RE: [Bug-gnubg] Question on Luck Analysis

[Ian Shaw]

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


> -----Original Message-----
> From: Christian Anthon [mailto:address@hidden 
> Sent: 15 December 2010 18:52
> To: Ian Shaw
> Cc: address@hidden
> Subject: Re: [Bug-gnubg] Question on Luck Analysis
> 
> Two things explains this result:
> 
> a) the neuralnet is not perfect and hence the luck evaluation 
> is not perfect. For example consider a really bad neuralnet 
> that always returned an equity of zero. The luck would be 
> evaluated as zero as well. The luck evaluation is constructed 
> in a way that ensures zero bias in an infinite number of 
> games, but not in a single game.
> 
> b) The summed luck is 1.133 point (in a perfect world this 
> number would be 1)  which means that Blue has gained 1.133 
> point by luck (his luck and whites bad luck here) and white 
> has lost 1.133 (his bad luck and Blues good luck here). In 
> reality Blue won one point and his luck adjusted result is 
> -0.133 pont (0 in a perfect world). White lost one point and 
> his luck adjusted result is 0.133 (also 0 in a perfect 
> world). If you set 0-ply to play against 2-ply in a high 
> number of 1-point matches you should see that the summed luck 
> averaged by the number of games is zero but that the Luck 
> adjusted result averaged by the number of matches is not zero.
> 
> Hope this explains your observations.
> 
> Christian.
> 
> > Luck total EMG (Points)                    +0.270 ( +0.270) 
>      -0.863
> > ( -0.863)
> > Actual result                          +1.000               -1.000
> >
> > Luck adjusted result                   -0.133               +0.133
> >
> >
> >
> > Cheers,
> > Ian Shaw
> >