Math CentralQuandaries & Queries


Question from farah:

I'm trying to calculate the odds of a 13 game bet. Each game has 2 teams with 3 possible outcomes (win,draw,lose).

What are the odds.

Hi Farah,

You have to make some significant assumptions to solve this problem with the information given. First of all you need to assume that for each of the 13 games the three outcomes are equally likely. You also need to assume the games are independent which implies that results of previous games have no influence of the probabilities of upcoming games.

With this in mind, on each game the probability of each possible result is $\large \frac{1}{3}.$ If you are going to place a 13 game bet then to win you have to pick the correct result 13 times. The probability of doing this is

\[ \left(\frac13 \right)^{13} = 0.000000627225.\]


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