Ask The Wizard #99

Wheel of Madness is another one of those silly blackjack side bets. It is not included in your ever growing list of exotics. Is it proprietary information that keeps you from its analysis?


The wheel in Wheel of Madness is weighted. In other words it is designed to stop on the lower prizes more often. Without knowing the exact weights I can’t analyze it. I have tried to get the weights from casinos and the manufacturer but alas have had no luck.

My wife knows blackjack basic strategy but insists on being a ’hunch’ player. What are the hands that are closest to 50-50 so that my wife can limit her hunch plays to those?


I’m pretty sure this has already been answered but it is a good question so I’ll take it again. Here are some borderline plays, as evidenced by having a card counting index equal to zero. This list is for multiple decks where the dealer stands on soft 17 and double after a split is allowed. The best play is listed first and an alternative second.

  • 9 against 2 (hit/double)
  • 12 against 4 (stand/hit)
  • 12 against 6 (stand/hit)
  • 16 against 10 (hit/stand)
  • Soft 13 against 5 (double/hit)
  • Soft 15 against 4 (double/hit)
  • 3,3 against 2 (split/hit)

I see that the return on a full pay deuces wild video poker machine is 100.76% with the strategy you have on your website. Obviously, this is with infinite play. My question is how many hands would you have to play to get that return with, let’s say 90% certainty?

p.s. Where can I find full pay full pay deuces wild in Vegas?


There is no number that will give you a 90% probability of attaining or exceeding that percentage. Although the more you play the closer your return will get to 100.76% about half the time it will be above and half the time it will be below. Perhaps a better question is how many hands would I have to play to have a 90% probability of getting to 100.66%?

The standard deviation of full pay deuces wild is 5.08. The standard deviation of the sample mean is 5.08/sqr(n), where n is the number of hands. I’ll skip over the rest of the math to the answer, which is 42,383,720 hands. That is a lot! Suppose your goal is to simply come out ahead with a 90% probability. Then you would only need 733,790 hands. This is still a lot, which just goes to show how volatile your bankroll will be in the short run. The general formula in Excel of your sample return being at least x is with a probability of p is (normsinv(1-p)*5.08/(1.0076-x))^2. In the case of my first example you would put the following in any cell:


This formula can be used for any game by substituting the correct standard deviation per hand.

I think all the Stations and Fiesta casinos have full pay deuces wild in the quarter coinage only. Green Valley Ranch too. When I moved to Vegas three years ago it was much easier to find.

Dear Wizard,

Great site! I’m a devoted fan who only bets on games with a small house edge.

I was surprised to find on the Nevada Gaming Control Board’s website, that the statewide casino win percentage for baccarat in 2003 was 19.62% and for mini baccarat, the casinos kept 13.81%. Why such a difference if the two games have the same house edge? By comparison, nickel slots (considered to have a lousy house edge) kept only 7.89% statewide! Why would slot machines (with a high house edge) keep less money than table games (with a low house edge)?


Thanks for the kind words. You are far from the only person to be confused about this. The reason is you are comparing the house advantage to the hold. The house advantage is the percentage you will lose on average of each dollar bet. The hold is the ratio of money the casino wins to chips purchased. This is going to be much higher than the house edge because in table games players circulate through the same chips for a while. So that baccarat figure is saying that of all the money dropped in the box in baccarat the casino won 19.62% and gave the players back the other 80.38%. Meanwhile the nickel slot figure is saying that of the total amount bet the casino kept 7.89% and gave players back 92.11%. To make a long answer short you are comparing apples and oranges.

Good Day. May I say that I have thoroughly enjoyed looking through your web site. Can the house advantage on any particular game be affected by the Limit/Maximum being too high (i.e. over $5000 on the pair plus), especially with three card poker? Best regards.

John from London, England

Thank you. No, the house edge is not affected by the table minimum and maximum. The greater the spread between minimum and maximum bet the greater the volatility but in the long run results will keep getting closer to the house edge. Some people incorrectly believe that setting a maximum bet increases the house edge, but it does not.

Hi, I read almost everything on your site and all I can say is WOW and THANKS so much for all the help you bring to everyone. I have however a question which I think is interesting and should be added in your FAQ section. You say there is no betting system that can beat a game of luck. I am 100% on your side with that as I have tried dozens of them and with no results. You just can’t beat the casino in the long run. HOWEVER, how come there are professional players? I mean, there are some people that are called ’Professional blackjack players’ who make their living by gambling. Everyone sees them on television in tournaments and things like that where they bet thousands and thousands. How come they make a living out of it if there is no possible way to win in the long run, it’s their job, so it’s necessarily in the long that they are winning. How come?


You’re welcome. It must have taken all day to read my entire site. You are confusing betting systems, which are worthless, to legitimate strategies that give the player an advantage. Two games that can be proven beatable with good rules and proper strategy are blackjack and video poker. So I call a system a worthless method of following trends in games with a house advantage, and a strategy something like card counting in blackjack that is mathematically proven to work. Video poker can be beaten by hunting down the best pay tables and then following a reliable strategy on which cards to keep and which to discard.

Is it permissible table etiquette to double down with your money (and the risks and rewards are yours) for a fellow player who refuses to double because of lack of money, fear or ignorance? [Actually I did do that for/with a woman who could not double an obvious double hand (I believe 10 against dealer 4) because she did not have enough chips. The dealer was encouraging her to "double for less" although the dealer permitted me to make this player the short term "loan". And I won, ha-ha! If so, could you conceivable turn the house’s edge in your favor?


As long as both players are agreeable then the casino is unlikely to stop you. In some situations it may not be practial because the player may want to take more than 3 cards. However with 10 against 4 the player should never take a fourth card, thus it was a good idea. Although a bit impractical you could always offer to buy the player’s hand and then you play it yourself, if you can agree on a price. My blackjack appendix 9 shows the fair value of all hands. As an example suppose another player had blackjack and the dealer had an ace up. Most players would take even money. You could make money by offering that player more than even money, but less than 103.8%, and then playing out the hand yourself. However don’t extend this offer to a card counter.

Are there any published card-counting strategies for Spanish 21? If not, do you think the rules of Spanish 21 make it conducive to counting?


There was discussion about this at under the Green Chip section about a couple years ago. As I recall the consensus was that counting was not as advantageous as in blackjack but you could get away with a lot more. I know of no published material on this.

Is there an optimal strategy for the amount of the Pair Plus bet in relationship to the Ante? (i.e. should the Pair Plus bet be 2x, 5x or some other increment of the ante to maximize potential return?)


Bet 100% on the Ante, because the ante has the lower element of risk.

Boxers or briefs?