In my last post I looked at extending Janowski's cubeful equity model to match play.

The conclusion: match play also favors a cube life index very close to 0.70.

I played a Janowski match strategy with different cube life indexes against a Janowski match strategy with cube life index 0.70 as a benchmark. I ran 40k matches with variance reduction and recorded the average points per match.

The results:

If I fit parabolas through the results and force them to pass through zero ppm at x=0.7, I find optimal cube life indexes of x=0.61 for match length 3, x=0.64 for match length 5, x=0.68 for match length 7, and x=0.69 for match length 9.

All average points per match have a standard error of +/- 0.004ppm, so the statistics are marginal for the shorter match lengths.

There is some evidence for a smaller cube life index for shorter matches, but not much. In general the optimal match cube life index looks very close to the optimal money cube life index.

That said, the performance difference for short matches of using a suboptimal cube life index is pretty infinitesimal. It becomes a bigger deal for longer matches.

The conclusion: match play also favors a cube life index very close to 0.70.

I played a Janowski match strategy with different cube life indexes against a Janowski match strategy with cube life index 0.70 as a benchmark. I ran 40k matches with variance reduction and recorded the average points per match.

The results:

Match Length | x=0.5 | x=0.6 | x=0.8 | x=0.9 |
---|---|---|---|---|

3 | -0.004 | 0.000 | -0.004 | -0.007 |

5 | -0.007 | +0.007 | +0.002 | -0.024 |

7 | -0.021 | -0.003 | -0.008 | -0.029 |

9 | -0.028 | -0.006 | +0.003 | -0.037 |

If I fit parabolas through the results and force them to pass through zero ppm at x=0.7, I find optimal cube life indexes of x=0.61 for match length 3, x=0.64 for match length 5, x=0.68 for match length 7, and x=0.69 for match length 9.

All average points per match have a standard error of +/- 0.004ppm, so the statistics are marginal for the shorter match lengths.

There is some evidence for a smaller cube life index for shorter matches, but not much. In general the optimal match cube life index looks very close to the optimal money cube life index.

**UPDATE**: I ran longer simulations for more values of the cube life index for match lengths 3, 5, and 7 to try to get more accurate statistics. From those data I get optimal cube life indexes of 0.70, 0.67, and 0.69 for match lengths 3, 5, and 7 respectively. So no evidence of a smaller optimal cube life index for shorter matches: everything should use 0.70.That said, the performance difference for short matches of using a suboptimal cube life index is pretty infinitesimal. It becomes a bigger deal for longer matches.

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