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Ask the Wizard #86

You have developed an excellent website for information concerning gambling, and I have found it very useful. Thank you for all the work. I have just a couple of quick questions. On your video poker tables you use the figure of 19,933,230,517,200 possible results. How did you determine that this is the number of total possible results? Secondly, I understand how the RNG function works on slot machines. Is there a RNG for video poker, (which means all the results are mapped), or does the program run differently than this?


To answer your first question, there are 2598960 ways to choose 5 cards out of 52 for the initial hand. On the draw there are 1, 47, 1081, 16215, 178365, or 1533939 ways to draw the replacement cards, depending on how many card the player holds. The least common denominator for these numbers is 7669695. The actual combinations are weighted to get a total of 7669695. So the total number of combinations is 2,596,960*7,669,695=19,933,230,517,200. To answer your second question video poker machines simply pick numbers at random from 1 to 52 and assign them to a card. The random number generators themselves are very complicated but the object is simple.

Your site is amazing. Here’s my question. Does match play change basic strategy at all? My non-math-based instincts tell my that surrender becomes a bad idea, that is if you have to surrender your coupon.


Thanks for the compliment. You are right that you shouldn’t surrender if they take the match play away. There are some other strategy changes but I never worked out a list. Generally the casinos don’t allow doubling the match play chip, in which case you should be less inclined to double. ’Basic Blackjack’ by Stanford Wong indicates when to double if doubling the match play is allowed. My advice is to use the match play on the Player bet in baccarat.

If ten people are each dealt two cards from a single deck what is the probability that two players will get a pair of aces?


First, there are 10*9/2=45 ways you can choose 2 players out of 10. The probability of two specific players getting four aces is 1/combin(52,4)=1/270725. So the probability of any two players getting a pair of aces is 45/270725=0.0001662.

How do you calculate the expected return for a blackjack game with a .5% house edge and a 20x play requirement and an initial Bank Roll including bonus of $1000. Does it matter if you flat bet (assuming that the bets are relatively small compared to the BR) or bet based on the Kelly criterion, or does the Kelly criterion just affect the risk of ruin?


Your expected loss of this play is 0.005*20*$1000=$100. The betting system will not affect the expected loss, but will affect the volatility.

It’s my understanding Casino’s put a lot of emphasis on a Player’s theoretical win. I would imagine my theoretical value has a direct correlation to compatibility from a house point of view. If I am a $10.00 average Player in Blackjack and play an average of 3 hours per trip, what is the formula a casino uses to determine my theoretical value? Thank you in advance.


Yes, the casinos do calculate the value of a player’s play and then comp back a certain percentage, roughly about 33% to 40%. According to my theoretical house edge table, the casinos assume a house edge of 0.75% in blackjack. So in your example the value of this play would be 0.0075×$10×60×3=$13.50. If the casino comps back 1/3 of the play then you could expect to get a comp worth $4.50. However, most places don’t like to fuss with such small comps.

In a St. Louis Post-Dispatch article, the reporter says, "A 500-year flood is one that has a 1-in-500 chance of happening in any given year. Stated another way, that would be a 1-in-10 chance of happening over 50 years, or a 1-in-5 chance of happening over a century." After reading through all your gambling pages, I believe this is not a correct way to put it, right? Extrapolating their assertion, it would mean that there is a 1-in-1 chance that a flood will occur every 500 years, and that can't possibly be right.


You are right, that article is incorrect. The probability of a 500-year flood in a period of x years is 1-e-x/500. So the probability of at least one 500-year flood in 50 years is 9.52% and in 100 years is 18.13%.