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? √ Gary

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.

The regular baseball season is 162 games. If a team wins 92 games, it will probably make the playoffs. If the team has a 55% chance of winning each game, what are the odds that it will win exactly 92 games? What are the odds that it will win at least 92 games? - kemprolemslev from Los Angeles

The probability of winning exactly 92 games and losing 70 is 162!/(92!×70!)×0.55⁹²×0.45⁷⁰ = 0.056868. To get the exact probability of winning at least 92 you would need to sum this formula for all wins from 92 to 162. The answer for at least 92 wins is 0.353239. December 26, 2006

How many possible combinations are there for the NCAA March Madness tournament. In other words had I wanted to cover every possible outcome for the 64 team tournament, how many differenct combinations would I have to cover. I have seen one answer that says it is 2 to the power of 64 which is 18.4 quintrillion. This number seems too large to me. I am a math major but don't have my old probability book handy to figure out the combinations/permutations, so I thought I would ask the wizard. Thanks - Kevin from Golden, CO

There are 63 total games (32+16+8+4+2+1). Each game has two possible outcomes. So the total number of ways the tournament could play out is 2⁶³ = 9,223,372,036,854,780,000. April 19, 2006

For in-running betting, if a tennis player has a chance "p" of winning a game, what chance does he have of winning a set? - Mike from Perth

As I understand the rules of tennis the winner of a set is the first to win six games, and by a margin of at least two games, except a 6-6 tie will result in a single tie-breaker game. The following table shows the probability of winning a set, given the probability of winning a game.

Probabilities in Tennis
Probability Game Win	Probability Set Win
0.05	0.000003
0.1	0.000189
0.15	0.001899
0.2	0.009117
0.25	0.028853
0.3	0.06958
0.35	0.138203
0.4	0.23687
0.45	0.361085
0.5	0.5
0.55	0.638915
0.6	0.76313
0.65	0.861797
0.7	0.93042
0.75	0.971147
0.8	0.990883
0.85	0.998101
0.9	0.999811
0.95	0.999997

The formula for any probability of winning a game p, and losing q, is 1*p⁶ + 6*p⁶*q + 21*p⁶*q² + 56*p⁶*q³ + 126*p⁶*q⁴ + 252*p⁷*q⁵ + 504*p⁷*q⁶. March 27, 2006

In the NBA, there are 3 divisions per conference, and 8 teams per conference make the playoffs. The top 3 seeds in each conference are the respective division winners, and the #4 through #8 seeds are the non-division winners with the best records. This year, 2 teams from the same division in the Western Conference, the Spurs and Mavericks, have the top record in the West. If this keeps up, it means that the 2nd best team in the Western Conference will end up with the #4 seed and will have to face the best team in the 2nd round if they both win. Many people are pointing to this as a problem with the system, while the NBA considers it an anomaly. In an effort to explain that its not an anomaly because it could happen frequently, an analyst from ESPN recently made the following statement in a blog: "There are 15 teams in each conference, and five teams in each of the three divisions. That means that there's a 4-in-14 chance that the team with the second-best record will be from the same division as the team with the best record." Is he correct that there is a 4/14 chance of it happening in a particular conference? How would you figure this out? If he is correct, than it would happen in at least 1 of the conferences 57% of the time, right? - AJ from Huntington Woods, MI

Yes, he is right. There are combin(15,2)=105 ways to choose the two best teams out of 15. There are 3*combin(5,3)=30 ways to choose them from the save division. So the probability the two best teams are from the same division is 30/105 = 4/14. The probability of this happening in at least one conference is 1-(10/14)² = 48.98%. March 20, 2006

Hello. I found your site very informative. Will you be providing any analysis on other sports like hockey betting and more on baseball in the future (such as o/u, selecting the best puck-line, etc)? Thanks, Clarence

I do plan to add more on sports betting in the future. That is where I'm personally focusing most of my gambling energy. I haven't found a good angle to exploit yet in baseball or hockey, but hopefully I'll think of something. April 17, 2003

Hi! I am very much interested in mathematics but I do not have an advance degree in this area. That's why I admire people who can solve difficult mathematical problems -- and be able to explain it in layman terms just like you do. I have a question: while I come from a city where horse racing is an event of daily lives, do you ever attempted to analyze the betting pools of horse racing? I would like to learn the tricks on how to determine which horses are overbet and which ones are underbet purely by mathematics, disregarding the quality of the runners. Is there such a rule? Thanks & regards, Danny from Hong Kong, China

One could write an entire book in answer to this question; however, I wouldn't be the one to do it. I do know that the best handicappers consider all available statistics and make bets when they feel the actual odds pay better than what they should. I don't know about Hong Kong but in the US the track takes about a 17% cut which is very difficult for even the best horse pickers to overcome. Personally, I don't know much about how to analyze the statistics on the racing form and I can't recommend any other source either. July 9, 2000

This page covers only specific non-football games. See also questions I've answered aboutfootball and sports betting in general.

The Wizard has answered questions about...

Specific Games
General Topics

Baccarat
Bingo
Blackjack
Caribbean Stud Poker
Craps
Horse Racing
Keno

Let It Ride
Lottery
Pai Gow Poker
Poker
Roulette
Slot Machines

Spanish 21
Sports Betting
Texas Hold 'Em
Three Card Poker
Video Poker
Other Casino Games
Non-Casino Games
TV Game Shows

Betting Systems
Boyfriends
Casinos
Dealers
General
Online Gaming
Probability
Table Games in general
The Wizard himself

Please save new questions for my bulletin board, coming in June.

The Wizard's other sites: Wizard of Macau, Sweat the Money, Math Problems
The Wizard's recommends: Casino Meister, Online Casino City, Online Poker Room Reviews, Video Poker Genius (See more of the Wiz's picks)