## Tuesday, April 10, 2012

### Average number of games in a match

Some more interesting statistics on match play: the average number of games per match.

I ran self-play for two players using Player 3.4 for checker play (cubeful equity optimization) and Janowski match model with cube life index 0.70 and looked at how many games it took on average to finish a match.

The most interesting result is that the average number of games divided by the match length seems to converge reasonably well to a value around 0.65.

Here is a chart of the results: blue line/left axis shows average number of games, red line/right axis shows the average number of games divided by the match length:

The only other source I could find for similar statistics gave similar results (out to match length 11).

I ran the experiment with x=0.5 and x=0.9 as well to see how that affected the converged average number of games per match length. x=0.5 gave a converged ratio of 0.51; x=0.9 gave 0.90. This compares to 0.65 for x=0.7.

So the average number of games per match divided by the match length converges (for long matches) to something surprisingly close to the cube life index itself! I'm sure this is just a coincidence, but an interesting one.