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Using two bots instead of a longer rollout: effect on confidence in result

Posted By: Tom Keith
Date: Saturday, 22 December 2012, at 12:40 a.m.

In Response To: Using two bots instead of a longer rollout: effect on confidence in result (leobueno)

There are two reasons a rollout could be wrong. (1) Random error -- the rollout errs because one side had luckier dice than the other; and (2) systematic error -- the rollout errs because the bot played one side better than the other. I assume your question is mostly to do with random error, so let's assume both bots play the same and do VR the same (to exclude systematic error). Further, let's assume we're comparing only two plays, and the sequence of random dice rolls are independent between the two bots.

An 89.9% chance of winning a rollout is the same as a JSD of about 1.28. (To get this number I consulted the table here: http://www.bkgm.com/rgb/rgb.cgi?view+1238)

You can combine two independent JSDs using the formula below. Here JSD1 = 1.28 (from above) and JSD2 = 1.803 (from your GNU rollout).

CombinedJSD = sqrt( JSD1^2 + JSD2^2 )
    = sqrt( 1.28^2 + 1.803^2 )
    = sqrt( 1.638 + 3.251 )
    = sqrt( 4.889 )
    = 2.21

The combined jsd is higher than either of the individual jsd's. But it is still lower than your goal of 3.5, so you're going to have to run your rollouts longer.

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