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Ask the Wizard #227
Myooligan from Greenfelt
There is no definitive point at which confidence is earned. It is a matter of degree. First, I would ask what is being tested for, and what the shooter estimates will happen. With any test there are two possible errors. A skilled shooter might fail, because of bad luck, or a random shooter might pass because of good luck. Of the two, I would prefer to avoid a false positive. I think a reasonable test would set the probability of a false negative at about 5%, and a false positive at about 1%.
For example, suppose the claimant says he can average one total of seven every seven throws of the dice. A random shooter would throw one seven every six throws, on average. By trial and error I find that a test meeting both these criteria would be to throw the dice 3,600 times, and require 547 or fewer sevens to pass, or one seven per 6.58 rolls.
A one in seven shooter should average 514.3 sevens, with a standard deviation of 21.00. Using the Gaussian approximation, the probability of such a skilled shooter throwing 548 or more sevens (a false negative) is 5.7%. A random shooter should average 600 sevens, with a standard deviation of 22.36. The probability of a random shooter passing the test (a false positive) is 0.94%. The graph below shows the possibe results for skilled and random shooters. If the results are to the left of the green line, then I would consider the shooter to have passed the test, and I would bet on him.
The practical dilemma is if we assume two throws per minute, it would take 30 hours to conduct the test. Perhaps I could be more liberal about the significance level, to cut down the time requirement, but the results would not be as convincing. I do think the time has come for a bigger test than the 500-roll Wong experiment.
Julie Jacques from Morristown, TN
I have not studied the effect of card counting of that bet for myself. However, Arnold Snyder has, and his results can be found in his Big Book of Blackjack. There he says you should make the bet in a six-deck game if it is the last two decks, and the count is +10 or greater, using the Red Sevens count. In a double-deck game he says to bet in the last deck, and a count of +6 or greater.
Sam from Las Vegas
Answers to questions like that can be found using my house-edge calculator by changing a rule and noting the effect on the house edge. Normally I would make you do it, but I’m in a patient mood today, so here you go:
6 decks, dealer stands on soft 17: 0.0726%
8 decks, dealer stands on soft 17: 0.0758%
6 decks, dealer hits on soft 17: 0.0882%
8 decks, dealer hits on soft 17: 0.0916%
J.J. from Oceanside, CA
The house edge on the Player bet is 1.2351%, assuming eight decks. The expected number of hands it takes to have a loss of ten units is 10/0.012351 = 809.66.
Don from Lihue, HI
Ultimately, the cards speak. You should have won that hand.