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Last Updated: January 8, 2019

# 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

1. The game draws a random number from 1 to 100.
2. 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.
3. A new random number from 1 to 100 will be drawn.
4. 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.

## 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%.

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