Centipawns vs Millipawns with NNUE

[Madeleine Birchfield]

The original reason why the centipawn system was adopted as the standard evaluation for alpha-beta engines is because handcrafted evaluations typically did not have any evaluation features that could achieve millipawn accuracy. However, the more complex and more accurate efficiently updatable neural networks (NNUE) have appeared in the past few months for evaluation, which makes me wonder if NNUE could achieve the millipawn accuracy or even finer accuracy that handcrafted evaluation could not, and if it is a good idea for engines that have adopted NNUE for evaluation to switch to the millipawn system.

[jorose]

I would be surprised if many engines are actually using centipawns as their most finegrained score internally. With regards to centipawn output I think it was also just a nice interpretable way for users to be able to understand engine output.

I will note that having more coarse grained values has benefits with regards to the search tree. Ie if a nw search returns a slightly better value with the fine-grained eval, it may trigger a re-search with an expensive open window.

I do wonder what changes will come with regards to engine scores both internally and externally.

Winter relies on scores consisting of win, (implicit) draw and (implicit) loss probabilities with a granularity of 1/40th of a percentage point. I think this should be more fine-grained than necessary.

[hgm]

I have severe doubts that milli-Pawn resolution could ever have any advantage. A milli-Pawn would correspond to a score change of ~0.1%. It is extremely unlikely that even very complex NN would ever be able to estimate the win probability of any complex individual position to that accuracy. And even if they could, being able to choose the 1mP better line over the other would give an advantage so small that it could only be noticed in a million games or so.

The detrimental effect of actually having to spend search time for deciding which of the two lines with a 1mP difference is better is probably much larger than the effect of always picking the best one. Your time would be ticking away while thinking over things that make no practical difference.