Objective pawn eval

[vdbergh]

This is an alternative proposal to #4216

Formula:

s=w+d/2 (w,d,l obtained from the win rate model)
eval_cp=400*log10(s/(1-s))

[amchess]

Great idea!
Congratulations!

[ddobbelaere]

I personally like this PR in the sense that it puts more emphasis on the WDL model. If the latter is accurate, indeed a more objective pawn eval is obtained. There are still two things that slightly bother me:

• How does the eval "feel"? Will it not be too "confusing" for the user? The reason being that the now non-linear formula between internal value (and ply) and reported value might lead to compression/decompression for low/high evals w.r.t. the current SF behavior.
• The reported value depends on ply, will this not cause inconsistencies during analysis? E.g. setting up a board position without the move number might lead to different reported values.

[robbai]

Suggested change

	return int(0.5 + 1000*win_rate_model(v, ply));
	return int(0.5 + 1000*win_rate_model_double(v, ply));

[vdbergh]

OMG that's a bug.

[vdbergh]

Fixed.

[vdbergh]

It seems that this method works well for small evals (e.g. the starting position has eval ~30). However for big evals it is rather counter intuitive. If I remove the white queen then master has an eval of ~ -1200 but this method has an eval of ~ -4500.

Of course SF will win against god with a queen ahead, so this high negative eval simply reflects the fact that the game is lost.

[nimr0d]

This is a cool idea. Centipawn would then directly mean elo difference starting in that position? It would give some more meaning to "average centipawn loss".

[vdbergh]

I personally like this PR in the sense that it puts more emphasis on the WDL model. If the latter is accurate, indeed a more objective pawn eval is obtained. There are still two things that slightly bother me:

* How does the eval "feel"? Will it not be too "confusing" for the user? The reason being that the now non-linear formula between internal value (and ply) and reported value might lead to compression/decompression for low/high evals w.r.t. the current SF behavior.

This appears to be the case. But I am not sure is this is bad. For example the eval is currently clamped to 8000cp. I observed in many games that if this value is reached then SF is close to announcing mate. So there is a smooth transition from the eval to mate scores.

* The reported value depends on ply, will this not cause inconsistencies during analysis? E.g. setting up a board position without the move number might lead to different reported values.

Personally I regret that the win rate model depends on the ply. Logically it can and should only depend on the board. One may try to replace ply by game phase, but according to Vondele this gives a less good fit.

[ddobbelaere]

Personally I regret that the win rate model depends on the ply. Logically it can and should only depend on the board. One may try to replace ply by game phase, but according to Vondele this gives a less good fit.

There was an interesting suggestion by zz4032 on Discord to let WDL depend on number of pieces instead of ply. Don't know if that would work equally well though (i.e. give an accurate model).

[vdbergh]

I am going to close this. After thinking it over I decided it is probably too controversial.

[vondele]

I think it is interesting, but yes, I'm sure especially the larger values would surprise people. This would also make it a little more difficult to derive the win_rate_model from pgns that contain search evals.