I've got a working doubling strategy in my backgammon framework now for money games, applying Janowski's model.

Now I can calculate some statistics on the values of the cube; kind of like an analysis on Jellyfish doubling that was done in 1999.

I'm interested in how doubling statistics change as Janowski's cube life index (sometimes called cube efficiency) varies. I ran 100k cubeful money games, using Player 3.3 for checker play, and Janowski's doubling model for different cube life index values.

In the case of x=1 (the live cube limit) the initial double point is right at the cash point, so the player never offers a double when the opponent will take. Most games then end in cashes.

Now I can calculate some statistics on the values of the cube; kind of like an analysis on Jellyfish doubling that was done in 1999.

I'm interested in how doubling statistics change as Janowski's cube life index (sometimes called cube efficiency) varies. I ran 100k cubeful money games, using Player 3.3 for checker play, and Janowski's doubling model for different cube life index values.

Statistic | x=0 | x=0.25 | x=0.50 | x=0.75 | x=1 |
---|---|---|---|---|---|

Percent cashed | 21.8 | 27.4 | 40.0 | 50.9 | 96.3 |

Percent single | 55.4 | 51.2 | 45.9 | 34.8 | 0.4 |

Percent gammon | 21.8 | 20.3 | 18.1 | 13.6 | 3.1 |

Percent backgammon | 1.2 | 1.1 | 1.0 | 0.7 | 0.2 |

Average cube | 14.7 | 4.49 | 2.72 | 1.89 | 1 |

Percent cube=1 | 0.6 | 3.2 | 12.3 | 33.9 | 100 |

Percent cube=2 | 24.2 | 47.8 | 61.0 | 56.7 | 0 |

Percent cube=4 | 24.4 | 31.3 | 21.2 | 8.5 | 0 |

Percent cube=8 | 18.6 | 12.2 | 4.5 | 0.8 | 0 |

Percent cube=16 | 12.8 | 4.1 | 0.8 | 0 | 0 |

Percent cube=32 | 8.2 | 1.1 | 0.1 | 0 | 0 |

Percent cube=64 | 11.1 | 0.4 | 0 | 0 | 0 |

In the case of x=1 (the live cube limit) the initial double point is right at the cash point, so the player never offers a double when the opponent will take. Most games then end in cashes.

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