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Luck Adjusted Result

Posted By: MaX
Date: Wednesday, 12 August 2009, at 11:45 a.m.

In Response To: Luck Adjusted Result (Maik Stiebler)

Sorry, I didn't formulate it the right way.

I know what unbiased means but I think that saying LAR is unbiased is somehow misleading (without any additional detail).

I often hear people say that "the error rate computed by a bot is biased", meaning the bot considers his strategy as optimal (when it probably isn't so) and hence the computed ER is "biased towards the bot's strategy". True, despite the small abuse of the term "unbiased" (when you know what unbiased means in stats).

After that, they add "However, luck estimstion is unbiased". Luck estimation is unbiased if the NN is perfect. And by the way, if the NN is perfect, ER estimation is unbiased too.

To me, the real advantage of LAR is that, as you said, it is a direct measure of what we want to know (skill difference between two strategies as winning changes of one against the other). ER is a useful thing, but assuming we know it exactly, we would still be left with the problem of transalting it into a skill differential (advantage).

The same for variance reduction: roll stratification (covering all 1296 2-rolls combinations) in a 1296 trials rollout do not add any bias, but using variance reduction in the gnubg/Snowie sense (which is similar to luck computation), do add some bias if the eval is not perfect.

MaX.

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