how do they know

Good morning fellow gamblers......I play video poker and I get the whole full pay vs bad pay table games. I also know that job pays back 99.64 I guess with perfect play and dueces pay back 100.74 with expert play and so on. My question is how do people know that payback is so and so on this game or that game? I am not talking about figuring it out by looking at the pay table as in what full house and flushes pay. How do they know that a dueces wild game with a full pay table pays back exactly 100.74%.....do they get this from the game makers or did someone math it out.....

They mathed it out.

You look at all possible deals and all possible draws to those deal. You add up the resulting paybacks and divide by the total number of hands.

I should probably be a little more specific. There are almost 2.6 million possible dealt hands (52C5). For each hand there are 32 possible holds (5C5+5C4+5C3+5C2+5C1+5C0). You look at each of the 32 hands and analyze all possible draws. This analysis adds up the wins from the various draws and divides by the total number of draws. The result is the average return for that hold.

The hold where the average return of all the draws is the highest becomes the optimal play for that hand. Once you compute the optimal play for all 2.6 million hands you add up all the results and divide by 2.6 million. This becomes the optimal return for the game.

In reality the computer programs that compute this have short cuts. Many of the hands are essentially identical. For example, a pair of 5s is no different than a pair of 6s for most games. This makes it a little easier to compute.

They return 99.54% and 100.76%.

Long story short, it's because someone did the math to figure it out. Remember, the return is based on the strategy used, and the return can only decrease based on strategy changes/mistakes -- you cannot have the game have a higher return than optimal strategy.

Thank you gentlemen for answering my question

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Originally Posted by lucky

Thank you gentlemen for answering my question

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Lucky, the paybacks for the games You mentioned were first published by Lenny Frome back in the late eighties. I think he used a program called masque to determine the paybacks. In the early nineties Dan Paymar used a program called panamint to confirm the paybacks. I like Paymar's video poker equation:

Probability times Payoff

The strategy used dictates the payback percentage. Unless you are Rob Singer. Then the wrong strategy generates a better payofff.