The horses A, B and C have the following amounts on bets:
| Horse 1 | $10000 |
| Horse 2 | $15000 |
| Horse 3 | $25000 |
How much should the track pay a bettor for winning on a $2 bet? Note the track will take 10% as their profit.
The first thing is to determine the odds. A Bayesian is not so worried about coming up with one. The simplest method is to go for the gut feeling. Another way is to estimate the win probability based on the bet amount (individual/total) and then determine the odds as,
(1 – probability) / probability
| Horse | Bet Amount | Probability | Odds |
| Horse 1 | $10000 | 10000 / 50000 = 0.2 | 4 to 1 |
| Horse 2 | $15000 | 15000 / 50000 = 0.3 | 2.3 to 1 |
| Horse 3 | $25000 | 25000 / 50000 = 0.5 | 1 to 1 |
For a $2 bet on horse 1, the payout will be 2 x 4 – 0.1 x 2 x 4 = $7.2
Introduction to Mathematical Statistics: PennState
