Randil's math problem revisited

http://tasvideos.org/forum/viewtopic.php?p=425971#425971
C++ code: http://pastebin.com/3ZqyhgyR

This time guessing 4-digit numbers by Bayesian probability distribution instead of maximum likelihood.

5000 simulations each.


Average tries for pr=0.10 , pw=0.05: 416.41
Average tries for pr=0.15 , pw=0.05: 174.35
Average tries for pr=0.20 , pw=0.05: 106.81
Average tries for pr=0.25 , pw=0.05: 76.02
Average tries for pr=0.30 , pw=0.05: 59.04
Average tries for pr=0.35 , pw=0.05: 47.75
Average tries for pr=0.40 , pw=0.05: 40.07
Average tries for pr=0.45 , pw=0.05: 34.11
Average tries for pr=0.50 , pw=0.05: 29.76
Average tries for pr=0.55 , pw=0.05: 25.72
Average tries for pr=0.60 , pw=0.05: 23.06
Average tries for pr=0.65 , pw=0.05: 20.55
Average tries for pr=0.70 , pw=0.05: 18.55
Average tries for pr=0.75 , pw=0.05: 16.67
Average tries for pr=0.80 , pw=0.05: 15.13
Average tries for pr=0.85 , pw=0.05: 13.58
Average tries for pr=0.90 , pw=0.05: 12.14
Average tries for pr=0.95 , pw=0.05: 10.77
Average tries for pr=0.15 , pw=0.10: 593.56
Average tries for pr=0.20 , pw=0.10: 231.96
Average tries for pr=0.25 , pw=0.10: 136.47
Average tries for pr=0.30 , pw=0.10: 93.05
Average tries for pr=0.35 , pw=0.10: 69.36
Average tries for pr=0.40 , pw=0.10: 55.60
Average tries for pr=0.45 , pw=0.10: 45.27
Average tries for pr=0.50 , pw=0.10: 38.61
Average tries for pr=0.55 , pw=0.10: 32.65
Average tries for pr=0.60 , pw=0.10: 28.03
Average tries for pr=0.65 , pw=0.10: 24.78
Average tries for pr=0.70 , pw=0.10: 21.98
Average tries for pr=0.75 , pw=0.10: 19.21
Average tries for pr=0.80 , pw=0.10: 17.26
Average tries for pr=0.85 , pw=0.10: 15.14
Average tries for pr=0.90 , pw=0.10: 13.34
Average tries for pr=0.95 , pw=0.10: 11.66
Average tries for pr=0.20 , pw=0.15: 728.93
Average tries for pr=0.25 , pw=0.15: 281.43
Average tries for pr=0.30 , pw=0.15: 159.02
Average tries for pr=0.35 , pw=0.15: 107.12
Average tries for pr=0.40 , pw=0.15: 78.70
Average tries for pr=0.45 , pw=0.15: 61.37
Average tries for pr=0.50 , pw=0.15: 49.57
Average tries for pr=0.55 , pw=0.15: 41.07
Average tries for pr=0.60 , pw=0.15: 34.69
Average tries for pr=0.65 , pw=0.15: 30.01
Average tries for pr=0.70 , pw=0.15: 25.59
Average tries for pr=0.75 , pw=0.15: 22.18
Average tries for pr=0.80 , pw=0.15: 19.58
Average tries for pr=0.85 , pw=0.15: 17.18
Average tries for pr=0.90 , pw=0.15: 14.82
Average tries for pr=0.95 , pw=0.15: 12.66
Average tries for pr=0.25 , pw=0.20: 845.41
Average tries for pr=0.30 , pw=0.20: 320.02
Average tries for pr=0.35 , pw=0.20: 178.47
Average tries for pr=0.40 , pw=0.20: 116.29
Average tries for pr=0.45 , pw=0.20: 84.44
Average tries for pr=0.50 , pw=0.20: 65.57
Average tries for pr=0.55 , pw=0.20: 52.48
Average tries for pr=0.60 , pw=0.20: 43.12
Average tries for pr=0.65 , pw=0.20: 35.69
Average tries for pr=0.70 , pw=0.20: 30.12
Average tries for pr=0.75 , pw=0.20: 25.85
Average tries for pr=0.80 , pw=0.20: 22.19
Average tries for pr=0.85 , pw=0.20: 19.33
Average tries for pr=0.90 , pw=0.20: 16.47
Average tries for pr=0.95 , pw=0.20: 13.87
Average tries for pr=0.30 , pw=0.25: 916.98
Average tries for pr=0.35 , pw=0.25: 346.65
Average tries for pr=0.40 , pw=0.25: 190.69
Average tries for pr=0.45 , pw=0.25: 125.23
Average tries for pr=0.50 , pw=0.25: 88.48
Average tries for pr=0.55 , pw=0.25: 68.49
Average tries for pr=0.60 , pw=0.25: 53.81
Average tries for pr=0.65 , pw=0.25: 43.98
Average tries for pr=0.70 , pw=0.25: 36.15
Average tries for pr=0.75 , pw=0.25: 30.47
Average tries for pr=0.80 , pw=0.25: 25.53
Average tries for pr=0.85 , pw=0.25: 21.70
Average tries for pr=0.90 , pw=0.25: 18.19
Average tries for pr=0.95 , pw=0.25: 15.20
Average tries for pr=0.35 , pw=0.30: 990.40
Average tries for pr=0.40 , pw=0.30: 367.51
Average tries for pr=0.45 , pw=0.30: 201.17
Average tries for pr=0.50 , pw=0.30: 131.61
Average tries for pr=0.55 , pw=0.30: 91.91
Average tries for pr=0.60 , pw=0.30: 70.23
Average tries for pr=0.65 , pw=0.30: 54.50
Average tries for pr=0.70 , pw=0.30: 44.48
Average tries for pr=0.75 , pw=0.30: 36.55
Average tries for pr=0.80 , pw=0.30: 30.08
Average tries for pr=0.85 , pw=0.30: 24.67
Average tries for pr=0.90 , pw=0.30: 20.73
Average tries for pr=0.95 , pw=0.30: 16.71
Average tries for pr=0.40 , pw=0.35: 1030.51
Average tries for pr=0.45 , pw=0.35: 382.23
Average tries for pr=0.50 , pw=0.35: 208.14
Average tries for pr=0.55 , pw=0.35: 133.33
Average tries for pr=0.60 , pw=0.35: 93.56
Average tries for pr=0.65 , pw=0.35: 69.39
Average tries for pr=0.70 , pw=0.35: 54.53
Average tries for pr=0.75 , pw=0.35: 43.75
Average tries for pr=0.80 , pw=0.35: 35.04
Average tries for pr=0.85 , pw=0.35: 28.46
Average tries for pr=0.90 , pw=0.35: 23.09
Average tries for pr=0.95 , pw=0.35: 18.50
Average tries for pr=0.45 , pw=0.40: 1052.67
Average tries for pr=0.50 , pw=0.40: 389.40
Average tries for pr=0.55 , pw=0.40: 212.34
Average tries for pr=0.60 , pw=0.40: 132.95
Average tries for pr=0.65 , pw=0.40: 93.78
Average tries for pr=0.70 , pw=0.40: 69.85
Average tries for pr=0.75 , pw=0.40: 53.19
Average tries for pr=0.80 , pw=0.40: 42.02
Average tries for pr=0.85 , pw=0.40: 33.25
Average tries for pr=0.90 , pw=0.40: 26.24
Average tries for pr=0.95 , pw=0.40: 20.62
Average tries for pr=0.50 , pw=0.45: 1062.85
Average tries for pr=0.55 , pw=0.45: 396.06
Average tries for pr=0.60 , pw=0.45: 212.18
Average tries for pr=0.65 , pw=0.45: 133.66
Average tries for pr=0.70 , pw=0.45: 91.59
Average tries for pr=0.75 , pw=0.45: 67.35
Average tries for pr=0.80 , pw=0.45: 50.77
Average tries for pr=0.85 , pw=0.45: 39.18
Average tries for pr=0.90 , pw=0.45: 30.46
Average tries for pr=0.95 , pw=0.45: 23.14
Average tries for pr=0.55 , pw=0.50: 1079.79
Average tries for pr=0.60 , pw=0.50: 392.47
Average tries for pr=0.65 , pw=0.50: 207.59
Average tries for pr=0.70 , pw=0.50: 130.21
Average tries for pr=0.75 , pw=0.50: 88.37
Average tries for pr=0.80 , pw=0.50: 64.67
Average tries for pr=0.85 , pw=0.50: 47.44
Average tries for pr=0.90 , pw=0.50: 35.52
Average tries for pr=0.95 , pw=0.50: 26.60
Average tries for pr=0.60 , pw=0.55: 1054.40
Average tries for pr=0.65 , pw=0.55: 380.51
Average tries for pr=0.70 , pw=0.55: 201.75
Average tries for pr=0.75 , pw=0.55: 124.79
Average tries for pr=0.80 , pw=0.55: 83.47
Average tries for pr=0.85 , pw=0.55: 58.94
Average tries for pr=0.90 , pw=0.55: 42.58
Average tries for pr=0.95 , pw=0.55: 30.60
Average tries for pr=0.65 , pw=0.60: 1022.24
Average tries for pr=0.70 , pw=0.60: 368.16
Average tries for pr=0.75 , pw=0.60: 190.32
Average tries for pr=0.80 , pw=0.60: 114.85
Average tries for pr=0.85 , pw=0.60: 76.91
Average tries for pr=0.90 , pw=0.60: 51.85
Average tries for pr=0.95 , pw=0.60: 35.69
Average tries for pr=0.70 , pw=0.65: 988.19
Average tries for pr=0.75 , pw=0.65: 346.02
Average tries for pr=0.80 , pw=0.65: 176.27
Average tries for pr=0.85 , pw=0.65: 104.02
Average tries for pr=0.90 , pw=0.65: 67.11
Average tries for pr=0.95 , pw=0.65: 43.55
Average tries for pr=0.75 , pw=0.70: 914.84
Average tries for pr=0.80 , pw=0.70: 315.30
Average tries for pr=0.85 , pw=0.70: 155.81
Average tries for pr=0.90 , pw=0.70: 90.25
Average tries for pr=0.95 , pw=0.70: 54.22
Average tries for pr=0.80 , pw=0.75: 837.82
Average tries for pr=0.85 , pw=0.75: 281.92
Average tries for pr=0.90 , pw=0.75: 133.05
Average tries for pr=0.95 , pw=0.75: 71.07
Average tries for pr=0.85 , pw=0.80: 737.27
Average tries for pr=0.90 , pw=0.80: 229.51
Average tries for pr=0.95 , pw=0.80: 102.52
Average tries for pr=0.90 , pw=0.85: 599.60
Average tries for pr=0.95 , pw=0.85: 171.93
Average tries for pr=0.95 , pw=0.90: 423.46

Exact time of code was lost but running this took about twice as long as the other.