## Tuesday, April 10, 2012

### Optimal Janowski cube life index in match play

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:

Match
Length
x=0.5x=0.6x=0.8x=0.9
3-0.0040.000-0.004-0.007
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.