## Wednesday, March 21, 2012

### Janowski-model money game cube statistics

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.

Statisticx=0x=0.25x=0.50x=0.75x=1
Percent cashed21.827.440.050.996.3
Percent single55.451.245.934.80.4
Percent gammon21.820.318.113.63.1
Percent backgammon1.21.11.00.70.2
Average cube14.74.492.721.891
Percent cube=10.63.212.333.9100
Percent cube=224.247.861.056.70
Percent cube=424.431.321.28.50
Percent cube=818.612.24.50.80
Percent cube=1612.84.10.800
Percent cube=328.21.10.100
Percent cube=6411.10.4000

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.