a mental image of evil-- a hand that brought fear into the hearts of men, even the roughest, who made a living with the pasteboards and reckless gun slinging.

             Leave it to the enterprising folks at CircusCircus to capitalize on this theme and then carry it out in high-tech fashion under their big top. They have come up with a sure winner in Aces and Eights, a 100% payback machine featuring four progressive Jackpots as added attractions which will frequently push the payback into positive territory.

            The pay schedule  is very straight-forward for a multi-progressive (or is it just that we are getting adjusted to the new regimen in such lengthy tables?)  It is an 8/5 schedule Jacks or Better with these four bonuses to offset the 2.3% shortfall vis-a-vis full-pay 9/6ers:

·         Four 7's pay 50 for 1 on 1 to 5 coin-play non-progressive.

·         Four 8's or Four Aces pay on a single progressive which resets at 80 for 1 (5-coin play only).                

·         A Royal Flush pays on an 800 for 1 minimum progressive jackpot.

·         Sequential Royals (either way) pay on a 10,000 for 1  minimum progressive

Looking at the payback situation, these bonuses work into the picture this way:

            Four of a Kinds in any one specified suit occur on average only  once in 5,500 hands; a regular Royal once in 40,000 and in either    sequence once in 2,400,000 hands.  The extra 25 on the 7's adds .47%. The extra 55 on the 8's adds a  minimum of 1% as does the extra 55 on Aces. The Sequential Royal gives us an extra 9,200 which is worth .38%. As the meters climb  upward the value of these jackpots further increases the payback. Together, these bonuses,  take the payback up from 97.3% to 100.15%. With some minor changes in strategy, we can pick up a little bit more.

            The first time we saw this machine, the Sequential was posting $13,204, the Royal  $1,030 and the Four Aces or Eights a whopping $154. The game was close to 102% payback. While watching it, the jackpot was hit on 8's by one of the players seated at about 50 machines on the floor.  The Aces/Eights progressive had gone an unusually long time since the last hit. We cannot expect many such generous jackpots. Frankly, we were genuinely surprised when the meter reset at $100, since that is more than three times the 25 for 1 normally paid on quads.

            Even with this liberal machine we need all the savvy we can muster to play the game expertly. The extra value of Aces and 8's dictates these modifications in the ranking order of 8-pairs: Even at minimum meter value of $100 on a quarter game (80 for 1), the pair of 8's is better than a 4-low-card flush and at $120 beats those 4-card flushes with two high cards.

            Incidentally, the player who hit the $154 would have been right in breaking up 8's full to go for the quads. I'm happy to report that it wasn't necessary to wrestle with that problem--but if it were you, what would you have done?

 

Don't Be Foolish!

            It was almost a year ago that I launched this blog (gambatria.blogspot.com).  I was very nervous about launching it.  If there is one thing I've learned about the internet over the years is that pretty much any idiot can have a blog - and quite frankly, I didn't want to be 'any idiot.'  I'd like to think that the name "Frome" is the gold standard in the industry where math analysis is concerned.  To our credit, we have Three Card Poker, Let It Ride, Caribbean Stud Poker, Spanish 21, Ultimate Texas Hold'em, Mississippi Stud, Imperial Pai Gow and countless sidebets.  That's a lot of the casino floor whose math was done by Leonard Frome or Elliot Frome. 

            So, I was quite surprised this past week when I came across a financial blog that was very unimpressed this year's G2E where table games were concerned.  Admittedly, I did write a column last year that called on more inventors to display their ideas at the G2E.  I recognize that the cost of even a small booth can be rather prohibitive for the individual inventor, but what a great opportunity to show your game to people in the industry.  I was pleasantly surprised to see at least two new inventors displaying their games and larger booths from some of the more established companies.

            What I found amazing about this financial blog, however, was not that the writer looked over every game and found none of them to his liking.  That would've been one thing.  Instead he essentially takes table game companies to task for "designing games that the gambler has no hope of beating, but they force the gambler to take the time to learn how to play them!"  This blew me away!  Does he truly expect the casino to introduce games that the Player can easily beat?  That's not going to happen.  The only game that has ever been put on the floor that can readily be beaten are certain variations of video poker. 

            Further, our blogger is annoyed that you have to take time to learn how to play them.  The only game which requires ZERO time to learn how to play them is perhaps slot machines.  As I've recounted in my column many times, I can't even figure out when I've won or lost anymore in today's video slots, but since all you need to do is press the 'spin' button and we can assume that the machine will properly tally your win or loss, I assume this meets the requirement of not needing to take time to learn how to play them.

            Thus, we can conclude from our blogger that what he is looking for is a slot machine with a 100%+ payback.  Perhaps he should've read my column from two weeks ago where I talked about a company that provides the payback information for their slot machines.  This WOULD necessitate learning how to use the smartphone 'app', so I don't know if this meets his strict criteria.

            A couple of days after this first column appeared, our blogger was back with more information for us.  First, he repeats some of his thoughts from the previous column, decrying the lack of innovation from table game companies and then stating, "how the gaming industry has not seen a blockbuster table game since blackjack, and how the industry may not see one until somebody steps up and creates a game that is theoretically beatable."

            That is quite a statement.  According to Wikipedia, blackjack's origins may be as much as 400 years old.  The game as it is played in most jurisdictions is hardly beatable - or at least not easily.  Yes, we're all aware of the MIT team that did it, but this took a rather significant effort on the part of a focused group of individuals. 

            In 1991, the table half of the casino floor consisted of nothing but blackjack, craps and roulette.  Twenty years later, it is estimated that as much as 15-20% of the tables in the U.S. market may be those that were invented AFTER blackjack.  Twenty years from now, I have little doubt that blackjack will make up an even smaller percent of that floor.   Let's not forget that a blackjack table is essentially FREE to the casino while they have to pay to put a proprietary table game on their floor.

            As a gaming analyst - and one that focuses mostly on table games - I am keenly aware of the math of the games.  Most of the newer games that are being introduced have paybacks in the higher 98% to low 99% range.  Yes, they do require that you 'learn' how to play them to achieve these paybacks.  No one, not myself, not the inventors nor the casinos will try and let you believe that the games are beatable in the long run.  That does NOT, however mean that you cannot have winning sessions in the short run and enjoy the entertainment value that they can provide.  Most table games are developed to have the Player win about 35-45% of the time over a 3-hour session - assuming you are willing to 'take the time to learn how to play them'

            Best of all, I won't "force" you to do this, but I'll give you the opportunity to!  There are now 7 books in the Expert Strategy series for table games (Let It Ride, Three Card Poker, Four Card Poker, Spanish 21, Caribbean Stud Poker, Mississippi Stud and Blackjack Switch) and for a limited time, you can order the entire set for $20 which includes postage and handling.  Send a check or money order to Gambatria, P.O. Box 36474, Las Vegas, NV 89133.

            

Progressing

            Last week, I alluded to the seemingly complex math associated with games that offer progressive payouts (i.e. "progressives").  Progressives are games where the top pays are not fixed dollar amounts or odds payouts, but rather have variable payouts that increase as more wagers are made since the last time the prize was won.

            Progressives have become very popular for table games sidebets.  They have long been used for some video poker machines for payouts on Royal Flushes.  Most commonly they are found on slot machines, which love to use a progressives ability to create a very large payout for a very rare occurrence.  As is always the case with a random event, the cycle between hits can frequently become far larger than 'average' and thus create an even larger than normal jackpot.

            As I described last week, Progressives essentially have two different paybacks.  The first is the long-term payback which is what concerns the casino.  The second is the payback of the wager at any point in time which is what should concern the Player.  Let's take a closer look at how these are calculated and why there are two different paybacks.

            Normally, to calculate payback, we take the frequency of a winning hand, multiply it by the payout of this hand which gives us the contribution rate for the hand.  We then sum up these contribution rates to arrive at the overall payback.  For most wagers, the frequency of a particular winning hand is fixed as it is unaffected by strategy.  So, if we are playing Caribbean Stud Poker, we don't have to worry about the strategy of Folding and Playing for the sidebet because you would never Fold a hand that is strong enough to earn a bonus.  Video Poker presents an additional challenge in that you can alter you strategy depending on the payouts and thus alter the frequency of winning hands.

            So, to calculate the payback of a Progressive at a particular point in time, we follow the calculation I just described.  For example, let's assume the following paytable at a particular point in time for a $1 wager:

Hand	Pays (For 1)
Royal Flush	$113,473
Straight Flush	250
Four of a Kind	50
Full House	10
Flush	7
Straight	5
Three of a Kind	3
Two Pair	2

           

            If we perform the calculation described, we get the following:

Hand	Frequency	Pays (For 1)	Contribution Rate
Royal Flush	0.00015%	$65,473	10.07680%
Straight Flush	0.00139%	2500	3.46292%
Four of a Kind	0.02401%	250	6.00240%
Full House	0.14406%	50	7.20288%
Flush	0.19654%	20	3.93080%
Straight	0.39246%	15	5.88697%
Three of a Kind	2.11285%	10	21.12845%
Two Pair	4.75390%	5	23.76951%
Total	7.62536%		81.46074%

            So, if you were to walk up to a table and see these payouts, the payback of the game at that very point in time is 81.46%

            But, the payback to the casino could be vastly different.  Let's assume that the Royal Flush is seeded at $50,000.  This means that every time someone wins the jackpot, the prize for the Royal Flush will be reset to $50,000.  Further, let's assume that for every $1 wager that is made, the Progressive increases by 10 cents (i.e. 10% of the wager).

            There are two changes that we must now make to calculate the payback for the casino.  The first is that we always use the seed amount as the payout for that hand.  Thus, we repeat the calculation shown above but we use $50,000 as the payout for the Royal Flush.  This is the amount that the casino itself directly paying out each time the jackpot is won.  When we do this, we find that the payback of this wager is 79.08%.

            However, we must now ADD to this payback the amount of each wager this added to the Progressive meter - in this case 10%.  Eventually this 10% will go back to a Player.  It might happen while the jackpot is at $50,000.10 or it might happen when it is at $120,000 or more.  From the casino's standpoint, it doesn't matter.  That 10% belongs to the players.  Essentially all the Players that don't win the jackpot are handing those dimes to the person who finally does.  So, when we add that 10% to the 79.08% we find that to the casino this wager really has an 89.09% theoretical payback.  Over time, the casino will keep 10.91% of every dollar wagered.

            So, if you were to play this wager while the Jackpot is $65,473, you would actually be playing it on the 'low side' of the average jackpot.  How big is the average jackpot?  To calculate that, we take the average number of hands between jackpots (in this case 649,740) and multiply it by that 10%.  On average the jackpot will grow by $64,974 before it is hit.  We add this to the seed amount and find that the average jackpot will be $114, 974.  At that point, the payback of the wager is the same as theoretical payback of the wager. 

            If the jackpot grows to be above $185,930 (which is very likely at times), then the payback of the wager at that point will actually be OVER 100%.  The only problem with this is that it will only be over 100% for the ONE person who actually wins the jackpot.  Everyone else will just be feeding dimes to the one person who wins.