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Pitfall of luck-adjusted result?

Posted By: Timothy Chow
Date: Wednesday, 8 June 2011, at 6:21 p.m.

In Response To: making a virtue out of necessity (Bob Koca)

Luck-adjusted results do have the advantage of not relying on the correctness of the bot, but I'm not totally convinced that they're better than MWC difference for the purposes of choosing the winner of a tournament.

What you're proposing is to add a certain mean-zero random variable X to the actual result. However, we get to sample only once. The probability that X>0 is not necessarily 1/2. So I might be incentivized to choose a move that increases the probability that our single sample of X is >0 (and gives me a favorable luck-adjusted result), even if that move slightly decreases the probability that I'll win the match.

The third moment of the luck adjustment isn't something I've thought about before so I don't have an example off the top of my head, but it seems to me that this sort of thing may not be that uncommon a phenomenon.

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