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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.


In our next issue: Implications + How to repair this ...

Some items for consideration:

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.

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.

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.

Thus an "obvious" fix would be to implement my previously suggested half-plies - averages between n- and (n+1)-ply

I have written the code to do so, and it compiles and works (as in doesn't play obviously bad)

I can send a patch to someone with an account.

For those interested, what I do is

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.


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)

So we might want to start using reduced evaluation settings for cube decisions



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.



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

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