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RE: [Bug-gnubg] Why is odd ply equity always lower?

From: Ian Shaw
Subject: RE: [Bug-gnubg] Why is odd ply equity always lower?
Date: Thu, 19 Jun 2003 11:59:17 +0100

> -----Original Message-----
> From: Nis
> Sent: 18 June 2003 21:25
> How does this affect higher plies?
> One would think that the same mechanism would lead to 2-ply 
> overestimating 
> the best 1-ply play, and thus cancel out some of the error of 
> the 1-ply 
> calculation. This is not necessarily so, however, since the 
> best play is 
> selected on 0-ply, and only evaluated at 1-ply. Only if the 
> errors of 1-ply 
> and 0-ply correlate, will some of the effect be cancelled out 
> at 2-ply.

I'm not sure I understand precisely what you mean by errors correlating,
but my tests showed that 0, 2 & 4 play equities tended to be very
similar. 1 & 3 ply equities were similar to each other, but lower than
the even plies. 

    1. Cubeful 0-ply    8/5 6/5                      Eq.:  +0.268
    1. Cubeful 1-ply    8/5 6/5                      Eq.:  +0.212
    1. Cubeful 2-ply    8/5 6/5                      Eq.:  +0.253
    1. Cubeful 3-ply    8/5 6/5                      Eq.:  +0.207
    1. Cubeful 4-ply    8/5 6/5                      Eq.:  +0.263

This is fairly typical, and shows some damping, with 0-ply > 4-ply >
2-ply and 3-ply > 1-ply. One would predict that 5 ply will fall between
1 and 3.

> ---
> Only relevant for cube decisions?
> The wrong estimations of equity is mainly a problem of 
> absolute equities. 
> As Joseph has pointed out, chequerplay relies almost solely 
> on the relative equities of positions.
> Thus a fix should only "need" to be applied for cube 
> decisions (and cubeful 
> chequerplay? Someone help me here)

Maybe the "need" is only there for cube decisions and chequer play can
get by quite happily "as is", but when we are analysing our matches or
doing research I think we would like to see equities as accurate as
possible for positions too.

> ---
> Measuring
> I am really interested in how this affects playing strength. 
> [snip]However, I think the really 
> interesting question will be how 1.5-ply relate to 1- and 2-ply - 
> especially for cube decisions.

As usual, I can't compile code (I ought to try Holger's instructions
sometime), but I can run it. If all that's needed is some PC power I can


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