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

 From: Nis Subject: RE: [Bug-gnubg] Why is odd ply equity always lower? Date: Wed, 18 Jun 2003 22:24:38 +0200

```Quoting myself:

```
```If 0-ply is unbiased but imprecise (as in having average error 0) then
the value of the best move will be overrated. Example

Move    True Equity    0-ply equity
A            0.4         0.35
B            0.4         0.45
C            0.5         0.45
D            0.5         0.55  (*BEST MOVE*)

Note that the average error is 0, but the best move is off by 0.05.

The result of this should be that 1-ply, which is the average of 21
BestMoves for the opponent, is underrated by some amount. This will be
added to the (negated) 0-ply, so if 0-ply is overrated, 1-ply is even
more underrated.

QED

In our next issue: Implications + How to repair this ...
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```
Some items for consideration:

How does this affect higher plies?

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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.
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Even if the correlation is there, the effect will be dampened by the imperfect correlation as well as the assumed smaller relative error on 1-ply compared to 0-ply.
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If we ASSUME that the effect only appears at 1-ply, we find that the error propagates through the plies, being negative for odd plies and positive for even plies.
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Thus an "obvious" fix would be to implement my previously suggested half-plies - averages between n- and (n+1)-ply
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I have written the code to do so, and it compiles and works (as in doesn't play obviously bad)
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I can send a patch to someone with an account.

For those interested, what I do is

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Please note that my code removes the ability of gnubg to do reduced 1-ply evaluations. I can reimplement it if people see a need.
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---

Only relevant for cube decisions?

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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.
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Thus a fix should only "need" to be applied for cube decisions (and cubeful chequerplay? Someone help me here)
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So we might want to start using reduced evaluation settings for cube decisions
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Training

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Another question is: Does this have any impact on the training of the nets? Anything that could be done better, or implications for how we want to train.
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Measuring

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I am really interested in how this affects playing strength. Joseph has already measured the strength difference between 0, 0.5 and 1-ply (0.5-ply calculated as the average of the other two). However, I think the really interesting question will be how 1.5-ply relate to 1- and 2-ply - especially for cube decisions.
```
--
Nis Jorgensen
Greenpeace
Amsterdam

```