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Old 05-04-2018, 10:11 AM   #26
ArtyMcFly
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Re: Poker Riddle from FiveThirtyEight.com

Nice work!
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Old 05-06-2018, 12:15 PM   #27
whosnext
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Re: Poker Riddle from FiveThirtyEight.com

In preparation for archiving all the stuff I did on this project, I made one final review of my logic and programs. I discovered two minor mistakes in my previous post.

First, for some bizarre reason, the program was incorrectly classifying a few full houses as quads (the bizarre reason was that I screwed up). Second, the program missed a very small number of nut hands due to extra-tricky blocking. (In case anyone is interested in an example, it was not able to figure out that 5d4c was the nuts on a 4d3d2d5s5h board. 5d4c blocks both possible straight flushes as well as quads, and therefore this particular top full house is the effective nuts.)

Anyway, I thought I should post the corrected tallies in the extremely unlikely event that this thread is ever looked at in the far distant future when discussing which NLHE starting hands make the most nuts becomes popular once more.


RankStarting HandRoyal Flush Nut_BoardsStraight Flush Nut_BoardsFour of a Kind Nut_BoardsFull House Nut_BoardsFlush Nut_BoardsStraight Nut_BoardsThree of a Kind Nut_BoardsTOTAL NUT_BOARDSNut_Board PctBachfan_Sim Pct
1
ATs
1,084
135
2,560
4,158
59,850
24,324
0
92,111
4.35%
4.34%
2
AJs
1,084
90
2,575
5,160
56,714
24,324
0
89,947
4.25%
4.24%
3
AQs
1,084
45
2,590
6,246
53,635
24,324
0
87,924
4.15%
4.14%
4
AKs
1,084
0
2,605
7,416
51,013
24,324
0
86,442
4.08%
4.08%
5
A9s
49
180
2,554
3,114
63,607
5,100
0
74,604
3.52%
3.53%
6
A6s
49
133
2,536
882
63,607
5,100
0
72,307
3.41%
3.41%
7
JTs
1,084
3,105
2,071
3,744
0
62,124
0
72,128
3.40%
3.40%
8
A8s
49
133
2,548
2,220
60,897
5,100
0
70,947
3.35%
3.34%
9
A7s
49
133
2,542
1,476
60,897
5,100
0
70,197
3.31%
3.31%
10
A5s
49
1,123
2,530
333
59,850
5,100
0
68,985
3.26%
3.26%
           
11
JTo
94
315
2,098
3,918
230
62,142
0
68,797
3.25%
3.25%
12
A4s
49
1,075
2,533
135
56,714
5,100
0
65,606
3.10%
3.10%
13
KQs
1,084
1,035
2,173
6,120
16,719
36,924
0
64,055
3.02%
3.02%
14
QJs
1,084
2,070
2,101
4,860
3,848
49,524
0
63,487
3.00%
3.00%
15
KJs
1,084
1,080
2,158
5,070
16,808
36,924
0
63,124
2.98%
2.98%
16
QTs
1,084
2,115
2,086
3,930
3,848
49,524
0
62,587
2.95%
2.95%
17
KTs
1,084
1,125
2,143
4,104
16,984
36,924
0
62,364
2.94%
2.95%
18
A3s
49
946
2,536
24
53,635
5,100
0
62,290
2.94%
2.94%
19
A2s
49
0
2,539
0
51,013
5,100
0
58,701
2.77%
2.78%
20
QJo
94
225
2,122
5,058
1,283
49,542
0
58,324
2.75%
2.76%
           
21
QTo
94
270
2,107
4,042
1,045
49,542
0
57,100
2.69%
2.70%
22
KQo
94
135
2,188
6,342
3,408
36,942
0
49,109
2.32%
2.32%
23
T9s
49
4,140
2,050
2,772
0
38,700
0
47,711
2.25%
2.25%
24
KJo
94
180
2,173
5,198
2,568
36,942
0
47,155
2.23%
2.23%
25
KTo
94
225
2,158
4,158
2,327
36,942
0
45,904
2.17%
2.16%
26
T9o
49
313
2,074
2,922
0
38,700
0
44,058
2.08%
2.08%
27
AKo
94
45
2,614
7,662
7,488
24,342
0
42,245
1.99%
1.99%
28
AA
94
0
16,624
0
10,028
5,100
9,300
41,146
1.94%
1.94%
29
AQo
94
90
2,599
6,390
6,164
24,342
0
39,679
1.87%
1.88%
30
AJo
94
135
2,584
5,222
5,317
24,342
0
37,694
1.78%
1.78%
           
31
KK
94
90
16,162
0
4,600
5,100
11,400
37,446
1.77%
1.77%
32
98s
4
3,013
2,038
1,944
0
30,000
0
36,999
1.75%
1.74%
33
ATo
94
180
2,569
4,158
5,070
24,342
0
36,413
1.72%
1.71%
34
87s
4
3,013
2,026
1,260
0
30,000
0
36,303
1.71%
1.71%
35
76s
4
3,013
2,014
720
0
30,000
0
35,751
1.69%
1.69%
36
65s
4
3,013
2,002
333
0
30,000
0
35,352
1.67%
1.67%
37
J9s
49
3,150
2,065
2,934
609
26,100
0
34,907
1.65%
1.65%
38
98o
4
266
2,062
2,070
0
30,000
0
34,402
1.62%
1.63%
39
87o
4
266
2,050
1,362
0
30,000
0
33,682
1.59%
1.59%
40
T8s
49
3,195
2,044
2,082
0
26,100
0
33,470
1.58%
1.58%
           
41
76o
4
266
2,038
798
0
30,000
0
33,106
1.56%
1.56%
42
65o
4
266
2,026
393
0
30,000
0
32,689
1.54%
1.54%
43
J9o
49
268
2,083
3,030
231
26,100
0
31,761
1.50%
1.50%
44
54s
4
3,007
1,999
135
0
26,400
0
31,545
1.49%
1.48%
45
T8o
49
313
2,062
2,162
0
26,100
0
30,686
1.45%
1.45%
46
K9s
49
1,170
2,137
3,222
17,771
5,100
0
29,449
1.39%
1.39%
47
K5s
49
178
2,113
513
20,946
5,100
0
28,899
1.36%
1.36%
48
54o
4
221
2,026
162
0
26,400
0
28,813
1.36%
1.36%
49
K4s
49
133
2,116
207
20,765
5,100
0
28,370
1.34%
1.34%
50
K3s
49
88
2,119
36
20,586
5,100
0
27,978
1.32%
1.32%
           
51
K2s
49
45
2,122
0
20,435
5,100
0
27,751
1.31%
1.31%
52
K8s
49
225
2,131
2,322
17,921
5,100
0
27,748
1.31%
1.31%
53
97s
4
3,058
2,032
1,374
0
21,000
0
27,468
1.30%
1.30%
54
86s
4
3,058
2,020
810
0
21,000
0
26,892
1.27%
1.26%
55
K7s
49
178
2,125
1,566
17,724
5,100
0
26,742
1.26%
1.26%
56
75s
4
3,058
2,008
405
0
21,000
0
26,475
1.25%
1.25%
57
64s
4
3,013
2,005
135
0
21,000
0
26,157
1.23%
1.23%
58
QQ
94
180
15,646
0
2,074
5,100
3,000
26,094
1.23%
1.23%
59
K6s
49
178
2,119
954
17,539
5,100
0
25,939
1.22%
1.23%
60
Q9s
49
2,160
2,080
3,084
4,463
14,100
0
25,936
1.22%
1.23%
           
61
97o
4
266
2,050
1,438
0
21,000
0
24,758
1.17%
1.17%
62
86o
4
266
2,038
858
0
21,000
0
24,166
1.14%
1.15%
63
75o
4
266
2,026
441
0
21,000
0
23,737
1.12%
1.12%
64
64o
4
221
2,023
159
0
21,000
0
23,407
1.10%
1.10%
65
53s
4
3,007
2,002
24
0
17,400
0
22,437
1.06%
1.06%
66
J8s
49
2,205
2,059
2,208
609
14,100
0
21,230
1.00%
1.00%
67
JJ
94
270
15,180
0
460
5,100
0
21,104
1.00%
0.99%
68
Q9o
49
223
2,092
3,130
1,046
14,100
0
20,640
0.97%
0.97%
69
TT
94
360
14,720
0
0
5,100
0
20,274
0.96%
0.96%
70
T7s
49
2,250
2,038
1,476
0
14,100
0
19,913
0.94%
0.94%
           
71
53o
4
176
2,023
28
0
17,400
0
19,631
0.93%
0.93%
72
J8o
49
268
2,071
2,246
231
14,100
0
18,965
0.90%
0.90%
73
T7o
49
313
2,050
1,506
0
14,100
0
18,018
0.85%
0.85%
74
43s
4
1,972
2,005
24
0
13,800
0
17,805
0.84%
0.84%
75
A9o
49
133
2,554
3,114
5,061
5,100
0
16,011
0.76%
0.75%
76
43o
4
131
2,026
28
0
13,800
0
15,989
0.75%
0.75%
77
99
4
266
14,456
0
0
600
0
15,326
0.72%
0.72%
78
Q8s
49
1,214
2,074
2,322
4,468
5,100
0
15,227
0.72%
0.72%
79
A8o
49
133
2,548
2,218
5,066
5,100
0
15,114
0.71%
0.71%
80
88
4
266
14,194
0
0
600
0
15,064
0.71%
0.71%
           
81
77
4
266
13,926
0
0
600
0
14,796
0.70%
0.70%
82
96s
4
2,200
2,026
888
0
9,600
0
14,718
0.69%
0.69%
83
66
4
266
13,652
0
0
600
0
14,522
0.69%
0.69%
84
A7o
49
133
2,542
1,470
5,066
5,100
0
14,360
0.68%
0.68%
85
85s
4
2,200
2,014
465
0
9,600
0
14,283
0.67%
0.68%
86
55
4
266
13,398
0
0
600
0
14,268
0.67%
0.67%
87
44
4
176
13,358
0
0
600
0
14,138
0.67%
0.67%
88
33
4
86
13,312
0
0
600
0
14,002
0.66%
0.66%
89
74s
4
2,155
2,011
177
0
9,600
0
13,947
0.66%
0.66%
90
22
4
0
13,262
0
0
600
0
13,866
0.65%
0.66%
           
91
A6o
49
133
2,536
870
5,061
5,100
0
13,749
0.65%
0.65%
92
63s
4
2,110
2,008
24
0
9,600
0
13,746
0.65%
0.65%
93
Q7s
49
270
2,068
1,566
4,471
5,100
0
13,524
0.64%
0.64%
94
A5o
49
133
2,557
375
5,070
5,100
0
13,284
0.63%
0.63%
95
A4o
49
88
2,548
153
5,079
5,100
0
13,017
0.61%
0.62%
96
K9o
49
178
2,143
3,222
2,324
5,100
0
13,016
0.61%
0.61%
97
A3o
49
43
2,545
28
5,089
5,100
0
12,854
0.61%
0.60%
98
Q6s
49
223
2,062
954
4,464
5,100
0
12,852
0.61%
0.60%
99
96o
4
266
2,038
910
0
9,600
0
12,818
0.60%
0.60%
100
A2o
49
0
2,548
0
5,101
5,100
0
12,798
0.60%
0.61%
           
101
Q5s
49
223
2,056
513
4,653
5,100
0
12,594
0.59%
0.59%
102
85o
4
266
2,026
481
0
9,600
0
12,377
0.58%
0.58%
103
Q4s
49
178
2,059
207
4,647
5,100
0
12,240
0.58%
0.58%
104
K8o
49
178
2,131
2,322
2,322
5,100
0
12,102
0.57%
0.57%
105
74o
4
221
2,023
187
0
9,600
0
12,035
0.57%
0.57%
106
Q3s
49
133
2,062
36
4,641
5,100
0
12,021
0.57%
0.57%
107
Q2s
49
90
2,065
0
4,636
5,100
0
11,940
0.56%
0.56%
108
63o
4
176
2,020
28
0
9,600
0
11,828
0.56%
0.56%
109
K7o
49
178
2,125
1,566
2,324
5,100
0
11,342
0.54%
0.53%
110
Q8o
49
223
2,080
2,322
1,046
5,100
0
10,820
0.51%
0.52%
           
111
K6o
49
178
2,119
954
2,327
5,100
0
10,727
0.51%
0.51%
112
J7s
49
1,259
2,053
1,566
609
5,100
0
10,636
0.50%
0.50%
113
K5o
49
178
2,113
513
2,315
5,100
0
10,268
0.48%
0.49%
114
52s
4
2,104
2,005
0
0
6,000
0
10,113
0.48%
0.47%
115
Q7o
49
223
2,068
1,566
1,046
5,100
0
10,052
0.47%
0.48%
116
K4o
49
133
2,116
207
2,318
5,100
0
9,923
0.47%
0.47%
117
K3o
49
88
2,119
36
2,320
5,100
0
9,712
0.46%
0.46%
118
K2o
49
45
2,122
0
2,321
5,100
0
9,637
0.45%
0.45%
119
T6s
49
1,304
2,032
954
0
5,100
0
9,439
0.45%
0.45%
120
Q6o
49
223
2,062
954
1,046
5,100
0
9,434
0.45%
0.44%
           
121
42s
4
1,972
2,008
0
0
5,400
0
9,384
0.44%
0.44%
122
J7o
49
268
2,059
1,566
231
5,100
0
9,273
0.44%
0.44%
123
J6s
49
315
2,047
954
609
5,100
0
9,074
0.43%
0.43%
124
Q5o
49
223
2,056
513
1,043
5,100
0
8,984
0.42%
0.42%
125
J6o
49
268
2,047
954
231
5,100
0
8,649
0.41%
0.41%
126
Q4o
49
178
2,059
207
1,043
5,100
0
8,636
0.41%
0.41%
127
J5s
49
268
2,041
513
615
5,100
0
8,586
0.41%
0.40%
128
T6o
49
313
2,038
954
0
5,100
0
8,454
0.40%
0.40%
129
Q3o
49
133
2,062
36
1,043
5,100
0
8,423
0.40%
0.40%
130
Q2o
49
90
2,065
0
1,043
5,100
0
8,347
0.39%
0.39%
           
131
J4s
49
223
2,044
207
615
5,100
0
8,238
0.39%
0.39%
132
J5o
49
268
2,041
513
231
5,100
0
8,202
0.39%
0.39%
133
52o
4
133
2,020
0
0
6,000
0
8,157
0.38%
0.38%
134
T5s
49
360
2,026
513
0
5,100
0
8,048
0.38%
0.38%
135
J3s
49
178
2,047
36
615
5,100
0
8,025
0.38%
0.38%
136
T5o
49
313
2,026
513
0
5,100
0
8,001
0.38%
0.38%
137
J2s
49
135
2,050
0
615
5,100
0
7,949
0.38%
0.37%
138
J4o
49
223
2,044
207
231
5,100
0
7,854
0.37%
0.37%
139
T4s
49
268
2,029
207
0
5,100
0
7,653
0.36%
0.36%
140
T4o
49
268
2,029
207
0
5,100
0
7,653
0.36%
0.36%
           
141
J3o
49
178
2,047
36
231
5,100
0
7,641
0.36%
0.36%
142
J2o
49
135
2,050
0
231
5,100
0
7,565
0.36%
0.35%
143
42o
4
88
2,023
0
0
5,400
0
7,515
0.35%
0.35%
144
T3s
49
223
2,032
36
0
5,100
0
7,440
0.35%
0.35%
145
T3o
49
223
2,032
36
0
5,100
0
7,440
0.35%
0.35%
146
T2s
49
180
2,035
0
0
5,100
0
7,364
0.35%
0.35%
147
T2o
49
180
2,035
0
0
5,100
0
7,364
0.35%
0.35%
148
32s
4
940
2,011
0
0
3,000
0
5,955
0.28%
0.28%
149
32o
4
43
2,026
0
0
3,000
0
5,073
0.24%
0.24%
150
95s
4
1,258
2,020
513
0
600
0
4,395
0.21%
0.21%
           
151
84s
4
1,213
2,017
207
0
600
0
4,041
0.19%
0.19%
152
73s
4
1,168
2,014
36
0
600
0
3,822
0.18%
0.18%
153
62s
4
1,123
2,011
0
0
600
0
3,738
0.18%
0.18%
154
95o
4
266
2,026
513
0
600
0
3,409
0.16%
0.16%
155
94s
4
268
2,023
207
0
600
0
3,102
0.15%
0.15%
156
94o
4
221
2,023
207
0
600
0
3,055
0.14%
0.14%
157
84o
4
221
2,023
207
0
600
0
3,055
0.14%
0.14%
158
83s
4
223
2,020
36
0
600
0
2,883
0.14%
0.14%
159
93s
4
176
2,026
36
0
600
0
2,842
0.13%
0.13%
160
93o
4
176
2,026
36
0
600
0
2,842
0.13%
0.13%
           
161
83o
4
176
2,020
36
0
600
0
2,836
0.13%
0.13%
162
73o
4
176
2,020
36
0
600
0
2,836
0.13%
0.14%
163
72s
4
178
2,017
0
0
600
0
2,799
0.13%
0.14%
164
92s
4
133
2,029
0
0
600
0
2,766
0.13%
0.13%
165
92o
4
133
2,029
0
0
600
0
2,766
0.13%
0.13%
166
82s
4
133
2,023
0
0
600
0
2,760
0.13%
0.13%
167
82o
4
133
2,023
0
0
600
0
2,760
0.13%
0.13%
168
72o
4
133
2,017
0
0
600
0
2,754
0.13%
0.13%
169
62o
4
133
2,017
0
0
600
0
2,754
0.13%
0.13%
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