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Ask the Wizard #36
Greg from Brighton, Massachusetts
Most online casinos shuffle after every hand. However, the six-deck game at Unified Gaming casinos shuffles at a random point in the deck. I have heard of other casinos that also penetrate more than one hand into a shoe, but I don't recall which ones. If the cards are shuffled after every hand there is no use in card counting, other than applying my composition dependent basic strategy exceptions.
Hugo from Santiago, Chile
I don't think so, I have never seen any.
Peter from Vancouver, Canada
The casinos would still win. Most players would indeed walk away with their one unit but some would lose their entire stake, whatever it may be. If you consider only even money games with a probability of winning of p then the probability of winning 1 unit before losing x units is (((1-p)/p)x- 1) / (((1-p)/p)x+1 - 1). In the case of double-zero roulette, with a bankroll of ten units, the probability of winning one unit is 85.4268%. For every one of these players the casino will profit 10*(1-0.854268)- 0.854268 = 0.603056 units.
Also, changing casinos after a one-win doesn't make any difference in the odds compared to staying at the same casino and table.
Michael from Philadelphia, USA
Spanish 21! Under Atlantic City rules blackjack has a house edge of 0.43% and Spanish 21 of .40%.
Since this question was submitted, a player held the dice for 154 rolls on May 23, 2009 in Atlantic City. The probability of this is 1 in 5,590,264,072. For the probability for any number of throws from 1 to 200, please see my craps survival tables. For how to solve the problem yourself, see my MathProblems.info site, problem 204.
Jon from Danville, New Hampshire
No combination of bets can give the player an advantage. In your example you would lose one unit for every 12 on the come out roll. You don't make up for it laying the odds. While you usually win laying the odds, you have to risk more. In the end, laying the odds has zero house edge.
The probability of rolling x ones out of y dice is combin(y,x)*(1/6)x*(5/6)y-x. See my section on probabilities in poker for an explanation of the combin(x,y) function. For example the probability of rolling 4 ones is combin(6,4)*(1/6)4*(5/6)2 = 0.803755%.
Number of Ones in Six Dice
Larry from Redwing, Minnesota
I don't like that expression either. At best it is a memory device to help people remember to hit a stiff hand if the dealer has a 7 to 10 showing. There is no simple rule of thumb that works in all situations.
Travis from Los Angeles, USA
Cryptologic casinos have one-cent minimums on their slots. Real Time Gaming casinos have a five-cent minimum. Most other places are 25 cents.
Dave from Los Angeles, California
If you win only even money on a blackjack, then that increases the house edge by 2.3%. I recommend the double or nothing feature because it is a zero house edge bet. However, only double up on amounts you're comfortable with losing.