これらから導かれたデータです。
ようやく計算式と答えが合致したので掲載。
なんだよ連続補正って…完全に忘れてたわ…
下の表の解説をします。
1番左が「あと何回攻撃を当てたら勝てるか」
左から2番目が「あと何回攻撃を当てられたら負けるか」
左から3番目はよくわからん人は無視していいけど「標準正規分布での累積分布でどの位置になったか」
一番右が「勝率」
例えばスマブラでこっちが１スト0％、相手が２スト0％として10回攻撃を当てたらバーストできると考えた場合の勝率は
「20 10 -1.8569533818 0.0307141729」
と書いてあるので3％になる。（一番右の0.0307141729が3％の意味）
逆にこっちが有利でこっちが2スト0％、相手が1スト0％なら勝率は97％になる。
当然じゃんけんには半々の確率で勝つ前提（つまり実力が五分と仮定）
1 1 +0.0000000000 0.5000000000
2 1 -0.7071067812 0.2500000000
2 2 +0.0000000000 0.5000000000
3 1 -1.1547005384 0.1250000000
3 2 -0.5000000000 0.3125000000
3 3 +0.0000000000 0.5000000000
4 1 -1.5000000000 0.0625000000
4 2 -0.8944271910 0.1875000000
4 3 -0.4082482905 0.3437500000
4 4 +0.0000000000 0.5000000000
5 1 -1.7888543820 0.0312500000
5 2 -1.2247448714 0.1093750000
5 3 -0.7559289460 0.2265625000
5 4 -0.3535533906 0.3632812500
5 5 +0.0000000000 0.5000000000
6 1 -2.0412414523 0.0156250000
6 2 -1.5118578920 0.0625000000
6 3 -1.0606601718 0.1445312500
6 4 -0.6666666667 0.2539062500
6 5 -0.3162277660 0.3769531250
6 6 +0.0000000000 0.5000000000
7 1 -2.2677868381 0.0078125000
7 2 -1.7677669530 0.0351562500
7 3 -1.3333333333 0.0898437500
7 4 -0.9486832981 0.1718750000
7 5 -0.6030226892 0.2744140625
7 6 -0.2886751346 0.3872070312
7 7 +0.0000000000 0.5000000000
8 1 -2.4748737342 0.0039062500
8 2 -2.0000000000 0.0195312500
8 3 -1.5811388301 0.0546875000
8 4 -1.2060453783 0.1132812500
8 5 -0.8660254038 0.1938476562
8 6 -0.5547001962 0.2905273438
8 7 -0.2672612419 0.3952636719
8 8 +0.0000000000 0.5000000000
9 1 -2.6666666667 0.0019531250
9 2 -2.2135943621 0.0107421875
9 3 -1.8090680675 0.0327148438
9 4 -1.4433756730 0.0729980469
9 5 -1.1094003925 0.1334228516
9 6 -0.8017837257 0.2119750977
9 7 -0.5163977795 0.3036193848
9 8 -0.2500000000 0.4018096924
9 9 +0.0000000000 0.5000000000
10 1 -2.8460498942 0.0009765625
10 2 -2.4120907566 0.0058593750
10 3 -2.0207259422 0.0192871094
10 4 -1.6641005887 0.0461425781
10 5 -1.3363062096 0.0897827148
10 6 -1.0327955590 0.1508789062
10 7 -0.7500000000 0.2272491455
10 8 -0.4850712501 0.3145294189
10 9 -0.2357022604 0.4072647095
10 10 +0.0000000000 0.5000000000
11 1 -3.0151134458 0.0004882812
11 2 -2.5980762114 0.0031738281
11 3 -2.2188007849 0.0112304688
11 4 -1.8708286934 0.0286865234
11 5 -1.5491933385 0.0592346191
11 6 -1.2500000000 0.1050567627
11 7 -0.9701425001 0.1661529541
11 8 -0.7071067812 0.2403411865
11 9 -0.4588314677 0.3238029480
11 10 -0.2236067977 0.4119014740
11 11 +0.0000000000 0.5000000000
12 1 -3.1754264805 0.0002441406
12 2 -2.7735009811 0.0017089844
12 3 -2.4053511772 0.0064697266
12 4 -2.0655911180 0.0175781250
12 5 -1.7500000000 0.0384063721
12 6 -1.4552137502 0.0717315674
12 7 -1.1785113020 0.1189422607
12 8 -0.9176629355 0.1796417236
12 9 -0.6708203932 0.2517223358
12 10 -0.4364357805 0.3318119049
12 11 -0.2132007164 0.4159059525
12 12 +0.0000000000 0.5000000000
13 1 -3.3282011774 0.0001220703
13 2 -2.9398736610 0.0009155273
13 3 -2.5819888975 0.0036926270
13 4 -2.2500000000 0.0106353760
13 5 -1.9402850003 0.0245208740
13 6 -1.6499158228 0.0481262207
13 7 -1.3764944032 0.0835342407
13 8 -1.1180339887 0.1315879822
13 9 -0.8728715609 0.1916551590
13 10 -0.6396021491 0.2617335320
13 11 -0.4170288281 0.3388197422
13 12 -0.2041241452 0.4194098711
13 13 +0.0000000000 0.5000000000
14 1 -3.4743961449 0.0000610352
14 2 -3.0983866770 0.0004882812
14 3 -2.7500000000 0.0020904541
14 4 -2.4253562504 0.0063629150
14 5 -2.1213203436 0.0154418945
14 6 -1.8353258710 0.0317840576
14 7 -1.5652475842 0.0576591492
14 8 -1.3093073414 0.0946235657
14 9 -1.0660035818 0.1431393623
14 10 -0.8340576562 0.2024364471
14 11 -0.6123724357 0.2706280947
14 12 -0.4000000000 0.3450189829
14 13 -0.1961161351 0.4225094914
14 14 +0.0000000000 0.5000000000
15 1 -3.6147844565 0.0000305176
15 2 -3.2500000000 0.0002593994
15 3 -2.9104275004 0.0011749268
15 4 -2.5927248644 0.0037689209
15 5 -2.2941573387 0.0096054077
15 6 -2.0124611797 0.0206947327
15 7 -1.7457431219 0.0391769409
15 8 -1.4924050145 0.0669002533
15 9 -1.2510864843 0.1050198078
15 10 -1.0206207262 0.1537281275
15 11 -0.8000000000 0.2121781111
15 12 -0.5883484054 0.2785985470
15 13 -0.3849001795 0.3505540192
15 14 -0.1889822365 0.4252770096
15 15 +0.0000000000 0.5000000000
16 1 -3.7500000000 0.0000152588
16 2 -3.3954987505 0.0001373291
16 3 -3.0641293851 0.0006561279
16 4 -2.7529888064 0.0022125244
16 5 -2.4596747752 0.0059089661
16 6 -2.1821789024 0.0133018494
16 7 -1.9188064472 0.0262393951
16 8 -1.6681153125 0.0465698242
16 9 -1.4288690166 0.0757948160
16 10 -1.2000000000 0.1147614717
16 11 -0.9805806757 0.1634697914
16 12 -0.7698003589 0.2210341692
16 13 -0.5669467095 0.2857940942
16 14 -0.3713906764 0.3555355519
16 15 -0.1825741858 0.4277677760
16 16 +0.0000000000 0.5000000000
17 1 -3.8805700006 0.0000076294
17 2 -3.5355339059 0.0000724792
17 3 -3.2118202742 0.0003643036
17 4 -2.9068883707 0.0012884140
17 5 -2.6186146828 0.0035986900
17 6 -2.3452078799 0.0084502697
17 7 -2.0851441406 0.0173448324
17 8 -1.8371173071 0.0319573283
17 9 -1.6000000000 0.0538760722
17 10 -1.3728129460 0.0843187720
17 11 -1.1547005384 0.1238942817
17 12 -0.9449111825 0.1724642254
17 13 -0.7427813527 0.2291291598
17 14 -0.5477225575 0.2923323559
17 15 -0.3592106041 0.3600500659
17 16 -0.1767766953 0.4300250330
17 17 +0.0000000000 0.5000000000
18 1 -4.0069384267 0.0000038147
18 2 -3.6706517419 0.0000381470
18 3 -3.3541019662 0.0002012253
18 4 -3.0550504633 0.0007448196
18 5 -2.7716093126 0.0021717548
18 6 -2.5021729687 0.0053110123
18 7 -2.2453655976 0.0113279223
18 8 -2.0000000000 0.0216426253
18 9 -1.7650452162 0.0377593488
18 10 -1.5396007178 0.0610390604
18 11 -1.3228756555 0.0924666710
18 12 -1.1141720291 0.1324654482
18 13 -0.9128709292 0.1807973040
18 14 -0.7184212081 0.2365648299
18 15 -0.5303300859 0.2983074479
18 16 -0.3481553119 0.3641662404
18 17 -0.1714985851 0.4320831202
18 18 +0.0000000000 0.5000000000
19 1 -4.1294832097 0.0000019073
19 2 -3.8013155617 0.0000200272
19 3 -3.4914862438 0.0001106262
19 4 -3.1980107453 0.0004277229
19 5 -2.9192017968 0.0012997389
19 6 -2.6536138880 0.0033053756
19 7 -2.4000000000 0.0073166490
19 8 -2.1572774865 0.0144796371
19 9 -1.9245008973 0.0261194929
19 10 -1.7008401285 0.0435792767
19 11 -1.4855627054 0.0680229738
19 12 -1.2780193008 0.1002442110
19 13 -1.0776318122 0.1405207575
19 14 -0.8838834765 0.1885427937
19 15 -0.6963106238 0.2434251208
19 16 -0.5144957554 0.3037956806
19 17 -0.3380617019 0.3679394004
19 18 -0.1666666667 0.4339697002
19 19 +0.0000000000 0.5000000000
20 1 -4.2485291572 0.0000009537
20 2 -3.9279220242 0.0000104904
20 3 -3.6244121780 0.0000605583
20 4 -3.3362306249 0.0002441406
20 5 -3.0618621785 0.0007719398
20 6 -2.8000000000 0.0020386577
20 7 -2.5495097568 0.0046776533
20 8 -2.3094010768 0.0095786452
20 9 -2.0788046016 0.0178490691
20 10 -1.8569533818 0.0307141729
20 11 -1.6431676725 0.0493685734
20 12 -1.4368424162 0.0748063922
20 13 -1.2374368671 0.1076635749
20 14 -1.0444659357 0.1481031843
20 15 -0.8574929257 0.1957641526
20 16 -0.6761234038 0.2497799166
20 17 -0.5000000000 0.3088596585
20 18 -0.3287979746 0.3714146794
20 19 -0.1622214211 0.4357073397
20 20 +0.0000000000 0.5000000000
21 1 -4.3643578047 0.0000004768
21 2 -4.0508136108 0.0000054836
21 3 -3.7532594530 0.0000330210
21 4 -3.4701104689 0.0001385808
21 5 -3.2000000000 0.0004552603
21 6 -2.9417420271 0.0012469590
21 7 -2.6943012562 0.0029623061
21 8 -2.4567690746 0.0062704757
21 9 -2.2283440581 0.0120597724
21 10 -2.0083160442 0.0213869726
21 11 -1.7960530203 0.0353777730
21 12 -1.5909902577 0.0550920826
21 13 -1.3926212476 0.0813778287
21 14 -1.2004900960 0.1147405065
21 15 -1.0141851057 0.1552523295
21 16 -0.8333333333 0.2025161231
21 17 -0.6575959492 0.2556878908
21 18 -0.4866642634 0.3135512851
21 19 -0.3202563076 0.3746293124
21 20 -0.1581138830 0.4373146562
21 21 +0.0000000000 0.5000000000
22 1 -4.4772150435 0.0000002384
22 2 -4.1702882811 0.0000028610
22 3 -3.8783587594 0.0000179410
22 4 -3.6000000000 0.0000782609
22 5 -3.3339742973 0.0002667606
22 6 -3.0792014357 0.0007568598
22 7 -2.8347335476 0.0018595830
22 8 -2.5997347345 0.0040650293
22 9 -2.3734644159 0.0080624009
22 10 -2.1552636243 0.0147246867
22 11 -1.9445436483 0.0250512299
22 12 -1.7407765596 0.0400716562
22 13 -1.5434872663 0.0607247425
22 14 -1.3522468076 0.0877326245
22 15 -1.1666666667 0.1214924770
22 16 -0.9863939238 0.1620043000
22 17 -0.8111071057 0.2088460954
22 18 -0.6405126152 0.2611986902
22 19 -0.4743416490 0.3179140013
22 20 -0.3123475238 0.3776143288
22 21 -0.1543033500 0.4388071644
22 22 +0.0000000000 0.5000000000
23 1 -4.5873171093 0.0000001192
23 2 -4.2866070499 0.0000014901
23 3 -4.0000000000 0.0000097156
23 4 -3.7262065676 0.0000439882
23 5 -3.4641016151 0.0001553744
23 6 -3.2126980206 0.0004561171
23 7 -2.9711254108 0.0011578500
23 8 -2.7386127875 0.0026114397
23 9 -2.5144742284 0.0053369203
23 10 -2.2980970389 0.0100308035
23 11 -2.0889318715 0.0175410167
23 12 -1.8864844366 0.0288063365
23 13 -1.6903085095 0.0447655395
23 14 -1.5000000000 0.0662490820
23 15 -1.3151918984 0.0938707795
23 16 -1.1355499479 0.1279375398
23 17 -0.9607689228 0.1683918176
23 18 -0.7905694150 0.2147952539
23 19 -0.6246950476 0.2663546276
23 20 -0.4629100499 0.3219844782
23 21 -0.3049971407 0.3803958213
23 22 -0.1507556723 0.4401979106
23 23 +0.0000000000 0.5000000000
24 1 -4.6948553403 0.0000000596
24 2 -4.4000000000 0.0000007749
24 3 -4.1184388379 0.0000052452
24 4 -3.8490017946 0.0000246167
24 5 -3.5906624936 0.0000899956
24 6 -3.3425160872 0.0002730563
24 7 -3.1037611592 0.0007154532
24 8 -2.8736848324 0.0016634464
24 9 -2.6516504294 0.0035001833
24 10 -2.4370871834 0.0067654934
24 11 -2.2294816069 0.0121532551
24 12 -2.0283702113 0.0204797958
24 13 -1.8333333333 0.0326226676
24 14 -1.6439898731 0.0494358748
24 15 -1.4599927902 0.0716533271
24 16 -1.2810252304 0.0997954335
24 17 -1.1067971811 0.1340936255
24 18 -0.9370425713 0.1744444397
24 19 -0.7715167498 0.2203995337
24 20 -0.6099942813 0.2711920059
24 21 -0.4522670169 0.3257939136
24 22 -0.2981423970 0.3829959121
24 23 -0.1474419562 0.4414979561
24 24 +0.0000000000 0.5000000000
25 1 -4.8000000000 0.0000000298
25 2 -4.5106711082 0.0000004023
25 3 -4.2339019741 0.0000028238
25 4 -3.9686269666 0.0000137202
25 5 -3.7139067635 0.0000518579
25 6 -3.4689095309 0.0001624571
25 7 -3.2328954365 0.0004389551
25 8 -3.0052038200 0.0010512008
25 9 -2.7852424953 0.0022756921
25 10 -2.5724787771 0.0045205927
25 11 -2.3664319132 0.0083369239
25 12 -2.1666666667 0.0144083598
25 13 -1.9727878477 0.0235155137
25 14 -1.7844356324 0.0364756943
25 15 -1.6012815381 0.0540645107
25 16 -1.4230249471 0.0769299721
25 17 -1.2493900951 0.1055117988
25 18 -1.0801234497 0.1399781193
25 19 -0.9149914220 0.1801888265
25 20 -0.7537783614 0.2256904162
25 21 -0.5962847940 0.2757421649
25 22 -0.4423258685 0.3293690385
25 23 -0.2917299830 0.3854334973
25 24 -0.1443375673 0.4427167486
25 25 +0.0000000000 0.5000000000
26 1 -4.9029033785 0.0000000149
26 2 -4.6188021535 0.0000002086
26 3 -4.3465914396 0.0000015162
26 4 -4.0852974399 0.0000076182
26 5 -3.8340579025 0.0000297381
26 6 -3.5921060405 0.0000960976
26 7 -3.3587572106 0.0002675264
26 8 -3.1333978072 0.0006593636
26 9 -2.9154759474 0.0014675278
26 10 -2.7044936151 0.0029940603
26 11 -2.5000000000 0.0056654921
26 12 -2.3015858223 0.0100369260
26 13 -2.1088784747 0.0167762198
26 14 -1.9215378457 0.0266259570
26 15 -1.7392527131 0.0403452339
26 16 -1.5617376189 0.0586376030
26 17 -1.3887301497 0.0820747009
26 18 -1.2199885627 0.1110264101
26 19 -1.0552897060 0.1456076183
26 20 -0.8944271910 0.1856490172
26 21 -0.7372097808 0.2306955911
26 22 -0.5834599660 0.2800323148
26 23 -0.4330127019 0.3327329060
26 24 -0.2857142857 0.3877248273
26 25 -0.1414213562 0.4438624137
26 26 +0.0000000000 0.5000000000
27 1 -5.0037023330 0.0000000075
27 2 -4.7245559126 0.0000001080
27 3 -4.4566881162 0.0000008121
27 4 -4.1992062742 0.0000042152
27 5 -3.9513166446 0.0000169766
27 6 -3.7123106012 0.0000565371
27 7 -3.4815531191 0.0001620317
27 8 -3.2584731177 0.0004106977
27 9 -3.0425553170 0.0009391127
27 10 -2.8333333333 0.0019665865
27 11 -2.6303837969 0.0038160393
27 12 -2.4333213170 0.0069264826
27 13 -2.2417941533 0.0118513512
27 14 -2.0554804791 0.0192386541
27 15 -1.8740851427 0.0297919440
27 16 -1.6973368496 0.0442147735
27 17 -1.5249857033 0.0631447372
27 18 -1.3568010506 0.0870855736
27 19 -1.1925695880 0.1163465960
27 20 -1.0320936931 0.1509978066
27 21 -0.8751899490 0.1908466988
27 22 -0.7216878365 0.2354395068
27 23 -0.5714285714 0.2840862064
27 24 -0.4242640687 0.3359055169
27 25 -0.2800560168 0.3898839653
27 26 -0.1386750491 0.4449419826
27 27 +0.0000000000 0.5000000000
28 1 -5.1025203856 0.0000000037
28 2 -4.8280787926 0.0000000559
28 3 -4.5643546459 0.0000004340
28 4 -4.3105272486 0.0000023246
28 5 -4.0658639918 0.0000096506
28 6 -3.8297084310 0.0000330938
28 7 -3.6014702880 0.0000975628
28 8 -3.3806170189 0.0002541302
28 9 -3.1666666667 0.0005966215
28 10 -2.9591817715 0.0012816040
28 11 -2.7577641592 0.0025488216
28 12 -2.5620504609 0.0047376521
28 13 -2.3717082451 0.0082945017
28 14 -2.1864326664 0.0137665779
28 15 -2.0059435495 0.0217792610
28 16 -1.8299828440 0.0329970172
28 17 -1.6583123952 0.0480708772
28 18 -1.4907119850 0.0675782254
28 19 -1.3269776054 0.0919624107
28 20 -1.1669199320 0.1214801086
28 21 -1.0103629711 0.1561634037
28 22 -0.8571428571 0.1958014553
28 23 -0.7071067812 0.2399438308
28 24 -0.5601120336 0.2879246739
28 25 -0.4160251472 0.3389043196
28 26 -0.2747211279 0.3919231511
28 27 -0.1360827635 0.4459615756
28 28 +0.0000000000 0.5000000000
29 1 -5.1994694690 0.0000000019
29 2 -4.9295030175 0.0000000289
29 3 -4.6697378527 0.0000002314
29 4 -4.4194173824 0.0000012780
29 5 -4.1778637429 0.0000054643
29 6 -3.9444674583 0.0000192791
29 7 -3.7186787208 0.0000584209
29 8 -3.5000000000 0.0001562756
29 9 -3.2879797461 0.0003764485
29 10 -3.0822070015 0.0008290263
29 11 -2.8823067685 0.0016889240
29 12 -2.6879360111 0.0032132880
29 13 -2.4987801902 0.0057538949
29 14 -2.3145502494 0.0097602364
29 15 -2.1349799847 0.0157697487
29 16 -1.9598237398 0.0243833830
29 17 -1.7888543820 0.0362271301
29 18 -1.6218615177 0.0519026778
29 19 -1.4586499150 0.0719325442
29 20 -1.2990381057 0.0967063264
29 21 -1.1428571429 0.1264348651
29 22 -0.9899494937 0.1611181602
29 23 -0.8401680504 0.2005309955
29 24 -0.6933752453 0.2442278347
29 25 -0.5494422558 0.2915660771
29 26 -0.4082482905 0.3417446141
29 27 -0.2696799450 0.3938530948
29 28 -0.1336306210 0.4469265474
29 29 +0.0000000000 0.5000000000
30 1 -5.2946513892 0.0000000009
30 2 -5.0289484567 0.0000000149
30 3 -4.7729707730 0.0000001232
30 4 -4.5260190548 0.0000007006
30 5 -4.2874646286 0.0000030824
30 6 -4.0567404227 0.0000111808
30 7 -3.8333333333 0.0000348008
30 8 -3.6167777207 0.0000955382
30 9 -3.4066498437 0.0002359934
30 10 -3.2025630761 0.0005325098
30 11 -3.0041637772 0.0011107169
30 12 -2.8111277140 0.0021620025
30 13 -2.6231569494 0.0039579487
30 14 -2.4399771253 0.0068590925
30 15 -2.2613350843 0.0113144206
30 16 -2.0869967790 0.0178489018
30 17 -1.9167454300 0.0270380159
30 18 -1.7503798980 0.0394703468
30 19 -1.5877132403 0.0557014455
30 20 -1.4285714286 0.0762038860
30 21 -1.2727922061 0.1013193755
30 22 -1.1202240672 0.1312187679
30 23 -0.9707253434 0.1658748817
30 24 -0.8241633837 0.2050513582
30 25 -0.6804138174 0.2483087177
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30 30 +0.0000000000 0.5000000000
