python3 binomial-select.py
# First experiment. Arm1 is much better than arm2.
# Error decreases quickly
p1 = 0.9, p2 = 0.2
Both have 1 simulations. Prob. of wrong arm choice 0.15
Both have 2 simulations. Prob. of wrong arm choice 0.059
Both have 3 simulations. Prob. of wrong arm choice 0.025259999999999994
Both have 4 simulations. Prob. of wrong arm choice 0.011246000000000004
Both have 5 simulations. Prob. of wrong arm choice 0.0051226799999999975
Both have 6 simulations. Prob. of wrong arm choice 0.0023690782400000005
Both have 7 simulations. Prob. of wrong arm choice 0.0011075557344000003
Both have 8 simulations. Prob. of wrong arm choice 0.0005220228824960002
Both have 9 simulations. Prob. of wrong arm choice 0.0002476139391167996
Both have 10 simulations. Prob. of wrong arm choice 0.0001180533944963841
# Second experiment - arms closer together
# Probability of error drops, but much slower
p1 = 0.5, p2 = 0.4
Both have 1 simulations. Prob. of wrong arm choice 0.45000000000000007
Both have 2 simulations. Prob. of wrong arm choice 0.425
Both have 3 simulations. Prob. of wrong arm choice 0.4065
Both have 4 simulations. Prob. of wrong arm choice 0.39125000000000015
Both have 5 simulations. Prob. of wrong arm choice 0.37804499999999996
Both have 6 simulations. Prob. of wrong arm choice 0.36628250000000023
Both have 7 simulations. Prob. of wrong arm choice 0.3556102500000004
Both have 8 simulations. Prob. of wrong arm choice 0.34580112500000043
Both have 9 simulations. Prob. of wrong arm choice 0.33669845249999975
Both have 10 simulations. Prob. of wrong arm choice 0.3281886762500006
# Arms very close. 10 simulations is not enough
p1 = 0.5, p2 = 0.49
Both have 1 simulations. Prob. of wrong arm choice 0.495
Both have 2 simulations. Prob. of wrong arm choice 0.49249999999999994
Both have 3 simulations. Prob. of wrong arm choice 0.4906252499999999
Both have 4 simulations. Prob. of wrong arm choice 0.4890631250000001
Both have 5 simulations. Prob. of wrong arm choice 0.48769640623124977
Both have 6 simulations. Prob. of wrong arm choice 0.4864664843093751
Both have 7 simulations. Prob. of wrong arm choice 0.48533916977422065
Both have 8 simulations. Prob. of wrong arm choice 0.48429248312774176
Both have 9 simulations. Prob. of wrong arm choice 0.4833113130366886
Both have 10 simulations. Prob. of wrong arm choice 0.48238474543395365
# Arms extremely close
p1 = 0.5, p2 = 0.49999
Both have 1 simulations. Prob. of wrong arm choice 0.499995
Both have 2 simulations. Prob. of wrong arm choice 0.4999925
Both have 3 simulations. Prob. of wrong arm choice 0.49999062500000024
Both have 4 simulations. Prob. of wrong arm choice 0.49998906250000086
Both have 5 simulations. Prob. of wrong arm choice 0.4999876953125009
Both have 6 simulations. Prob. of wrong arm choice 0.4999864648437519
Both have 7 simulations. Prob. of wrong arm choice 0.4999853369140652
Both have 8 simulations. Prob. of wrong arm choice 0.4999842895507847
Both have 9 simulations. Prob. of wrong arm choice 0.4999833076477082
Both have 10 simulations. Prob. of wrong arm choice 0.49998238029480513
# The remaining experiments are the same, but we print results less frequently
# and go up to 32 simulations each
p1 = 0.9, p2 = 0.2
Both have 1 simulations. Prob. of wrong arm choice 0.15
Both have 2 simulations. Prob. of wrong arm choice 0.059
Both have 4 simulations. Prob. of wrong arm choice 0.011246000000000004
Both have 8 simulations. Prob. of wrong arm choice 0.0005220228824960002
Both have 16 simulations. Prob. of wrong arm choice 1.485045900139101e-06
Both have 32 simulations. Prob. of wrong arm choice 1.6290741775267398e-11
p1 = 0.5, p2 = 0.4
Both have 1 simulations. Prob. of wrong arm choice 0.45000000000000007
Both have 2 simulations. Prob. of wrong arm choice 0.425
Both have 4 simulations. Prob. of wrong arm choice 0.39125000000000015
Both have 8 simulations. Prob. of wrong arm choice 0.34580112500000043
Both have 16 simulations. Prob. of wrong arm choice 0.28587248838323653
Both have 32 simulations. Prob. of wrong arm choice 0.21101388026526183
p1 = 0.5, p2 = 0.49
Both have 1 simulations. Prob. of wrong arm choice 0.495
Both have 2 simulations. Prob. of wrong arm choice 0.49249999999999994
Both have 4 simulations. Prob. of wrong arm choice 0.4890631250000001
Both have 8 simulations. Prob. of wrong arm choice 0.48429248312774176
Both have 16 simulations. Prob. of wrong arm choice 0.47761811979347407
Both have 32 simulations. Prob. of wrong arm choice 0.46824030016951507
p1 = 0.5, p2 = 0.49999
Both have 1 simulations. Prob. of wrong arm choice 0.499995
Both have 2 simulations. Prob. of wrong arm choice 0.4999925
Both have 4 simulations. Prob. of wrong arm choice 0.49998906250000086
Both have 8 simulations. Prob. of wrong arm choice 0.4999842895507847
Both have 16 simulations. Prob. of wrong arm choice 0.4999776080105575
Both have 32 simulations. Prob. of wrong arm choice 0.4999682090388194