# Betting

Based on the betting model in the Two-horse race_01.xls spreadsheet, prove that no matter what the posted odds and the bets received are, the expected loss/gain is always zero.

How can the bookmaker make sure he can earn a certain amount that is above the expected zero income from the betting?

See attached file for full problem description.

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#### Solution Preview

Please see the attached file.

(1) Based on the betting model in the Two-horse race_01.xls spreadsheet, prove that no matter what the posted odds and the bets received are, the expected loss/gain is always zero.

Let the odds be n-to-m

Probability of first horse winning / second horse losing = m / (n+m)

Probability of first horse losing / second horse winning ...

#### Solution Summary

Answers questions on payoffs from betting. The expert proves that no matter what the posted odds are.