Overview

SPRT is a simulator for Sequential Probability Ration Test, applied to chess testing, using the BayesElo model.

Compiling

• Code should compile with any C++11 capable compiler (no dependancy).
• On Linux, or POSIX systems with g++, run make.sh.

Syntax

sprt BayesEloMin BayesEloMax BayesEloStep Simulations DrawElo BayesElo0 BayesElo1 Quantiles...

• BayesEloMin, BayesEloMax, BayesEloStep: Range of elo values to test.
• Simulations: Number of simulation to run for every step.
• DrawElo: Parameter of the BayesElo model. To calibrate this value, use the following formula: DrawElo = 200.log10[(1-w)/w.(1-l)/l], where w and l are the win and loss ratio.
• BayesElo0, BayesElo1: Hypothesis H0 and H1 of the test.
• Quantiles...: Quantile(s) of the stopping time distribution.

Note that alpha and beta are always 5%. You do not need to change these values. Instead, modify the bounds (BayesElo0,BayesElo1).

Example

$ ./sprt -1 5 1 20000 250 0 4 0.25 0.5 0.75 0.9
BayesElo	Elo	%Pass	Avg	Q25%	Q50%	Q75%	Q90%
-1.00	-0.62	0.0128	28982	15842	24199	36892	53050
0.00	-0.00	0.0515	40145	19796	31951	51911	77467
1.00	0.62	0.1888	55858	24872	43094	73794	113389
2.00	1.24	0.5031	65163	27763	48987	85860	134934
3.00	1.86	0.8149	55612	24676	42561	73334	112514
4.00	2.48	0.9506	39821	19647	31877	51575	76254
5.00	3.10	0.9875	28835	15796	24049	36825	52675

For example, +3 BayesElo with DrawElo = 250 corresponds to +1.86 Elo, and the SPRT(0,4) test has 81.49% chance to pass, with an average run of 55612 games. The remaining columns are quantiles of the stopping time distribution.