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Ask the Wizard #198
I knew somebody would eventually write about that. It wasn’t I who showed that machine. The producers didn’t understand I was referring to 9/6 Jacks or Better. Later in the editing room they showed somebody pointing to a 9/6 Double Double Bonus Poker game, which has a return of 98.98%. That is much worse than 9/6 Jacks or Better, at 99.54%. An embarrassing moment for me, much like the many incorrect edits I had no control over, in my old Casino Player articles.
Stewart from Glasgow
Assuming that no numbers are skipped, the probability depends very little on the number of participants, as long as that number is fairly large. The greater the number of participants, the more the probability of at least one match will approach 1-(1/e) = 63.21%.
Steve from Milwaukee
I don’t just blindly bet underdogs, even if I have to lay -105 only, which is the case this season at the Plaza in downtown Las Vegas. If I detect only a small advantage on a sports bet, I won’t bet it. In sports I always assume a certain margin of error, because ultimately people play the game, not statistics. However, if I can find a better than the market line, or the side comes with the recommendation of a trusted handicapper, then I would be happy to make the bet.
James from Santa Cruz
Yes, the probability of each double is 1/36. However you have to compare that to the probability of rolling a losing combination. For a hard four, there are 8 losing rolls (two each of 1-6, 2-5, 3-4, and 1-3), so the probability of winning is 1/9. For a hard six, there are ten losing rolls (two each of 1-6, 2-5, 3-4, 1-5 and 2-4), so the probability of winning is 1/11. The hard six pays more because the probability of winning is less.
Yes, I do indeed bet on elections. In 1996 I made my biggest bet to date on Clinton over Dole at even money. That was also one of the best bets I ever made. I have been betting every election ever since, most of the time against friends. At major online sites that take political bets, I think it is a close to efficient market. In other words, I think the market is basically right, and the odds can be used to estimate the probability of each candidate winning. Currently I think that TradeSports is a good source for election odds. As I write this, on September 29, 2007, the odds given equate to the following probabilities of victory.
Party to Win
Allan from San Diego, CA
With 3-45-x odds, you don’t have to bet as much on a point of four as a six, yet the reward is the same. With all gambling, you shouldn’t just look at the reward, you also have to look at how much you are risking.