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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
help.

--Ian

```