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MoreLess
Introduction
MoreLess is a simple game in which the player predicts whether a random number from 1 to 100 will be less, equal, or greater than the previous number chosen. Odds are commensurate with the probability of winning.
Rules
- The game draws a random number from 1 to 100.
- The player may bet on whether the next random number draw, on the same basis, will be higher, lower, or equal to the last number drawn.
- A new random number from 1 to 100 will be drawn.
- If the player wins, then he is paid at odds equal to 0.96 divided by the probability of winning. These odds will be rounded down to the nearest 0.01.
- Return to step 2
Analysis
The expected return in his game generally ranges from 95% to 96%. While the winning odds are calculated to achieve an expected return of 96%, sometimes rounding down causes the actual return to be a little less.
For example, consider the following situation where the last number drawn was 17.
17 Example
| Bet | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Under | 6 | 16 | 0.160000 | 0.960000 |
| Equal | 96 | 1 | 0.010000 | 0.960000 |
| Over | 1.15 | 83 | 0.830000 | 0.954500 |
You can see the return for the Equal and Over bets equal exactly 96%. However, to achieve an expected return of 96%, the Over bet would have to pay 96%/83% = 1.1566 for 1. This gets rounded down to 1.15. The return then becomes 83% × 1.15 = 95.45%.