Ask the Wizard #99

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)

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:

=(NORMSINV(1-0.9)*5.08/(1.0076-1.0066))^2

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.

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.

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.

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.

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.

There was discussion about this at www.bj21.com 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.

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

Briefs.