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Pairs are not equal when playing video poker

One of the things that makes learning video poker so complex is also one of the things that made it so successful. Some of the earlier versions of video poker only paid on two pairs or better. This greatly lowered the win frequency, sort of.

In reality, we only get our wager back when we have a pair of Jacks or better. The payout of 1 for 1 is just a push. But it was all those pushes, which don’t feel like pushes when you’re playing on a machine that takes your money before you start playing, that made video poker so acceptable to the public.

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But, it was also the fact that having card ranks that truly had different monetary value to the player that made our strategy table far more complicated. In a regular poker game, a pair of 2’s are worth a lot less than a pair of aces. On a video poker machine that pays on two pair or better, they are both completely worthless. If they are what you dealt on the deal, they will have the exact same expected value. Getting three aces is worth no more than three deuces.

With the advent of Jacks or Better, jacks, queens, kings and aces were not worth more than all the other cards. A pair of jacks means the return of your money and a pair of 8’s means you lost. That’s a big difference.

How did this change muck up our strategy? A few weeks ago, I discussed one of the obvious cases. We play a 4-card flush over a low pair, but we play a high pair over the 4-card flush. If all pairs had the same value to the player this would not be the case. We play all pairs over all 4-card straights, with one exception. If the straight has 3 high cards, we play it over the low pair.

Since this cannot be an Inside straight, we are actually talking about only one possible combination — 10-J-Q-K. We have eight ways we can complete the straight, just like all other 4-card straights. But this particular one also has nine ways to hit to a high pair.

To calculate the expected value of this hand we add up all the possible pays. This is 8 x 4 (payout of a Straight) plus 9 x 1 (payout of a high pair) which adds up to 41. We divide this by 47, which is the number of possible draws. This gives us 0.87. The low pair has an expected value 0.82.

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We always play the way that gives us the highest expected value, so the 4-card straight with 3 high cards is the right play. The 4-card straight with 2 high cards (9-10-J-Q) has three less ways to make a high pair. This lowers the expected value to 0.81, which is why we play a low pair over it. The high cards made all the difference.

Before Jacks or Better came along, the number of high cards in a 4-card straight did not matter one bit. You would either play them or not over a pair depending on the paytable. There would be no counting high cards in order to know what to do.