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Ask the Wizard #141
Brendan from Winston Salem, North Carolina
Good question. I have run across numerous system believers and the one thing they all seem to have is a lot of conceit. Despite the fact that they never seem to have gone much past algebra, if they made it that far, they all think they know better than greatest names in mathematics. This inability to consider contradicting evidence or other points of view is certainly not confined to betting system chasers. The more ridiculous a belief is the more tenaciously it tends to be held, and there is no shortage of ridiculous things for weak-minded people to believe in.
Jonah from Davis, California
The probability of pocket aces is combin(4,2)/combin(52,2) = 6/1326 = 1 in 221. Over 10,000 hands you could expect to get pocket aces 10,000/221 = 45.25 times. The standard deviation over 10,000 hands would be (10,000*(1/221)*(1-(1/221)))1/2 = 6.71149. 67 pocket aces would be (67-45.25)/6.71149=3.24 standard deviations above expectations. The probability of results this skewed or more is 0.06%, or 1 in 1673.
Stan from Coconut Creek
The reason has nothing to do with team loyalty. My program rated them the fifth best team at the close of the 2004 season, and that I carry that power rating over into the 2005 season. However maybe it is too slow too react to recent history. Something for me to think about.
Andy from Hollywood
I get a lot of questions about combinations of craps bets. Normally I don’t answer them but when you address me as "the great and powerful Wizard" it greatly improves your odds of getting a reply. Your mistake is that both bets are not resolved all of the time. When you win either the 6 or 8 you are taking the other bet down, which brings down the expected loss because you are betting less. So your math is right but you are comparing apples to oranges.
Roger from Atlantic City
It just so happens that I have four computers cranking away on that game right now. The number of combinations in that game is so huge the game requires about 56 days of computer time to cycle through them all. I should have the analysis completed about October 20.
Spence from Red Deer, Alberta
The chances of any number occurring exactly 5 times in 10 spins in a double-zero roulette game could be closely approximated by 38*combin(10,5)*(1/38)5*(37/38)5 = 1 in 359275.
Gary from Milwaukee, Wisconsin
You’re right. A come bet would have been just as good and require no waiting. I should have added that.
Lauren from Fort Worth
I don’t think so. I set the lines at yes +240, no -300.
Josh from Stamford
The 96.7% applies to total money bet and transaction fees generally only apply to deposits and/or withdrawals. Players generally circulate through the same money and thus bet much more than they deposit. As I discussed in the September 18, 2005, column a player could bet through about 1.5 million dollars with a $10,000 bankroll and betting $5 at a time in blackjack. In this case the casino would make their profit based on 1.5 million in bets but pay expenses based only on $10,000.