Extrapolate equalizer handicap values to the opening (zero ply)

Derive equalizer Elo/Glicko‑2 handicap values for material removal at the opening (zero ply) by rigorously extrapolating from earliest observed ply estimates in standard chess, and validate the resulting handicaps against quiescent starting positions.

Background

Using earliest‑ply estimates, the authors propose approximate Elo/Glicko‑2 handicap values for material removal to equalize games but note by inspection that zero‑ply values likely differ.

They explicitly leave the formal extrapolation back to zero ply as future work, emphasizing the need for rigorous derivation and validation.

References

By eyeball, however, it seems that if one were to extrapolate back from around 15 plies to 0 plies, these equalizer values would be somewhat different. We leave this exercise to future research.

— Inferring Piece Value in Chess and Chess Variants  (2509.04691 - Pav, 4 Sep 2025) in Standard Chess, Section Results (end of subsection)