Can the Wrong Thing Be Right?

            For those who read my column regularly, it may seem as if my columns jump around through unrelated topics.  In one regard, this is essentially correct.  Strategy in blackjack has very little to do with video poker.  Sometimes, I discuss a generic topic about math which is a bit more broad.  And, once in a while, I even surprise myself with how seemingly disparate topics can come together.  Today is one of those days.

            I've written numerous columns about the right way to play Two Pairs and Full Houses in the Bonus variations of video poker.  It can be both confusing and incredibly alluring.  Those Four of a Kinds (A's - 4's) can pay a LOT of money.  Tonight's column, however, isn't about when to throw the Two Pair or the Full House correctly, it's about the allure of when you're not supposed to but you're so tempted to do so.

            This meshes with another topic that I have discussed from time to time.  Namely, how Players are willing to accept lower paybacks for significant payouts.  If blackjack had a 94% payback, I don't think anyone would play it.  You have no chance for a quick big win and with a 94% payback, all you would have would be a slow sucking sound of your bankroll shrinking.  But, add a sidebet to blackjack and all of a sudden, Players who would never play 6 to 5 blackjack because of the house advantage are willing to risk $1 - $5 on a 92% payback (or worse) as long as there is a payout (no matter how rare) that can translate into a big win.

            Three Card Poker is another example of this.  It's payback is about 98%, but Pair Plus, has a payback in the low to mid 90's.  The very popular 6-Card Bonus sidebet can go down to the mid 80% range.  But, for the opportunity to win $1,000,000 on a $5 wager (at Caesars' properties) and the math goes mostly out the window.  And of course, the ultimate example are the state Lottos.  Boasting paybacks of 60-70%, with the overwhelming majority of it in the 190 million to 1 shot of the jackpot, the Lotto is the ultimate example of the math being meaningless.  Give someone the slimmest chance of a life altering jackpot and that's enough math for just about anyone.

            So, how do these two topics come together.  This happens when you are dealt three 2's and two 10's on a Double Double Bonus machine.  If a full-pay machine, the Full House pays 9 and the Trip Deuces have an expected value of 7+.  It's not much of a math decision going on.  But, if you're playing max-coin quarters, you're talking about winning $11.25 vs. having a shot at the Quad Deuces paying $100 without the kicker and $200 with it.  Of course, the most likely outcome is that you don't hit the Four of a Kind and you're 'stuck' with your Trips paying $3.75.

            So, $200 is not exactly life altering.  But what happens if you're playing Multi-Play Multi-Strike and you get this hand on the 4th level where all pays are multiplied by 8 and you have 3 hands still alive, giving you 3 shots at it.  Each of those Full Houses is worth 72 coins for a total of 216 and this with 1-coin in.  With 5 coins in, it's just over 1000 coins.  If quarters, you just won $250 (roughly).  Are you willing to risk it to go for the Quads?

            It all gets a bit more complex because you're not likely to hit Quads on all 3 hands.  What if you hit just one?  160 coins payout if you can hit it with a kicker.  Multiplied by 5 coins in is 800 coins.  Multiplied by the 8x payout and you've got 6400 coins.  That's over $1500.  Maybe you get super lucky and hit two of them (1 with and 1 without the kicker).  You're up over $2000.  Worst case, you get stuck with three Three of a Kinds and you win 360 coins. 

            To be clear, I'm not advocating that you go for the Four of a Kinds.  But, as the potential payout increases, you give it a lot more thought.  Even though, relatively speaking, you are still risking the same amount to go for it.  A $2000 win might pay for your whole trip.  $250 pays for a night out.  Are you willing to risk the $250 to go for the $2000?  Of course, this really isn't the right equation.  If the Full House pays 9 and the Trips have an Expected Value of just over 7, what you really are talking about is a wager with a payback of about 80%.  Mathematically, it's not the right move.  But, then again, neither is wagering $5 on a sidebet with an 85% payback.  $2000 isn't $1 million either. 

            For the record, if you're dealt a Full House with Three ACES, your decision is made much easier.  You throw the Full House to go for the Quads.  Those Aces are worth twice as much, potentially, and this puts the math in alignment with your emotions.