Odds in statistics and Odds in a horse race
Definition of Odds in statistics
[math]\displaystyle{ Odds=\frac{probability\ that\ the\ outcome\ occurs}{probability\ that\ the\ outcome\ does\ not\ occur} }[/math]
Example of a horse rase
Assumption
In order to simplify, the bookmaker in the following scenario does not charge any betting fees
A race that 5 horses start and 10 bettors bet
Here is a horse race that 5 horses start and 20 people — 20 bettors — bet each of 5 horses.
Names of horses are A, B, C, D and E.
| Horses |
|---|
| A |
| B |
| C |
| D |
| E |
Each bettor bets $1 for one horse. All bet money are pooled ($20 pooled in total) and will be redistributed for bettors who bet a winning horse.
Now each all bettors bet as following:
| Horses | Bettors |
|---|---|
| A | 10 bettors |
| B | 5 bettors |
| C | 3 bettors |
| D | 2 bettors |
| E | 1 bettor |
Results
If each horse wins, pooled $20 are redistributed as following:
| Horses | Bettors | If the horse wins | Calculation |
|---|---|---|---|
| A | 10 bettors | $20 into 10 bettors | $20 ÷ 10 = $2 |
| B | 5 bettors | $20 into 5 bettors | $20 ÷ 5 = $4 |
| C | 3 bettors | $20 into 3 bettors | $20 ÷ 3 = $6.66... |
| D | 2 bettors | $20 into 2 bettors | $20 ÷ 2 = $10 |
| E | 1 bettor | $20 into 1 bettor | $20 ÷ 1 = $20 |
