40-Ball Keno

Introduction

Internet casinos using Gamesys software offer a game called "40-Number Instant Keno." It is like conventional keno, except it uses only 40 numbers and the game draws ten balls instead of twenty.

Rules

The player picks 3 to 10 numbers from 1 to 40 and then the game shall pick 10. The more numbers drawn by the casino that match the player's picks, the more he wins.

The following table shows what each number of catches pays by the number of picks.

Analysis

The following table shows the number of combinations for each number of picks and catches.

The next table shows the probability, to six decimal points, for each number of picks and catches.

The next table shows the contribution to the return, to six decimal points, for each number of picks and catches. The bottom row shows the total return for each number of picks.

Strategy

As you can see in the table above, the greatest return is for the pick-10 at 97.90%.