## Saturday, April 7, 2012

### Cubeful vs cubeless equities in checker play decisions

So far all my players have made checker play decisions by choosing the position with the best cubeless equity, even after I introduced doubling strategies to decide when to offer & take doubles. This is clearly suboptimal: the doubling strategies can calculate cubeful equity, so the checker play should choose moves based on the position with the best cubeful equity, not best cubeless equity.

I'm referring to money games; for match play they should optimize match equity.

I extended my backgammon framework to allow the players to optimize on cubeful equity in checker play to see how much that would improve things.

The answer, it seems: at least for my intermediate-strength players, not much!

I played 100k cubeful money games (with variance reduction) between two players (both Player 3.4) that both use Janowski x=0.7 for their doubling strategy. The first used cubeful equities for checker play and the second used cubeless equity.

The first player scored -0.0004ppg +/- 0.0044ppg. Hardly a significant advantage to using cubeful equity when choosing the best move - the score is indistinguishable from zero.

I also thought I'd run the cubeful-equity player through the GNUbg benchmarks. The benchmarks are for cubeless play, so that should give something worse than for the cubeless-equity player. But the benchmarks are all about choosing the best move out of the possible moves, so all that matters there is relative equity difference, not absolute equity, and perhaps that's not affected much by cubeful vs cubeless.

The cubeless benchmark scores are Contact 13.32, Crashed 11.69, and Race 0.766.

Using a cubeful-equity player, always assuming a centered cube, the scores were 13.44, 12.16, and 0.766. So the Contact and Crashed scores got a little bit worse, but hardly changed. Using cubeful equity in checker play decisions does not seem to make a big difference in almost every case.

Assuming player-owned cube the scores were 13.41, 12.03, and 0.768. Assuming opponent-owned cube the scores were 13.42, 11.82, and 0.764. So cube position does not matter much either.

The conclusion: it doesn't matter much if you use cubeful or cubeless equity in checker play decisions.

Nonetheless the cubeful equity performance is marginally better, and there are probably edge case conditions where it matters more, so I'll start using cubeful equity in money play.