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Ask the Wizard #198

On the ’Vegas FAQ’ show on the Travel Channel, you recommend the 9-6 Jacks or Better machines. However, the machine that you showed was a short pay 9-6 machine because two pair only paid 1 instead of the normal 2 giving the house an extra 5% advantage. Changing the value of two pair from 1 to 2 is a common trick by the casinos to increase the house edge.


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.

In a race, if the competitors’ race numbers are allocated randomly, and have no effect on race performance, what are the chances that at least one person will finish the race in a position that matches his race number? For example, the winner has number one on his chest or the person who finishes three hundred and fifth happens to sport number 305.

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%.

You have talked about your betting of the underdogs in the NFL. Did you simply bet the home underdog each time or was it more complicated than that? And most importantly, what line determined if it was a home dog...The early line or the line just before the game. Thanks.

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.

Why are the odds of a hard four different from the odds of a hard six? Isn’t there just one way out of thirty-six possible combinations to hit doubles (double 1,2,3...)?

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.

Do you have any opinions about presidential futures? I.e., betting on which candidate will win his/her primary or the general election? Is there any way of calculating the house edge? Would you ever consider making such wagers for real money? Personally, I think that watching the current betting lines may be better than polls to predict election results. Do you think there’s any validity to them?


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.

Republican Primary

Candidate Probability
Giuliani 40.0%
Thompson 8.4%
Romney 28.5%
Paul 6.7%
McCain 7.0%

Democratic Primary

Candidate Probability
Clinton 71.0%
Obama 12.3%
Gore 8.2%
Edwards 4.9%

Party to Win

Candidate Probability
Democrat 63.0%
Republican 35.8%
Other 1.2%

You can use my sports betting appendix 5 to calculate the overall house edge of any type of futures bet. For politics, my hunch is that betting on the favorites is probably the better way to go, in general. For example, I would be happy to buy a contract on Hillary Clinton if I had an account at TradeSports. Just my two cents.

It seems to me 3-4-5x odds are a scam because the player is paid out the same regardless if the point is 4 or 6. If a player bets 2x odds, regardless of the point, at least he is rewarded a higher payout. What is your opinion on this?

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.