Guaranteed Play Video Poker Appendix 1 — 9/6 Double Double Bonus Expected Value Table

Last update: Sept. 5, 2007

The following table shows the expected return for any given state in Guaranteed Play Video Poker. By recursively moving backwards the player can enter the expected values into Video Poker strategy software, such as "Video Poker for Winners", "Frugal Video Poker", or "Video Poker Strategy Master."

This particular table is for 9/6 Double Double Bonus, in which the player buys 100 hands. The first hand the player plays is numbered 1, and the last (assuming he doesn't quit) is 100. The bankroll column is the number of units in the player's bankroll at the start of the hand, before paying for it. The expected value column is just that, what the state of the game is worth at that moment.

If the player's bankroll is ever more than the number of hands remaining, then he should quit. These rows are omitted from the table. Some rows in the table are impossible to achieve, so please don't write in about that, I know.

You can see in the last row the hand number is 1, the bankroll is 0, and the expected value is 17.24752. The player must pay 20 units for these 100 hands, so the expected return of the game is 17.24752/20 = 86.2376%.

To generate a strategy for the first hand, note the expected value for all possible outcomes of the first hand. For example, if the player loses, then he will be at hand 2 with a bankroll of -1. The value of this state is 16.868927. If the player gets a royal flush the value of his state will be 799 (deducting one unit for the cost of the bet). The player should subtract the expected value of a loss from the expected value of each win, then multiply by a large number, such as 1000, round to the nearest integer, and put these values into the desired video poker strategy engine. This is what the last column of the following table shows. The reason for the subtracting is that the video poker software does not allow for a win on what is normally a losing hand. The reason for the multiplying by a large number is because the software does not allow decimal values for wins.

The next table shows the strategy table generated by Video Poker for Winners.

Finally, here is the exhaustive Expected Value table for hand #1 of 100-hand, 9/6 Double Double Bonus. If the expected value equals the hand number, then the player should collect his balance and quit.