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Match analyzing paradox

Posted By: Rich Munitz
Date: Wednesday, 6 July 2011, at 8:10 p.m.

In Response To: Match analyzing paradox (Bob Koca)

The eval of bot2 is actually not random around the eval of bot1. Rather it is random around the true equity of the position which will be better approximated by the average of the two evals. As a result, if the bot2 eval is lower than bot1, it suggests bot1 was too high to begin with and thus a >50% chance that another eval would be lower. That probability distribution exists before we do the bot2 eval even if we lack the info to know it yet.

This can be better seen by imagining that bot1 and bot2 are the same bot, each doing an identical rollout but with different seeds. The probability distribution for the second rollout depends on the infinite rollout, not the first rollout. The average of the two rollouts is more statsig as to the likely infinite rollout result than either of the two alone.

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