Great, can't believe it generalizes to multinomial by simplifying with expansion for small differences. I hope there is no need for ELO model, draw model, bias model and all these. They seemed to me a bit a complication to SPRT. What are nuissance parameters? Must be related to draw ratio and bias (empirical variance?). Empirical variance must be inputted, right? Will draw ratio subjected to condition be estimated by MLE or is inputted (without a draw model)? Can we include large bias (unbalanced openings, in Bayeselo terms of order of 200 ELO, probably by empirical variance again)? A simulator would be needed.Michel wrote:After a long and complicated computation I came up with a surprisingly simple formula for the log likelihood ratio for the GSPRT in the multinomial case (for small score differences). Since any distribution can be approximated by a multinomial one I assume it is a general fact (and the proof should be much easier than one given here).

See the boxed formula at the end of this file

http://hardy.uhasselt.be/Toga/MLE_for_multinomial.pdf

I jackknifed another database containing ultra-fast games at fixed nodes with balanced openings, the effect on variance is even larger. Probably the games are more deterministic and related. I would need some databases of SF self-games with reasonable time control.