EV: in video poker

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Last week’s discussion on expected value (EV) was the “cliff notes” version of the topic.

I used a very simplistic example of a roulette wheel to show how expected value is calculated. Of course, if it were that simple to always calculate the EV, I’d probably be out of a job!

The more complex the game, the more complex the expected value calculation gets. In a game where there is no decision at all – other than which wager to make – the calculation can involve simple multiplication.

If we move to video poker, the process becomes infinitely more difficult.

The good news is that as a player, you almost never have to actually calculate the expected value itself. You simply need to learn the strategy that was built based on these values.

When there is a decision to be made in a casino game, the calculation of expected value must take a look at every possible outcome from that point forward.

So, if we’re talking about three card poker and we want to know the expected value of a particular player hand, we have to look at every possible dealer hand and figure out how many of those hands would the dealer wind up qualifying and of those that qualify, how many will win/lose against the player.

Once we know this, we can figure out how many units the player will have returned to him and divide this by the possible number of dealer hands (in this case 18,424) and voila – we have the expected value.

In the case of three card poker, the decision is to play or fold. If wanting to play, then we use the method just described to figure out the expected value.

If one decides to fold, then the original wager is lost. In the case of video poker, the decision is not this simple.

The player has to choose which of 32 possible ways to play the hand. This can range from holding the dealt cards to discarding all of them. The process to determine the right strategy must analyze each of these 32 ways.

Fortunately, with a computer program, this is not nearly as daunting as it might sound. The computer will look at every possible draw for each of these 32. It will sum up the pays for each of these draws and divide this total by the number of possible draws.

If you hold four cards, there are 47 possible draws. If you hold only two, there are 16,215. The computer program then compares the expected value of each of these 32 ways and whichever is highest will be the proper strategy for that dealt hand.

The program does this for each of 2,598,960 possible 5-card deals (from a 52-card deck). The process that provides us with video poker strategy is no different than the one that shows why we should play a single-zero roulette wheel over a double-zero.

It is the same process that tells us we should not hit a 14 looking into a dealer’s 6 and to play any three card poker hand Q-6-4 or better. The math may be a bit more complex and the number of possible combinations absolutely staggering, but all a player needs to do is trust the process and use the eventual output – the strategy.

The only real alternative is to play by hunches. While many decisions are plainly obvious – no one is going to throw away a three-of-a-kind to go for a 3-card straight.

There are many decisions that are not nearly as obvious and require a full analysis to determine which is correct. I remember when my father, Lenny Frome, worked out his first strategy for jacks or better.

What a surprise it was to find out that you hold a 4-card flush over a low pair, but hold the low pair over a 4-card straight! In the end, this strategy is as obviously correct as playing that single-zero roulette wheel over the double-zero.

NOTE: (There are about a dozen Winning at Video Poker (featuring Lenny Frome) VHS Tapes left for $7 each, including first class postage and handling. Send check or money order to Compu-Flyers, P.O. Box 132, Bogota, NJ 07603. For more articles and gaming information, check Eliott’s website at www.gambatria.com.)

About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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