Début du sujet 20/01/2009 2:35 pm
En provenance du site de Victor...
Hi all,
I happened to see that someone had posted statistics from a multimillion spins investigation on "another" board.
Because I like you people here so much, I post these tables so that you don't have to do the same kind of boring and time-consuming tests again, just because your amount of spins isn't 12M...
And NO; I didn't run some thousands of billions of spins to get to these figures: [b]I used my calculator[/b] ;D
Very simple.
[i]Please [b]compare[/b] these figures to tests that you have seen or done![/i]
(The "50/50" values are true 50% chance - like coin-tossing)
[size=12pt][i][b]SINGLE ZERO TABLES[/b][/i][/size]
[b]How many trials do we need, MATHEMATICALLY AND IN AVERAGE, to find a sequence of AT LEAST length X?[/b]
[tt]X 50/50 "Even" Cl/Dz DblStr
2: 3 3 8 37
3: 7 7 28 233
4: 15 16 89 1,445
5: 31 35 277 8,916
6: 63 74 858 54,991
7: 127 154 2,648 339,118
8: 255 317 8,167 2,091,238
9: 511 654 25,186 [b]12,895,976[/b]
10: 1,023 1,345 77,660 79,525,192
11: 2,047 2,767 239,454 490,405,361
12: 4,095 5,689 738,320 3,024,166,401
13: 8,191 11,696 2,276,491 18,649,026,147
14: 16,383 24,043 [b]7,019,184[/b] 115,002,327,911
15: 32,767 49,423 [b]21,642,486[/b] 709,181,022,129
16: 65,535 101,592 66,731,001 4,373,282,969,801
17: 131,071 208,830 205,753,922
18: 262,143 429,264 634,407,931
19: 524,287 882,377 1,956,091,122
20: 1,048,575 1,813,778 6,031,280,963
21: 2,097,151 3,728,322 18,596,449,640
22: 4,194,303 [b]7,663,775[/b] 57,339,053,061
23: [b]8,388,607[/b] [b]15,753,316[/b] 176,795,413,608
24: [b]16,777,215[/b] 32,381,819 545,119,191,962
25: 33,554,431 66,562,629 1,680,784,175,221
26: 67,108,863 136,823,183 5,182,417,873,600
27: 134,217,727 281,247,655
28: 268,435,455 578,120,181
29: 536,870,911 1,188,358,151
30: 1,073,741,823 2,442,736,201
[/tt]
[b]How many trials do we need, MATHEMATICALLY AND IN AVERAGE, to find a sequence of AT LEAST length X?[/b]
[tt]X Corner SngStr Split Single
2: 84 151 341 1,368
3: 790 1,875 6,330 50,652
4: 7,319 23,136 117,134 [b]1,874,160[/b]
5: 67,717 285,365 [b]2,166,997[/b] [b]69,343,956[/b]
6: 626,397 [b]3,519,513[/b] [b]40,089,474[/b] 2,565,726,408
7: [b]5,794,180[/b] [b]43,407,350[/b] 741,655,289 94,931,877,132
8: [b]53,596,182[/b] 535,357,330 13,720,622,865 3,512,479,453,920
9: 495,764,692 6,602,740,424 253,831,523,036
10: 4,585,823,413 81,433,798,580 4,695,883,176,188
11: 42,418,866,580 1,004,350,182,499
12: 392,374,515,880
13: 3,629,464,271,903
[/tt]
... and the opposite:
[b]How long sequences can we expect, MATHEMATICALLY AND IN AVERAGE, in X trials?[/b]
[tt]X 50/50 "Even" Cl/Dz DblStr Corner SngStr Split Single
1,000 9 9 6 3 3 2 2 1
5,000 12 11 7 4 3 3 2 2
10K 13 12 8 5 4 3 3 2
50K 15 15 9 5 4 4 3 2
100K 16 15 10 6 5 4 3 3
500K 18 18 11 7 5 5 4 3
1M 19 19 12 7 6 5 4 3
5M 22 21 13 8 6 6 5 4
10M 23 22 14 8 7 6 5 4
[b]12M 23 22 14 8 7 6 5 4[/b]
15M 23 22 14 9 7 6 5 4
20M 24 23 14 9 7 6 5 4
25M 24 23 15 9 7 6 5 4
50M 25 24 15 9 7 7 6 4
100M 26 25 16 10 8 7 6 5
1000M 29 28 18 11 9 8 7 5
[/tt]
[size=12pt][i][b]DOUBLE ZERO TABLES[/b][/i][/size]
[b]How many trials do we need, MATHEMATICALLY AND IN AVERAGE, to find a sequence of AT LEAST length X?[/b]
[tt]X 50/50 "Even" Cl/Dz DblStr
2: 3 3 9 39
3: 7 8 30 253
4: 15 18 99 1,607
5: 31 40 317 10,188
6: 63 87 1,007 64,533
7: 127 185 3,192 408,719
8: 255 393 10,110 2,588,562
9: 511 831 32,018 16,394,232
10: 1,023 1,757 101,395 103,830,144
11: 2,047 3,711 321,088 657,590,920
12: 4,095 7,835 1,016,781 4,164,742,499
13: 8,191 16,543 3,219,811 26,376,702,500
14: 16,383 34,925 10,196,071 167,052,449,175
15: 32,767 73,732 32,287,561 1,057,998,844,780
16: 65,535 155,659 102,243,946 6,700,659,350,280
17: 131,071 328,614 323,772,499
18: 262,143 693,743 1,025,279,584
19: 524,287 1,464,571 3,246,718,687
20: 1,048,575 3,091,873 10,281,275,844
21: 2,097,151 6,527,289 32,557,373,510
22: 4,194,303 13,779,833 103,098,349,450
23: 8,388,607 29,090,761 326,478,106,596
24: 16,777,215 61,413,830 1,033,847,337,557
25: 33,554,431 129,651,422 3,273,849,902,267
26: 67,108,863 273,708,558
27: 134,217,727 577,829,180
28: 268,435,455 1,219,861,604
29: 536,870,911 2,575,263,388
30: 1,073,741,823 5,436,667,154
[/tt]
[b]How many trials do we need, MATHEMATICALLY AND IN AVERAGE, to find a sequence of AT LEAST length X?[/b]
[tt]X Corner SngStr Split Single
2: 89 159 360 1,443
3: 856 2,031 6,858 54,871
4: 8,144 25,741 130,320 2,085,135
5: 77,377 326,069 2,476,098 79,235,167
6: 735,090 4,130,227 47,045,880 3,010,936,383
7: 6,983,371 52,316,223 893,871,738 114,415,582,591
8: 66,342,042 662,672,173 16,983,563,040 4,347,792,138,495
9: 630,249,408 8,393,847,545 322,687,697,778
10: 5,987,369,391 106,322,068,924 6,131,066,257,800
11: 56,880,009,226 1,346,746,206,390
12: 540,360,087,661
13: 5,133,420,832,794
[/tt]
... and the opposite:
[b]How long sequences can we expect, MATHEMATICALLY AND IN AVERAGE, in X trials?[/b]
[tt]X 50/50 "Even" Cl/Dz DblStr Corner SngStr Split Single
1,000 9 9 5 3 3 2 2 1
5,000 12 11 7 4 3 3 2 2
10K 13 12 7 4 4 3 3 2
50K 15 14 9 5 4 4 3 2
100K 16 15 9 6 5 4 3 3
500K 18 17 11 7 5 5 4 3
1M 19 18 11 7 6 5 4 3
5M 22 20 13 8 6 6 5 4
10M 23 21 13 8 7 6 5 4
12M 23 21 14 8 7 6 5 4
15M 23 22 14 8 7 6 5 4
20M 24 22 14 9 7 6 5 4
25M 24 22 14 9 7 6 5 4
50M 25 23 15 9 7 6 6 4
100M 26 24 15 9 8 7 6 5
1000M 29 27 17 11 9 8 7 5
[/tt]
If you've got a calculator... WHY spend time doing boring multimillion spins tests?
The end results are the same... Aren't they?
Regards,
KFS
20/01/2009 5:40 pm
Qui est ce Victor qui a l'air d'avoir un site bien connu ??
J'ai cherché mais je n'ai pas trouvé .
Merci .
20/01/2009 7:47 pm
Merci,
j'avais déjà mis ce forum dans mes favoris et n'avais pas fait le lien avec Victor.
Très intéressant.
Comme je me débrouille assez bien en Anglais, j'arrive à comprendre.
Par contre, les forums allemands, c'est plus compliqué