Created by Charles Jenkins

Dice Wars is a cross between the classic card game of War and the board game Risk (without the board!). Players try to capture their opponents dice by rolling against each other.

Explaining the rules can be confusing, but playing the game itself is quite easy. All you need is two people and four dice, and you’re ready to go!

Object of the game:• To capture your opponent’s dice!Instructions:1. Both players roll two dice. The higher die of each player are

compared. Whoever has the higher die captures their opponent’s die. The other two dice are compared and the winner captures the lower die. A player can now have anywhere from zero to four dice. No dice are captured in the event of a tie.

2. Players again roll all of their dice and compare each player’s highest dice, and in the case both players still have two dice each, their other dice are compared.

3. The first player to capture all four dice wins!

1. Player A and Player B start out with 2 dice each. 2. Both players roll both dice.

3. Player A wins one of Player B’s dice because four beats three.

4. But Player B also wins one of Player A’s dice because two beats one.

5. Both players still have two dice.

Player A rolls: Player B rolls:

6. Both players roll again.

7. This time the two highest dice are both three, so neither player captures those any die.

8. But Player A does win one of Player B’s dice because two beats one.

9. Now Player A has three dice and Player B only has one.

Player A rolls: Player B rolls:

10. Both players roll again.

11. Player A captures Player B’s remaining die because six is higher than three. Because Player A only uses his highest die, his other two dice are not compared to any other dice.

12. Player A wins because he has captured all 4 dice!

Player A rolls: Player B rolls:

This game starts off fair because both players are rolling two dice. As soon as a player captures a die, however, they has an advantage because they are now rolling three dice to one.

We must look at all of the possible combinations. We know with one die, there are 6 possible outcomes. When we have two dice, there are 36 possible outcomes. In Dice Wars, we’re always playing with four dice for a totally of 1296 outcomes (64)! Because the dice are compared to one another, there is no simple math formula to figure out the probability, so I had to list out all of the possible combinations.

1. Is this game fair?

2. How can we measure if the game is fair?

2 Dice vs. 2 Dice

Event Occurrence Probability

A wins 2 295 295/1296 22.76%

B wins 2 295 295/1296 22.76%

A and B Split 200 25/162 15.43%

A wins and Ties 220 55/324 16.98%

B wins and Ties 220 55/324 16.98%

Both Tie 66 11/216 5.09%

3 Dice vs. 1 Dice

Event Occurrence Probability

A Wins 855 855/1296 65.97%

B Wins 225 25/144 17.36%

Tie 216 1/6 16.67%

Since both “A and B Split” and “Both Tie” have the same outcome (both players still have 2 dice each), the total probability of this outcome is 133/648 or 20.52%

As you can see, when Player A rolls 3 dice, he has a huge advantage over player B!

A total list of the permutations can be found in the attached Excel spreadsheet.

Dice Wars Probability

Thanks for watching. Have fun playing!

Thanks for watching. Have fun playing!