Match Equities |

*World Class Backgammon, Move by Move*, © 1989 Roy Friedman

*World Class Backgammon, Move by Move*.

## Notes on Methodology

To determine a player’s match equity from a given position, one must assume a set of underlying match equities that apply at the start of a game. For example, at the start of a game where one player needs two points to win the match and the opponent needs three points, the match equity of the leading player is 59% and the match equity of the trailing player is 41%. The set of start-of-game match equities that I use is shown in the table below.

A computer model developed by the author generates this match-equity table. The primary model parameter is the probability of a gammon in a cubeless game, which has been calibrated from empirical results.

In general, my match-equity table gives surprisingly high equities for the player who trails in the match. This is because the gammon parameter described above has been set to a relatively high value. The high value of the gammon parameter reflects the fact that gammons in cubeless games occur more frequently than most players realize.

## Match Equity Table

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | |

1 | 50 | 66 | 75 | 80 | 83 | 87 | 90 | 92 | 94 |

2 | 34 | 50 | 59 | 64 | 72 | 77 | 82 | 85 | 88 |

3 | 25 | 41 | 50 | 56 | 63 | 69 | 74 | 78 | 82 |

4 | 20 | 36 | 44 | 50 | 57 | 63 | 68 | 72 | 77 |

5 | 17 | 28 | 37 | 43 | 50 | 56 | 62 | 66 | 71 |

6 | 13 | 23 | 31 | 37 | 44 | 50 | 56 | 60 | 65 |

7 | 10 | 18 | 26 | 32 | 38 | 44 | 50 | 55 | 60 |

8 | 8 | 15 | 22 | 38 | 34 | 49 | 45 | 50 | 55 |

9 | 6 | 12 | 18 | 23 | 29 | 35 | 40 | 45 | 50 |