 # Answers

## Basic dice duelling

Probability of a draw: 6 out of 36: 636 = 16: 16 × 100 = 16.67% Excel version of Matrix for Player 1 winning draws

Probability of Player 1 winning: 21 out of 36: 2136 = 712: 712 × 100 = 58.33%
Probability of Player 2 winning: 15 out of 36: 1536 = 512: 512 × 100 = 41.67% Excel version of matrix for Player 2 having plus 1 and Player 1 wins draws

Probability of Player 1 winning: 15 out of 36: 1536 = 512: 512 × 100 = 41.67%
Probability of Player 2 winning: 21 out of 36: 2136 = 712: 712 × 100 = 58.33%

## Changing the dice

Mean average roll on a standard 6-sided die: (1 + 2 + 3 + 4 + 5 + 6) ÷ 6 = 3.5
Mean average roll with the red die: (1 + 4 + 4 + 4 + 4 + 4) ÷ 6 = 3.5
Mean average roll with the green die: (2 + 2 + 2 + 5 + 5 + 5) ÷ 6 = 3.5
Mean average roll with the blue die: (3 + 3 + 3 + 3 + 3 + 6) ÷ 6 = 3.5 Excel version of a matrix for red vs blue

Probability of red winning: 25 out of 36: 2536: 2536 × 100 = 69.44%
Probability of blue winning: 11 out of 36: 1136: 1136 × 100 = 30.56% Excel version of a matrix for blue vs green

Probability of blue winning: 21 out of 36: 2136 = 712: 712 × 100 = 58.33%
Probability of green winning: 15 out of 36: 1536 = 512: 512 × 100 = 41.67% Excel version of a matrix for red vs green

Probability of red winning: 15 out of 36: 1536 = 512: 512 × 100 = 41.67%
Probability of green winning: 21 out of 36: 2136 = 712: 712 × 100 = 58.33%
So, red beats blue, blue beats green, but green beats red. None of the dice are an outright winner.