Longshot Stakes: Probability Or Edge
Notwithstanding the specifc advice outlined in Kelly's Multiple Personality Disorder and Kelly And Mutually-Exclusive Outcomes relating to AvK events, consider an idealized horse-racing scenario where you have identified two selections: High Expectations at 2/1 with a 40% win probability and In With A Chance at 20/1 and a 10% chance of winning. Assume further that you are planning to bet ¤50 (Bankroll: ¤500) on High Expectations. How much should you bet on In With A Chance?
Win Probability Stakes
| Selection | S/P | Win% | Edge | Stake | Profit |
|---|---|---|---|---|---|
| High Expectations | 2/1 | 40% | 0.20 | ¤50.00 | ¤100.00 |
| In With A Chance | 20/1 | 10% | 1.10 | ¤12.50 | ¤250.00 |
Edge Stakes
| Selection | S/P | Win% | Edge | Stake | Profit |
|---|---|---|---|---|---|
| High Expectations | 2/1 | 40% | 0.20 | ¤50.00 | ¤100.00 |
| In With A Chance | 20/1 | 10% | 1.10 | ¤27.50 | ¤550.00 |
If your answer is ¤12.50, then your handicapping is driven by win probability as High Expectations (40%) is four times more likely to win than In With A Chance (10%). Alternatively, if your answer is ¤27.50, then your handicapping is driven by edge as In With A Chance (1.10) has 5.5 times more edge than High Expectations (0.20).
The Kelly Criterion advises that you choose the stake so that the amount you win is proportional to your edge. Most punters choose stakes based on win probability and, as a result, they are not exploiting their advantage and are 'leaving money on the table'!