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Play the strategy based on the math of the game

Jerry “Stickman” Stich

A vast majority of video poker players do not follow a playing strategy based on the math of the game. They use hunches. They use wishful thinking by saving any card or cards that could produce a royal flush or other high-paying hand. Others save cards based on the flow of the game. For example, if several flushes or straights have appeared recently, they will save for the flush or straight. Some will save based on what they feel the odds are of completing paying hands without really knowing what those odds are.

Any of these methods can produce good results for a time, but all are ultimately doomed to cost the player more than playing a strategy based on the math of the game.

Unfortunately, the math of the game does not always follow logic. Let’s look at how the proper playing strategy is developed.

Developing video poker strategy requires a lot of calculations and comparisons. There are 2,598,960 possible starting hands in a 52-card video poker game where the order of the cards doesn’t matter. For each of these hands, the return on each possible save must be calculated and then compared to all other possible saves to determine which save has the highest average return.

Let’s look at a very basic example of how this works in a standard 52-card deck game (no wild cards). In this example we will use the following initial hand: 3♣ 4♣ 5♦ 6♦ 9♥. There are many possible holds for this hand but we will look in detail at just one: saving everything but the 9♥. By discarding the one card, there are 47 possible cards to complete the hand—the number of cards left in the deck after dealing the first five. Of the 47 cards, eight of them will make a paying hand and the remaining 39 will make a non-paying hand. The eight cards that make paying hands (straights are only paying hands) are the four 7’s and the four 2’s. In a full-pay Jacks or Better game a straight pays 4-for-1. The total return for all 47 possible hands is 4 (the pay) times 8 (the number of winning hands), so the expected return for any one hand is 4 X 8 / 47 = 0.68.

This same process is repeated for all remaining possible discards and the results are compared. For this particular hand, discarding the 9 has the highest expected return even though it is an overall loser.

Because playing strategy is based on expected return, sometimes holds that might seem logical do not have the highest expected return and therefore aren’t the proper play. For example, in a full-pay Jacks or Better game when dealt a hand that includes a suited ace/10, the proper play may be to discard the 10 and any chance of a royal flush, depending on the other cards in the hand. This is because the chances of completing the royal are so remote that the expected return for saving the ace/10 can be less than other expected returns. There are even situations where three of a royal flush might be broken up in favor of higher expected returns.

Video poker playing strategy is all about the math and the math means the highest expected return from each dealt hand. The only way for a video poker player to get the most from their play is to follow a playing strategy based on expected return. As you can see from the example above, the amount of work required to develop a strategy manually is overwhelming. Fortunately there are several video poker strategy software programs and smartphone apps that make determining proper strategy a breeze. And, considering that playing hunches typically costs the player three to five percent, the cost of the programs is extremely reasonable.

If you are serious about video poker play or even if you are just a casual player who plays several hours a year, getting a strategy program and practicing the strategy will pay for itself in just a few hours’ play. Don’t let the casinos take more from you than necessary. You deserve every penny you can get.


How Would You Play This Hand?

Let’s look at a couple of hands where the proper save might not seem obvious, but the math says it is the way to go. The following hands are played on a full-pay Jacks or Better game with the max credits of five played. The first hand is A♣ K♥ Q♣ T♣ 4♣.

This hand contains three of a royal flush (A♣ Q♣ T♣), four of a flush (A♣ Q♣ T♣ 4♣) and four of an inside straight with three high cards (A♣ K♥ Q♣ T♣).

You might think that saving the three of a royal is the way to go. Let’s see!

Keeping four of a straight returns 2.66 credits on average. It is not surprising that this return is fairly low as straights do not pay that well.

Keeping the three cards of a royal returns 6.35, significantly more than saving the straight and a fairly nice return at that.

But, saving the four cards of a flush returns 6.38 credits, which is better than saving three of the royal. The difference may not be much, but every little bit helps.

Let’s look at another hand that may not be intuitive: A♣ 3♠ T♣ 7♥ 4♣.

Here you have two of a royal (A♣ T♣), three of a flush (A♣ T♣ 4♣) and a high card (A♣). Do you think holding for the royal is the way to go? Holding the ace/10 returns 2.22 credits.

What about saving three of a flush? That returns 2.23, better than the two of a royal by a hair.

Saving the lone ace, however, is the best way to go, returning 2.30 credits.

Is that the way you would have played them? If you did not pick the highest returns, you need to work on your math-based strategy. It will pay in the long run.

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