SPRT LLR calculation

[sethtroisi]

I'm writing SPRT calculator and I'm confused by the sprt math.

I wrote up the three methods I know in this gist
LLF = my optimized version
wiki = my take on likelihood-ratio_test
LLR = the code from leela-zero-server

Other links:
https://www.chessprogramming.org/Match_Statistics#SPRT
^ uses similar math to this repo but with draws
^ draws it's justification from http://hardy.uhasselt.be/Toga/GSPRT_approximation.pdf

https://nowak.ece.wisc.edu/ece830/ece830_fall11_lecture9.pdf
^ maybe I'm misunderstanding p0(x) and p1(x)

[sethtroisi]

I think maybe it's because I'm testing likelihood that θ = θ1 not θ > θ1

[roy7]

Yeah we don't care if it's exactly 35 ELO better, only that is 35 or more better. On the lower end test we'd tweaked it to test at 0 since if it's under 0 we don't care if it's -5 or -75, so why waste time figuring out if it's better or worse than -35.

[roy7]

Past discussions that might help (or not).

leela-zero/leela-zero#378
leela-zero/leela-zero#543
leela-zero/leela-zero#545

[sethtroisi]

It appears fishtest also uses my methodology.

https://github.com/glinscott/fishtest/blob/master/fishtest/fishtest/stat_util.py#L112

[sethtroisi]

The author michel van den bergh has a bunch of comments on github and talkchess
http://talkchess.com/forum3/viewtopic.php?f=7&t=57465&start=20#p737797