Ask The Wizard #110

Do there exist any famous unsolved problems facing gaming mathematicians? Like a Fermat's Last Theorem in the gambling world. If so, would you please share an example.


Good question. I can't think of any.

What is the basic strategy for "charity blackjack" where the dealer wins on ties?


Here it is. I assumed the dealer stands on soft 17 and double after a split is allowed. I assumed an infinite number of decks for the sake of simplicity. Any differences between this strategy and 8 or fewer decks would be very borderline. The house edge assuming infinite decks is 9.36%.

How can one get started in a career as a gaming mathematician?


The vast majority of gaming mathematicians are employed by manufacturers of slot machines. To break into this field all I can suggest is to let the resumes fly. It would also help to attend the Global Gaming Expo to learn more about the business. If you wish to follow in my footsteps in self-employment it will take a few years at least to build up enough business to make a living at it. Again, it would help to attend the gaming shows to drum up some business.

First off, great site you have here; it’s a great gaming resource. In (omitted) , I ran across an interesting game, and unless I misread the rules/paytable, I think it returns over 100%, although it is very volatile. The game is called "Shockwave Poker". For the majority of hands, the game has a negative expectation:

Royal Flush 800
Straight Flush 100
Four of a Kind 50
Full House 10
Flush 7
Straight 5
Three of a Kind 3
Two Pair 1
Jacks or Better 1

But if you hit a four-of-a-kind, the game goes into "Shockwave Mode" and for the next 10 hands or until you hit another four-of-a-kind (whichever comes first) the machine will pay a Four of a Kind 800 units; the same as a Royal Flush!


Thanks for the compliment. Ordinarily the return would be 97.107% in normal mode and 287.6532% in Shockwave mode, using Cindy Liu's Video Poker Calculator (no longer online). Ignoring the rule about one four of a kind per Shockwave Mode the expected value of Shockwave Mode is 10*(2.876532-1) = 18.76532. Adding this to the value of a four of a kind in the regular game we get an expected return of 101.43%.

Does the RNG in a keno machine pick the numbers and if they come up you win or just determines if you win or lose and the numbers are just for show?


In Nevada, and I think other major gambling markets in the United States, the balls truly are random and the outcome determined by the balls. However in class II slots, sometimes found in Indian casinos, anything goes.

I am a casino dealer in a non-tribal facility in the lovely state of Washington. I saw the comments (April 4, 2004 column) that people posted on tip sharing and I couldn't resist adding a few words of my own. I work in a "keep your own" house and I wouldn't have it any other way. I am not a beautiful Asian female. I am white male, I have Friday nights off, I do not always get the good tables, and I consistently average over $900/week in tips. The casino that trained me to deal cards was tribal and tokes were shared. I worked there for just over 3 months and finally I got fed up with having to share my hard-earned tokes with the chump on the next table with no personality. I say, let me keep my own. I will be rewarded for my own work. It also helps to keep me sharp. I can't afford to have a bad day at work. I have to put a smile on my face and at least try to have a good time and be professional and courteous. This is obviously a benefit to me, the casino, and the players. I don't care if a "pooled" house has a toke rate of $50/hour. I will never share tips again. My advice to other white males (or any other economically repressed dealers for that matter) is to go to work every day and concentrate on being the best dealer that you can be. Do not worry about how much money is or isn't going into your toke box. You will get stiffed sometimes, it doesn't matter. Try to provide the best service you can, when you go to cash out at the end of your shift, there will be money there.


Thanks for your comments. I had a feeling the other dealer was overstating the race/gender effect on tipping.