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Re: [Bug-gnubg] Question on Luck Analysis

From: Jim Segrave
Subject: Re: [Bug-gnubg] Question on Luck Analysis
Date: Thu, 16 Dec 2010 18:21:53 +0100
User-agent: Mutt/1.5.16 (2007-06-09)

On Thu 16 Dec 2010 (10:09 -0000), Ian Shaw wrote:
> Hi Christian,
> Thanks for the explanation.
> So, just to clarify, the discrepancy of 0.133 from the theoretical 0 in
> the result reflects discrepancies in the gnubg evaluation function.
> To calculate luck, gnubg evaluates the equity after each of the 21
> possible dice combinations, and calculates the luck as the difference
> between the actual roll and the average. Each of these evaluations is
> likely to have some error, so the luck calculation is inevitably
> inaccurate for every move. 
> Over a large number of moves, you would expect these discrepancies to
> cancel out. Over the 51 moves in my sample game, this 0.133 total
> discrepancy averages out at 0.0026 points per move.
> Cheers,
> Ian

Maybe I'm missing something here, but gnubg's luck figures apply to
each player's rolls separately. Rolling a joker for player A can add
3% to his luck, it does not take 3% away from his opponent's luck, so
there's no reason to assume they should be equal.  One player, playing
perfectly, could have a fairly low luck rating if the spread in
possible equities is small for all his rolls. Another player could
have a high luck rating if he rolls the least of all evil rolls (the
average roll leaves two blots, his roll only leaves one). He's lucky,
but he's not all that lucky, he still has a blot. Luck is the measure
of getting the most favourable of all possible rolls, not a measure of
game winning chances in and of themselves.

Jim Segrave           address@hidden

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