# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
# #
# OpenBench is a chess engine testing framework authored by Andrew Grant. #
# <https://github.com/AndyGrant/OpenBench> <andrew@grantnet.us> #
# #
# OpenBench is free software: you can redistribute it and/or modify #
# it under the terms of the GNU General Public License as published by #
# the Free Software Foundation, either version 3 of the License, or #
# (at your option) any later version. #
# #
# OpenBench is distributed in the hope that it will be useful, #
# but WITHOUT ANY WARRANTY; without even the implied warranty of #
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the #
# GNU General Public License for more details. #
# #
# You should have received a copy of the GNU General Public License #
# along with this program. If not, see <http://www.gnu.org/licenses/>. #
# #
# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #
import math
def erf_inv(x):
a = 8*(math.pi-3)/(3*math.pi*(4-math.pi))
y = math.log(1-x*x)
z = 2/(math.pi*a) + y/2
return math.copysign(math.sqrt(math.sqrt(z*z - y/a) - z), x)
def phi_inv(p):
return math.sqrt(2)*erf_inv(2*p-1)
def bayeselo_to_proba(elo, drawelo):
pwin = 1.0 / (1.0 + math.pow(10.0, (-elo + drawelo) / 400.0))
ploss = 1.0 / (1.0 + math.pow(10.0, ( elo + drawelo) / 400.0))
pdraw = 1.0 - pwin - ploss
return pwin, pdraw, ploss
def proba_to_bayeselo(pwin, pdraw, ploss):
elo = 200 * math.log10(pwin/ploss * (1-ploss)/(1-pwin))
drawelo = 200 * math.log10((1-ploss)/ploss * (1-pwin)/pwin)
return elo, drawelo
def SPRT(wins, losses, draws, elo0, elo1):
# Estimate drawelo out of sample. Return LLR = 0.0 if there are not enough
# games played yet to compute an LLR. 0.0 will always be an active state
if wins > 0 and losses > 0 and draws > 0:
N = wins + losses + draws
elo, drawelo = proba_to_bayeselo(float(wins)/N, float(draws)/N, float(losses)/N)
else: return 0.00
# Probability laws under H0 and H1
p0win, p0draw, p0loss = bayeselo_to_proba(elo0, drawelo)
p1win, p1draw, p1loss = bayeselo_to_proba(elo1, drawelo)
# Log-Likelyhood Ratio
return wins * math.log(p1win / p0win) \
+ losses * math.log(p1loss / p0loss) \
+ draws * math.log(p1draw / p0draw)
def ELO(wins, losses, draws):
def _elo(x):
if x <= 0 or x >= 1: return 0.0
return -400*math.log10(1/x-1)
# win/loss/draw ratio
N = wins + losses + draws;
if N == 0: return (0, 0, 0)
w = float(wins) / N
l = float(losses)/ N
d = float(draws) / N
# mu is the empirical mean of the variables (Xi), assumed i.i.d.
mu = w + d/2
# stdev is the empirical standard deviation of the random variable (X1+...+X_N)/N
stdev = math.sqrt(w*(1-mu)**2 + l*(0-mu)**2 + d*(0.5-mu)**2) / math.sqrt(N)
# 95% confidence interval for mu
mu_min = mu + phi_inv(0.025) * stdev
mu_max = mu + phi_inv(0.975) * stdev
return (_elo(mu_min), _elo(mu), _elo(mu_max))
