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All five cards away there are combin(47,5)= 1533939 possible replacement hands. The total number of hands that must be analyzed to determine the best play of a specific hand is combin(47,5)+5*combin(47,4)+10*combin(47,3)+10*combin(47,2)+5*47+1, which coincidentally also equals 2598960. So if we took no short cuts at all we would have to analyze 25989602= 6,754,593,081,600 hands. Just reducing the initial hands to 191659 we still have 498,114,074,640 hands to analyze. Clearly more short cuts are in order. It would take a desktop computer several hours at least to work through this many hands. Personally I don’t actually score any hand but use carefully chosen formulas to determine the probability of improving a hand. For example with any pair and 3 singletons the probability of improving the hand to a two pair is always the same. Things get more complicated with straights and flushes but still manageable. My program can calculate the expected return for a game of jacks or better in about one minute. Considering it used to take me over a day I’m rather proud of it. I hope this answers your question. You give a standard deviation for a 9/6 Jacks or Better VP is 4.417542. I’m trying to figure out what that means. If I have played 100 hands, does that mean that 2/3 of the time my result would be within 441 Wagers? It seems counter to my experience playing the game. Ray from Maple Glen, Pennsylvania The standard deviation of 100 hands of 9/6 Jacks or Better is 1001/2*4.416 = 44.16. You can then use this information to determine what is the probability of winning or losing more than a specified number of units. For example the winning or losing within two standard deviations, or 88.31 units, is 4.55%. There is more to it than this. Please see my part on the standard deviation in my section on the house edge. Which of these ways to play jacks or better video poker has the greater risk of loss, assuming the payoff schedules are the same (9/6): 1000 plays of a dollar machine ($5 each play) or 1000 plays

In 1,186,106. 9/6 Jacks Royal Combinations Cards Held Combinations Probability 0 1,426,800 0.002891 1 16,805,604 0.034053 2 96,804,180 0.196154 3 195,055,740 0.395240 4 152,741,160 0.309498 5 30,678,780 0.062164 Total 493,512,264 1.000000 I was wondering if I could get your help on computing the probability distribution table for Jacks or Better. I know that 52 choose 5 = combin(52,5) = 2,598,960, yet in every table that I have looked at for video poker, there are 19,933,230,517,200 total combinations. I was wondering why there are so many more than 52 choose 5, and how to compute them. Mic There are combin(52,5)=2,598,960 possible combinations on the deal. The reason my video poker return tables have almost 20 trillion combinations is you also have to consider what could happen on the draw. Here are the number of combinations according to how many cards the player discards. Combinations on theDraw in Video Poker Discards Combinations 0 1 1 47 2 1,081 3 16,215 4 178,365 5 1,533,939 The least common multiple of all those combinations is 5×combin(47,5)= 7,669,695. Regardless of how many cards the player discards, the return combinations should be weighted so that the total comes to 7,669,695. For example, if the player discards 3, there are 16,215 possible combinations on the draw, and each one of them should be weighted by 7,669,695/16,215 = 473. So the total number of combinations in video poker is 2,598,960 × 7,669,695 = 19,933,230,517,200 . For more on how to program video poker returns yourself, please see my page on Methodology for Video Poker analysis. This question was raised and discussed in the forum of my companion site Wizard of Vegas.

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The player and banker draw a card, only 8 cards will remain in the shoe for the last hand. If you are tracking the cards, and know the last 8 cards are all 0-value cards, a table max bet on tie would net you a huge profit. My question is, what are the odds that the last 8, 9, or 10 cards in an 8 deck shoe are all 10 value? Also if you knew exactly what the last 8 cards were, could you use a formula or program to figure the odds that the next hand will be banker, player, or tie? Mike S. from Michigan City To answer your first question, the probability that the last 8 cards in an 8-deck shoe are all 0-valued cards is combin(128,8)/combin(416,8) = 0.0000687746. So, it isn't something to wait around for. I know of no easy formula for what to bet in other situations. If you could find a casino that would allow you to use a computer, the advantages would sometimes be huge towards the end of the shoe, especially on the tie. Why do casinos burn cards in blackjack and baccarat? Matt from Fort Myers, FL A minor reason is to foil card counters. However, instead of burning x cards, the dealer could move the cut card x cards forward, and achieve the same purpose. The major reason is game protection. For one, the player might catch a glimpse of the top card, and alter his bet and strategy,