Six Shooter

Introduction

Six Shooter is a dice game by 1x2, a supplier of software for Internet casinos. The object of the game is for the player to roll every number represented in a dealer roll in as few throws as possible.

Rules

1. Play begins with the player making a bet.
2. The dealer shall then roll six dice. These shall be referred to as the Target Dice.
3. The player shall then roll three dice.
4. Any face represented in the player's roll shall be checked against the Target Dice. Any face that matches shall be said to be eliminated. For example, if there is at least one six among the Target Dice, and the player rolls at least one six, then all sixes in the Target Dice shall be eliminated.
5. The player shall keep rolling until all Target Dice are eliminated, or three times, whichever happens first.
6. If the player eliminates all the Target Dice, then he shall be paid according to how many throws it took and the pay table below.

Rolls Pays
1 12 to 1
2 8 to 5
3 1 to 1

Example

Following is an example game. Click on any image for a larger version.

In the image above, the dealer's roll was a 2-2-2-3-4-4. So the target dice are 2, 3, and 4.

The player's first roll is a 1-4-1. The two ones don't help but the four eliminates both fours from the Target Dice. A 2 and 3 are the only Target Dice remaining.

The player's second roll is a 6-2-6. The sixes don't help but the two eliminates every two from the Target Dice. Just a three needed now and one roll left.

The player's third roll is a 1-2-3. The one and two don't help but the three eliminates the last three from the Target Dice. With the goal achieved in three rolls, the player's wager is paid 1 to 1.

Analysis

An analysis of this game is a fun exercise in combinatorial mathematics. The following table shows the conclusion of such analysis. The lower right cell reflects a house edge of 5.88%.

Six Shooter Analysis

Event Pays Combinations Probability Return
Win after one roll 12 4,350,485,376 0.009253 0.111033
Win after two rolls 1.6 61,771,746,960 0.131378 0.210204
Win after three rolls 1 112,684,244,190 0.239659 0.239659
Loss -1 291,378,508,050 0.619710 -0.619710
Total 470,184,984,576 1.000000 -0.058814