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Are video poker/video keno games fair? Speaking for the major U.S.-made machines, YES! In both games the expected cards/balls are the same as in a live game. In fact, it is a law in Nevada that video representations of cards and dice follow the same odds as a real game with a human dealer. There is no reason to cheat when the games are profitable based on a fair game. An exception worth mentioning is the pull-tab machine. These are sometimes found in Indian casinos that do not allow normal video poker. Pull-tabs are similar to a gumball machine in that you put money in and a slip of paper comes out showing how much you won. Sometimes there is a graphic representation of what you win, for example a video poker game. The machine determines how much you are to win and then show you cards that match your predestined win. A game I saw in Tulsa was a five-card stud game but I have heard there are five-card draw pull tabs in Washington State. I'm told in these games, even if you throw away a dealt royal, you will get another one on the draw. Wild "match cards" can be used to ensure you do not snatch defeat from the hands of victory. You said your video poker program can analyze a pay table in 20 seconds. I wrote my own program but it takes months! How did you get yours to run so fast? I'm going to share with you what took me years to learn on my own. Here is my video poker computer methodology. I understand that video poker games are programmed to shuffle a deck and deal the first five cards. My question is how are the draw cards determined? For example, are the draw cards the next five cards in the deck or are ten cards dealt on the deal, with one specific replacement card for each card on the deal? Mathematically it doesn't make any difference and this should not be a question to be concerned about. However, I understand that IGT continuously shuffles the remaining 47 cards and when you press the draw button you get whatever cards are on top of the deck at that moment. In your video poker tables the number of combinations always adds to 19,933,230,517,200 for a 52-card game. Where did you come up with this number? I get combin(52,5)=2,598,960 on the deal and for the draw as follows.
Keep all 5: combin(5,5)*combin(47,0) = 1 This makes sense because for any hand on the deal you can still get any possible hand on the draw. So I get 2,598,9602 = 6,754,593,081,600 for the total possible combinations. You are a factor of 3 higher. Why? Suppose the player gets a junk hand and tosses all five cards. There are combin(47,5)=1,533,939 ways to get the replacement cards. Suppose the next hand the player keeps one card and discards four. There are combin(47,4)=178,365 ways to get the replacement cards. Since both initial hands are equally likely, I weight the replacements hands so that the total final combinations are equal. An exact weighting for discarding four to come up with a total of 1,533,939 would be 8.6. However, I want to keep everything in integers so a greater weighting factor is required. It turns out the least common multiple is LCM(combin(47,0),combin(47,1),combin(47,2),combin(47,3),combin(47,4),combin(47,5)) = LCM(1,47,1081,16215,178365,1533939) = 5*combin(47,5) = 7669695. So I use the following weighting factors to produce a total weighting of 7,669,695 for each draw.
Discard 0: 7,669,695 I hope that explains it. What is the expected return of the following video poker pay table...? I would suggest running it through my Video Poker Calculator.
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Frequently Asked Questions about Video Poker