# probabilities of dice

Probabilities regarding a game in which two players roll six-sided dice and the player with the larger sum wins.

Columns:

- P1: number of dice rolled by player 1
- P2: number of dice rolled by player 2
- P1 wins: probability of the sum of player 1's dice being greater than player 2's
- draw: probability of the sum of player 1's dice being equal to player 2's
- P2 wins: probability of the sum of player 2's dice being greater than player 1's

The percentages are approximate.

P1 | P2 | P1 wins | draw | P2 wins |
---|---|---|---|---|

1 | 1 | 41.67% | 16.67% | 41.67% |

1 | 2 | 9.26% | 6.94% | 83.80% |

1 | 3 | 1.16% | 1.54% | 97.30% |

1 | 4 | 0.08% | 0.19% | 99.73% |

1 | 5 | 0.00% | 0.01% | 99.98% |

1 | 6 | 0.00% | 0.00% | 100.00% |

2 | 2 | 44.37% | 11.27% | 44.37% |

2 | 3 | 15.20% | 6.94% | 77.85% |

2 | 4 | 3.59% | 2.49% | 93.92% |

2 | 5 | 0.61% | 0.60% | 98.79% |

2 | 6 | 0.08% | 0.10% | 99.82% |

3 | 3 | 45.36% | 9.28% | 45.36% |

3 | 4 | 19.17% | 6.55% | 74.28% |

3 | 5 | 6.07% | 2.99% | 90.93% |

3 | 6 | 1.49% | 0.98% | 97.53% |

4 | 4 | 45.95% | 8.09% | 45.95% |

4 | 5 | 22.04% | 6.15% | 71.81% |

4 | 6 | 8.34% | 3.26% | 88.40% |

5 | 5 | 46.37% | 7.27% | 46.37% |

5 | 6 | 24.24% | 5.79% | 69.96% |

6 | 6 | 46.67% | 6.65% | 46.67% |