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All results obtained using SolverCUDA from one of the following systems:
NVIDIA GeForce RTX 4090, 13th Gen Intel(R) Core(TM) i9-13900K, CUDA Toolkit 12.2 on Ubuntu 22.04.2 LTS, 5.15.90.1-microsoft-standard-WSL2
I only show results for games where I've determined the best starting guess which yields the lowest maximum turns, then the lowest average turns. This takes a long time for larger games, thus the tables are only partially filled.
All runs have all gameplay optimizations enabled, like small fully discriminating sets, case equivalence, etc. See Mastermind on the GPU for details. Note: for the CUDA impl, the case equivalence opt applies when $c^p > 400000$.
Times reported are from the first system unless otherwise marked.Raw data is in the .json files in subdirectories here.
Average turns over all games
Knuth
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
2.0000
2.3333
2.8125
3.3600
3.6667
4.1224
4.4531
4.8642
5.2000
5.5868
5.9236
6.2959
6.6326
6.9956
3p
2.2500
2.7407
3.2656
3.6400
4.0463
4.4140
4.7871
5.1824
5.5050
5.8107
6.1291
6.4329
6.7085
7.0006
4p
2.7500
3.0741
3.5898
4.0336
4.4761
4.8367
5.1831
5.5053
5.8103
6.1408
6.4177
6.7223
7.0014
7.3959
5p
3.0312
3.4074
3.9824
4.4374
4.8772
5.2321
5.6084
5.9507
6.2656
6.5547
6.8587
7.1615
7.4602
7.7118
6p
3.5156
3.7435
4.3787
4.8696
5.3186
5.7151
6.0867
6.4289
6.7372
7.0563
7.3499
7.6248
7.9085
8.1726
7p
4.0000
4.1367
4.7997
5.3401
5.8044
6.2222
6.6100
6.9710
7.2908
7.6011
7.8941
8.1754
8p
4.3984
4.5138
5.2406
5.8407
6.3456
6.7802
7.1810
7.5542
Most Parts
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
2.0000
2.3333
2.8125
3.2400
3.6667
4.0612
4.4531
4.8272
5.2000
5.5620
5.9236
6.2781
6.6326
6.9822
3p
2.2500
2.7037
3.2188
3.6240
3.9769
4.3498
4.7012
5.0316
5.3770
5.7077
6.0347
6.3673
6.6928
7.0169
4p
2.7500
3.0370
3.5547
3.9568
4.3735
4.7430
5.0874
5.3999
5.7320
6.3312
6.3777
6.7027
7.0294
7.3563
5p
3.0312
3.3580
3.8799
4.3514
4.8322
5.1686
5.5491
5.9035
6.2502
6.5941
6.9381
7.2716
7.6014
7.9318
6p
3.5000
3.6653
4.2676
4.7807
5.2336
5.6554
6.0275
6.3920
6.7433
7.0934
7.4425
7.8573
8.1291
8.5658
7p
3.9531
4.0210
4.6763
5.2409
5.7253
6.3962
6.5526
6.9279
7.2910
7.6484
8.0217
8.3514
8p
4.3867
4.3976
5.1320
5.7528
6.2755
6.7353
7.1544
7.5448
Expected Size
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
2.0000
2.3333
2.8125
3.2400
3.6667
4.0408
4.4375
4.7901
5.1700
5.5124
5.8819
6.2189
6.5816
6.9156
3p
2.2500
2.7037
3.2344
3.6320
3.9769
4.3411
4.6934
5.0055
5.3920
5.6995
5.9832
6.3077
6.6017
6.8738
4p
2.7500
3.0370
3.5781
3.9760
4.4475
4.7530
5.0598
5.3396
5.6940
5.9356
6.2244
6.4892
6.7640
7.0225
5p
3.0312
3.3580
3.9062
4.3693
4.7759
5.1521
5.4997
5.8168
6.1152
6.5396
6.8616
7.2504
7.7405
8.1590
6p
3.5000
3.6708
4.2920
4.8058
5.2117
5.6040
5.9610
6.4650
6.8712
7.3345
7.8254
8.2320
8.6830
9.1092
7p
3.9531
4.0338
4.6968
5.2294
5.6915
6.1978
6.6694
7.1081
7.5439
8.0010
8p
4.3789
4.4097
5.1351
5.7233
6.3377
6.8702
7.2923
Entropy
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
2.0000
2.3333
2.8125
3.2400
3.6667
4.0408
4.4375
4.7901
5.1700
5.5124
5.8819
6.2189
6.5867
6.9200
3p
2.2500
2.7037
3.2344
3.6240
3.9861
4.3353
4.6777
5.0014
5.3090
5.6439
5.9340
6.2813
6.5758
6.8495
4p
2.7500
3.0370
3.5586
3.9616
4.3850
4.7372
5.0525
5.3254
5.6225
5.9115
6.1819
6.4456
6.7133
6.9750
5p
3.0312
3.3580
3.8848
4.3514
4.8268
5.1414
5.4856
5.8073
6.1075
6.3823
6.6487
6.9054
7.1525
7.4905
6p
3.5312
3.6584
4.2588
4.7818
5.1972
5.5954
5.9535
6.2847
6.5971
6.8904
7.1669
7.4254
7.6785
7.9200
7p
3.9375
4.0270
4.6738
5.2128
5.6765
6.0880
6.4661
6.8075
7.1291
7.4309
8p
4.3711
4.3856
5.1111
5.6938
6.1951
6.6301
7.1621
Max turns over all games
Knuth
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
3
3
4
5
5
6
6
7
7
8
8
9
9
10
3p
3
4
4
5
5
6
6
7
7
7
8
8
8
9
4p
4
4
4
5
5
6
6
7
7
8
8
9
9
9
5p
4
4
5
6
6
7
7
8
8
9
9
9
10
10
6p
5
5
6
6
7
8
8
9
9
9
10
10
10
11
7p
6
5
6
7
8
8
9
9
10
10
11
11
8p
6
6
7
8
9
9
10
10
Most Parts
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
3
3
4
4
5
5
6
6
7
7
8
8
9
9
3p
3
4
4
5
5
6
6
7
7
8
8
9
9
10
4p
4
4
5
5
6
6
7
7
8
8
9
9
10
10
5p
4
4
5
6
6
7
8
8
9
9
10
10
11
11
6p
5
5
6
7
8
8
9
9
10
10
11
11
12
12
7p
6
6
7
8
9
9
10
11
11
12
12
13
8p
6
6
7
9
10
11
12
12
Expected Size
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
3
3
4
4
5
5
6
6
7
7
8
8
9
9
3p
3
4
4
5
5
6
6
7
7
7
8
8
8
9
4p
4
4
4
5
5
6
7
7
7
8
8
9
9
9
5p
4
4
5
6
6
7
7
8
8
9
9
10
10
11
6p
5
5
6
6
7
8
8
9
10
11
11
12
13
14
7p
6
5
6
7
8
9
9
10
11
12
8p
6
6
7
8
9
10
10
Entropy
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
3
3
4
4
5
5
6
6
7
7
8
8
9
9
3p
3
4
4
5
5
6
6
7
7
7
8
8
8
9
4p
4
4
4
5
6
6
7
7
8
8
8
9
9
9
5p
4
4
5
6
6
7
7
8
8
9
9
10
10
10
6p
5
5
6
6
7
8
8
9
9
10
10
10
11
11
7p
6
5
6
7
8
9
9
10
10
11
8p
6
6
7
8
9
10
10
Run time
All times in seconds.
Knuth
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
0.004
0.002
0.003
0.003
0.004
0.003
0.004
0.004
0.005
0.004
0.005
0.004
0.006
0.005
3p
0.004
0.003
0.003
0.004
0.003
0.004
0.003
0.005
0.005
0.004
0.004
0.005
0.005
0.007
4p
0.005
0.003
0.003
0.003
0.003
0.004
0.005
0.007
0.012
0.010
0.018
0.027
0.038
0.080
5p
0.005
0.003
0.003
0.004
0.006
0.009
0.018
0.053
0.119
0.301
0.661
1.518
2.710
3.363
6p
0.004
0.003
0.005
0.009
0.029
0.106
0.407
1.385
3.967
7.536
23.574
67.654
134
201
7p
0.006
0.004
0.009
0.055
0.438
2.786
15.529
83.311
372
848
3,237
12,796
8p
0.006
0.007
0.048
0.993
14.887
141
959
8,850
Most Parts
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
0.002
0.003
0.002
0.002
0.003
0.003
0.004
0.004
0.005
0.004
0.005
0.004
0.004
0.005
3p
0.002
0.002
0.003
0.003
0.004
0.004
0.003
0.004
0.006
0.004
0.005
0.005
0.005
0.007
4p
0.003
0.002
0.003
0.002
0.004
0.004
0.005
0.006
0.010
0.040
0.019
0.026
0.040
0.058
5p
0.002
0.002
0.003
0.004
0.007
0.010
0.017
0.051
0.119
0.292
0.695
1.607
1.901
2.583
6p
0.003
0.003
0.004
0.009
0.026
0.106
0.402
1.367
2.934
6.278
13.636
21.218
56.701
80.141
7p
0.004
0.004
0.009
0.051
0.421
3.452
11.800
74.280
253
725
2,121
3,870
8p
0.004
0.005
0.045
0.929
12.379
127
844
6,586
Expected Size
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
0.002
0.002
0.002
0.002
0.003
0.003
0.004
0.004
0.004
0.004
0.005
0.004
0.004
0.004
3p
0.003
0.003
0.003
0.003
0.003
0.004
0.003
0.005
0.004
0.005
0.004
0.005
0.005
0.007
4p
0.003
0.003
0.002
0.003
0.040
0.003
0.006
0.006
0.014
0.010
0.019
0.024
0.035
0.050
5p
0.003
0.002
0.003
0.004
0.005
0.009
0.017
0.050
0.112
0.280
0.654
1.510
2.172
3.264
6p
0.003
0.003
0.005
0.013
0.027
0.101
0.404
1.203
3.710
7.052
12.923
26.205
52.187
104
7p
0.004
0.004
0.008
0.053
0.455
2.222
21.383
122
344
802
8p
0.004
0.005
0.047
0.950
12.887
184
1,538
Entropy
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
0.002
0.002
0.002
0.004
0.002
0.003
0.005
0.004
0.003
0.004
0.004
0.004
0.004
0.004
3p
0.002
0.003
0.002
0.003
0.003
0.004
0.003
0.005
0.004
0.005
0.005
0.006
0.005
0.007
4p
0.002
0.002
0.002
0.004
0.004
0.003
0.005
0.006
0.011
0.011
0.019
0.024
0.035
0.050
5p
0.002
0.004
0.003
0.004
0.031
0.009
0.018
0.049
0.116
0.271
0.631
1.426
2.691
3.815
6p
0.003
0.003
0.005
0.012
0.028
0.102
0.418
1.734
4.457
11.804
30.027
82.902
188
388
7p
0.004
0.004
0.009
0.054
0.464
2.980
14.536
99.703
414
1,597
8p
0.004
0.006
0.048
0.964
15.141
146
1,584
Initial guess
These were determined by running all unique initial guesses and selecting the one with the lowest average turns.
Knuth
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
12
12
12
12
12
12
12
12
12
12
12
12
12
12
3p
112
112
112
112
123
123
123
123
123
123
123
123
123
123
4p
1112
1123
1123
1123
1122
1234
1234
1234
1234
1234
1234
1234
1234
1123
5p
11122
11122
11223
11223
11223
11223
11223
11234
12345
12345
12345
12345
12345
11234
6p
111222
111223
112233
112233
111234
112234
112234
112234
112345
112234
112345
123456
123456
112345
7p
1111222
1112233
1112233
1112234
1122334
1122334
1122345
1112234
1122345
1122334
1122345
1123456
8p
11111222
11122233
11122334
11122334
11122334
11223344
11223344
11223345
Most Parts
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
12
12
12
12
12
12
12
12
12
12
12
12
12
12
3p
112
112
112
123
123
123
123
123
123
123
123
123
123
123
4p
1112
1123
1123
1123
1123
1123
1234
1234
1234
1122
1234
1234
1234
1234
5p
11122
11123
11223
11223
11122
11223
11223
11234
11234
11234
11234
12345
12345
12345
6p
111122
111223
111223
111223
112233
112234
112233
112234
112234
112234
112234
112233
112345
111234
7p
1111222
1111223
1112223
1112233
1112233
1234567
1122334
1122334
1122334
1122334
1122345
1122334
8p
11112222
11112223
11122233
11122233
11122233
11122334
11122334
11122334
Expected Size
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
12
12
12
12
12
12
12
12
12
12
12
12
12
12
3p
112
112
112
112
123
123
123
123
123
123
123
123
123
123
4p
1112
1123
1123
1123
1122
1234
1234
1234
1123
1234
1234
1234
1234
1234
5p
11122
11123
11223
11223
11223
11223
11223
11234
11234
11223
11234
12345
11234
11234
6p
111122
111223
111234
111234
112233
112234
112234
112233
123456
123456
112345
112345
112345
112345
7p
1111222
1112223
1112233
1112233
1112233
1112233
1234567
1234567
1234567
1234567
8p
11111222
11122233
11122233
11122334
11112223
11234567
12345678
Entropy
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
12
12
12
12
12
12
12
12
12
12
12
12
12
12
3p
112
112
112
123
123
123
123
123
123
123
123
123
123
123
4p
1112
1123
1123
1123
1123
1123
1234
1234
1234
1234
1234
1234
1234
1234
5p
11122
11123
11223
11223
11122
11223
11223
11234
11234
11234
11234
12345
12345
11223
6p
111122
111223
111223
112234
111223
112234
112233
112234
112234
112234
112234
112345
112345
112345
7p
1111222
1112223
1112233
1112233
1112233
1122334
1122334
1122334
1122334
1122345
8p
11112222
11122233
11122233
11122334
11122334
11122334
12345678
Codeword scores performed
Knuth
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
8
37
237
959
2,302
5,448
10,451
19,517
32,802
53,782
82,739
124,715
180,142
255,924
3p
27
349
4,655
20,308
82,076
246,048
666,360
1,552,939
3,239,900
6,293,479
11,574,141
20,124,334
33,365,298
54,072,587
4p
295
5,883
73,055
684,812
3,454,547
14,504,604
47,191,496
136,110,862
350,326,688
822,324,322
1,766,777,678
3,613,004,214
6,946,645,908
13,054,792,086
5p
1,146
63,357
1,742,819
19,962,957
151,389,136
806,379,304
3,455,514,359
12,492,630,435
38,804,382,440
108,709,981,374
279,019,798,351
664,458,801,621
221,997,737,749
192,694,591,994
6p
6,871
773,451
33,492,304
603,953,600
6,350,988,508
45,982,760,423
253,759,838,005
391,185,522,015
1,656,721,118,522
3,199,457,315,883
10,858,425,592,971
32,889,665,862,260
62,472,732,590,695
83,261,167,884,700
7p
33,385
8,430,875
658,538,021
18,024,115,236
267,526,288,124
1,688,549,605,473
12,071,528,765,135
43,526,479,577,075
202,563,623,599,338
454,226,266,052,537
1,786,843,116,423,295
7,241,968,681,210,185
8p
153,818
93,497,904
12,270,461,992
526,976,844,351
9,068,132,002,615
97,720,579,295,094
701,717,829,399,382
4,682,574,122,447,169
Most Parts
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
8
37
237
840
2,302
5,233
10,451
19,174
32,802
53,279
82,739
124,020
180,142
255,005
3p
27
348
4,387
20,860
85,152
251,739
671,218
1,533,518
3,236,027
6,375,811
11,708,574
20,572,084
34,634,326
56,079,986
4p
295
5,880
77,528
652,972
3,463,134
14,270,384
47,208,015
135,472,446
350,464,893
878,817,869
1,797,140,727
3,680,119,986
7,174,306,215
13,312,144,408
5p
1,146
63,919
1,614,138
19,550,530
152,135,569
806,052,142
3,472,351,604
12,614,051,942
39,772,670,331
112,444,933,934
290,373,086,196
694,294,146,799
90,988,224,939
136,084,491,252
6p
7,119
720,784
33,027,100
595,258,454
6,341,359,719
46,072,975,414
255,246,785,068
383,523,838,927
1,046,858,939,830
2,459,853,019,348
5,087,144,152,500
6,734,551,527,982
19,841,112,296,443
23,280,249,903,990
7p
35,705
8,459,920
637,840,915
17,927,773,941
267,261,019,920
2,601,990,666,174
8,880,122,701,504
38,504,450,538,551
133,497,278,948,495
386,646,879,778,684
1,150,080,343,861,908
2,049,146,692,910,936
8p
162,189
93,044,769
12,180,822,787
527,293,108,359
7,485,302,242,714
92,083,690,331,092
643,575,570,820,001
3,464,187,208,779,301
Expected Size
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
8
37
237
756
2,259
4,862
10,269
18,154
32,228
51,032
81,340
119,704
177,257
247,466
3p
27
348
4,379
20,307
83,362
242,810
645,654
1,488,796
3,147,410
6,120,529
11,164,205
19,602,641
32,673,475
52,519,289
4p
295
5,880
71,469
674,138
3,414,542
13,943,407
45,652,480
129,723,306
339,204,689
782,091,005
1,689,882,163
3,435,613,183
6,639,130,529
12,168,202,360
5p
1,146
62,416
1,705,150
19,655,689
145,002,496
788,677,783
3,358,602,869
12,111,253,903
37,711,653,297
108,629,719,737
279,857,499,313
678,186,317,197
83,320,978,338
127,159,880,291
6p
6,315
706,069
32,432,560
592,871,529
6,188,149,187
44,610,788,824
246,812,861,651
275,708,427,535
1,504,549,849,624
2,863,387,679,682
4,262,149,789,918
7,865,731,904,423
13,464,528,036,793
23,321,531,102,914
7p
31,201
8,279,821
629,713,290
17,524,870,209
260,398,373,052
1,092,172,939,382
17,016,283,283,955
66,068,747,261,859
184,234,347,122,086
411,275,065,012,046
8p
156,400
88,589,231
11,891,779,695
511,534,385,555
6,886,477,705,836
138,534,093,924,209
1,240,207,360,811,578
Entropy
2c
3c
4c
5c
6c
7c
8c
9c
10c
11c
12c
13c
14c
15c
2p
8
37
237
756
2,259
4,862
10,269
18,154
32,228
51,032
81,340
119,704
177,258
247,467
3p
27
348
4,379
19,696
85,102
240,659
648,610
1,490,245
3,066,171
6,098,395
11,050,237
19,481,846
32,610,998
52,326,875
4p
295
5,880
70,979
661,683
3,416,360
13,902,154
45,715,242
130,339,726
332,329,994
779,981,695
1,675,611,376
3,405,477,137
6,569,120,811
12,084,250,313
5p
1,146
63,181
1,601,576
19,527,248
149,702,727
787,883,746
3,359,885,206
12,087,333,783
37,778,545,052
105,292,045,887
267,744,752,466
632,934,443,503
317,908,538,869
346,134,520,308
6p
6,317
703,901
33,015,522
588,525,525
6,190,771,615
44,686,332,233
247,164,602,609
543,555,521,863
1,864,615,331,489
5,499,350,695,255
14,318,938,189,045
41,345,836,241,048
94,618,989,667,561
192,025,742,386,105
7p
30,941
8,256,099
625,605,978
17,490,706,992
259,734,446,561
1,683,004,716,928
10,009,426,166,809
50,340,716,513,854
217,263,812,165,510
861,938,290,687,204
8p
150,395
88,589,586
11,837,060,563
508,673,859,696
8,962,484,316,997
98,143,129,935,191
1,227,502,324,546,207
Grouped by Game
The same metrics grouped by game, to easily compare algorithms.