# Ask the Wizard #48

Chuck from New York

You’re right, the discards are not mixed among all the cards but can not be placed close to the top of the shoe. I don’t know the exact size of this buffer but it is about 10-20 cards I think. As a card counter it would probably be safe to use a true count from just the last hand played and off the top of a shoe. When converting to the true count you will rarely get anything far from +/-1. If you’re any kind of counter at all I would forget about playing against a CSM, it isn’t worth the bother.

Chuck from New York

Yes, same as a regular shoe with the same number of decks. Most CSMs use five decks, for which you should use my 4-8 deck strategies.

Amyn from Brantford, Canda

Your method is a good approximation. However by that logic, when flipping a coin, the probability of at least one person in 3 flipping a heads would be 3*50%=150%. Assuming independent events the probability of at least one success out of n trials, where the probability of each success is p, is 1-(1-p)^{n}. In the case of the coin flipping example this would be 1-.5^{3}=0.875. In the case of four players of Caribbean Stud Poker the probability of at least one royal flush would be 1-(1-4/2598960)^{4} = 0.00000615629. However since all the cards are dealt out of the same deck the events are not independent. The math gets very complicated to determine the exact right answer and the approximation should be very close to the right answer.

Joe from San Diego

Yes, you should keep splitting as long as you keep getting tens. Playing one hand and losing does not disprove anything. Millions of hands must be played both ways and the results tabulated to truly know the best play.

Rodrigo from Costa Rica

I attempt to work this out in my blackjack appendix 8 but I’ll work through it more slowly here. We’ll ignore dealer blackjacks to keep things simple and assume the player always hits after two cards. The number of ways to arrange 3 cards in a 6-deck shoe is combin(312,3)=5,013,320. There are 24 sevens in the shoe. The number of ways to arrange 3 sevens out of 24 is combin(24,3)=2024. The probability is the number of winning combinations divided by total combinations, or 2024/5013320=0.0004, or about 1 in 2477.

Gil from Saint Petersburg

You’re right, the mathematical answer is that it doesn’t matter. I would choose the machine either randomly or based on environmental factors. My highest priority is that if there were any smokers in the vicinity I would sit as far from them as possible. Otherwise I would distance myself from any loud noises, including other players. If the machines were crowded I would pick an aisle machine, giving me a little more elbow room and one less neighbor.

Jeffrey from Loveland

You are forgetting that there are two possible orders, either the ace or the ten can be first. Multiply by 2 and you’ll have your answer.

John from Crestwood, Illinois

In the long run it doesn’t matter what you do. As I have said numerous times measured by long term results all betting systems are equally worthless. Systems in which you chase loses with bigger bets increase the probability of a modest short term win but at the cost of even bigger losses when your luck is at it’s worst.