Ask the Wizard #43

Thanks for the compliment. The Spanish 21 rules are the same across Atlantic City. I only know of two that have the game, the Tropicana and the Claridge, but there could be others by now. If I'm not mistaken, the best craps game is at the Sands, which offers 5X odds. When I say to take the maximum odds I mean bet the maximum allowed on the odds. For example, $50 after a $10 line bet. Keep in mind that you won't win more money by taking the odds, you just get to bet more without losing more in the long run.

Atlantic Interbet has full pay deuces wild (return of 100.77%). I think their highest coinage is 50 cents in that game.

According to Extra Stuff by Peter Griffin the cost due to player mistakes of the average player is 1.41%. This is above whatever the house edge is assuming proper basic strategy. It also varies by place, Atlantic City players are better than Las Vegas players, for example. Your other question about bad strategies was such a good one I added information to my blackjack section about it. See my remarks on bad strategies.

No, that information won’t help you at all. Your odds are always the same on every spin, regardless of the counters.

Yes, I've seen that bet in Tunica. I address it in my blackjack appendix 8. I agree that side bet would seem very countable.

Thanks for the kind words. Yes, the probability of a three of a kind depends on the pay table, which affects player strategy. My video poker program always makes the optimal play for every hand by looping through all the possible cards on the draw. However, creating a strategy in writing is very time consuming.

Thanks for the compliment. That is a good question. Not having enough money to double or split, but otherwise playing correctly, adds 1.9% to whatever the house edge is.

I don't like using probabilities in that form but they are generally used in this kind of syntax, "The odds against drawing a royal flush are 649,739 to 1." That means there are 649,739 ways you can't draw a royal flush and 1 way you can. In your examples 12 to 1 is a probability of 1/13, or 7.69%, and 3 to 2 is 2/5, or 40.00%, so the 3 to 2 is the better chance of winning.

The probability of getting exactly x right in your example is combin(100,x)*(1/5)^x*(4/5)^(100-x). To get the exact answer you have to calculate this for all values of x from 0 to 24, add them up, and take the difference from 1. The answer is 13.14%.

Well, anyone can make a mistake, but craps is an easy game to analyze mathematically so I would be very confident my odds on craps are right. Yes, gambling in one way or another is my full time self-employed profession. I have been to Atlantic City many times in the last few years but two months ago I moved to Las Vegas. So, I'm afraid I wouldn't be gracing Atlantic City with my presence much any longer. I prefer a combinatorial approach as opposed to random simulations whenever I can. Either way, I roll my own software with Visual C++. For random numbers I use a Mersenne Twister.

You correctly calculated the number of player combinations as combin(52,5)=2,598,960. From there, the dealer can have combin(47,5)=1,533,939 possible hands. Then any one of five dealer cards can be face up. So 2,598,960*1,533,959*5=19,933,230,517,200.