Originally Posted by
toolyp
Don Cacarulo, if I may rewong the game. Hopefully you or Don Vito wont whack me. Our argument is caused by the definition of streak. Warren Weaver and I define a streak in the context of n trials. For example a string of 2 consecutive heads H: THHT; 2 H surrounded by 2 Tails.
You Don Cacarulo, as well as Don Vito define a streak as the probability of n consecutive successes. Sometimes you convert p to 1/p to get the string as some like 1 in n.
You said “streak of 0 heads”. No offence, but there is no string of length 0. Nobody has ever seen a 0-length string. You also a programmer. Think what happens when you set a string to length 0. Methinks you have in mind the probability of exactly 0 successes when you say streak of 0. Of course the probability of at least 0 successes in n trials is always 1.
The example with 4 coin tosses is utterly limited for all intents and purposes. I went a little further and generated all possibilities of 10 coin tosses. Sure its still not sufficient. Ill say 100 trials is the minimum. I think of playing over 100 blackjack hands in a session.
Total possibilities is 2^10=1024. The probability of 10 consecutive wins (eg. H) is 0.5^10=0.0009765625 or 1 in 1024. Don Cacarulo and Don Vito say most of the time “1 string of 10 consecutive successes”.
I sez we need 12 tosses to get a 10-length streak: THHHHHHHHHHT. The probability for such string is lower now: 0.5^12=0.000244140625 or 1 in 4096.
As per my previous posts. When calculating the number of streaks as Warren Weaver, a number of trials are uncounted for. I know why. The streaks at the very beginning and the very end of any experiment explain why. They are open-ended. like HHT or THH. The formula doesn’t catch them. They are missing the 4th parameter, the probability of T.
However 2 streaks, we don’t know which ones, will have 1 added to the values in the report. The longer the number of trials the less significant the difference is. The chance is the shorter streaks are favored.
Here is the report.
I did a search in Notepad++ (free editor with very capable search functions). I counted the streaks for T(ails), each length from 1 to 10. I followed the definition of streak as per my previous posts.
I searched the 1024-line file I posted previously. The streak must be defined strictly as it appears in the file. For example the length-4 streak: H T T T T H. There are 2 spaces between the elements. The following reports shows also the line where the streak hits at least once.
The number of streaks certainly come very close to Warren Weaver’s calculations and mine as well.
No offence, no whack, just my honest opinion.
Code:
Length of Tails-streaks (Ln) and hits (in 1024 total possibilities)
L1 L2 L3 L4 L5 L6 L7 L8 L9 L10
860, 417, 188, 80, 32, 12, 4, 1, 0, 0 hits
Each streak has 2 more hits unaccounted for: 1 at the beginning and 1 at the end of the 10-toss possibility. The L10 streak has only 1 hit, with no H limits.
The lower streaks have more than one occurrence in each possibility.
Search performed with Notepad++
-------------------------------
There are NO L9, L10 fully-defined streaks (Ts surrounded by H)
Search "H T T T T T T T T T H" (0 hits in 0 files of 1 searched)
Search "H T T T T T T T T T T H" (0 hits in 0 files of 1 searched)
L10 (open-ended): Search "T T T T T T T T T T" (1 hit in 1 file of 1 searched)
Line 1024: T T T T T T T T T T
L9 (H at end): Search "T T T T T T T T T H" (1 hit in 1 file of 1 searched)
Line 1023: T T T T T T T T T H
L9 (H at beginning): Search "H T T T T T T T T T" (1 hit in 1 file of 1 searched)
Line 512: H T T T T T T T T T
L8: Search "H T T T T T T T T H" (1 hit in 1 file of 1 searched)
Line 511: H T T T T T T T T H
L7: Search "H T T T T T T T H" (4 hits in 1 file of 1 searched)
C:\Scientia\Expon0-1-10.NS (4 hits)
Line 255: H H T T T T T T T H
Line 509: H T T T T T T T H H
Line 510: H T T T T T T T H T
Line 767: T H T T T T T T T H
L6: Search "H T T T T T T H" (12 hits in 1 file of 1 searched)
Line 127: H H H T T T T T T H
Line 253: H H T T T T T T H H
Line 254: H H T T T T T T H T
Line 383: H T H T T T T T T H
Line 505: H T T T T T T H H H
Line 506: H T T T T T T H H T
Line 507: H T T T T T T H T H
Line 508: H T T T T T T H T T
Line 639: T H H T T T T T T H
Line 765: T H T T T T T T H H
Line 766: T H T T T T T T H T
Line 895: T T H T T T T T T H
L5: Search "H T T T T T H" (32 hits in 1 file of 1 searched)
Line 63: H H H H T T T T T H
Line 125: H H H T T T T T H H
Line 126: H H H T T T T T H T
Line 191: H H T H T T T T T H
Line 249: H H T T T T T H H H
Line 250: H H T T T T T H H T
Line 251: H H T T T T T H T H
Line 252: H H T T T T T H T T
Line 319: H T H H T T T T T H
Line 381: H T H T T T T T H H
Line 382: H T H T T T T T H T
Line 447: H T T H T T T T T H
Line 497: H T T T T T H H H H
Line 498: H T T T T T H H H T
Line 499: H T T T T T H H T H
Line 500: H T T T T T H H T T
Line 501: H T T T T T H T H H
Line 502: H T T T T T H T H T
Line 503: H T T T T T H T T H
Line 504: H T T T T T H T T T
Line 575: T H H H T T T T T H
Line 637: T H H T T T T T H H
Line 638: T H H T T T T T H T
Line 703: T H T H T T T T T H
Line 761: T H T T T T T H H H
Line 762: T H T T T T T H H T
Line 763: T H T T T T T H T H
Line 764: T H T T T T T H T T
Line 831: T T H H T T T T T H
Line 893: T T H T T T T T H H
Line 894: T T H T T T T T H T
Line 959: T T T H T T T T T H
L4: Search "H T T T T H" (80 hits in 1 file of 1 searched)
Line 31: H H H H H T T T T H
Line 61: H H H H T T T T H H
Line 62: H H H H T T T T H T
Line 95: H H H T H T T T T H
Line 121: H H H T T T T H H H
Line 122: H H H T T T T H H T
Line 123: H H H T T T T H T H
Line 124: H H H T T T T H T T
Line 159: H H T H H T T T T H
Line 189: H H T H T T T T H H
Line 190: H H T H T T T T H T
Line 223: H H T T H T T T T H
Line 241: H H T T T T H H H H
Line 242: H H T T T T H H H T
Line 243: H H T T T T H H T H
Line 244: H H T T T T H H T T
Line 245: H H T T T T H T H H
Line 246: H H T T T T H T H T
Line 247: H H T T T T H T T H
Line 248: H H T T T T H T T T
Line 287: H T H H H T T T T H
Line 317: H T H H T T T T H H
Line 318: H T H H T T T T H T
Line 351: H T H T H T T T T H
Line 377: H T H T T T T H H H
Line 378: H T H T T T T H H T
Line 379: H T H T T T T H T H
Line 380: H T H T T T T H T T
Line 415: H T T H H T T T T H
Line 445: H T T H T T T T H H
Line 446: H T T H T T T T H T
Line 479: H T T T H T T T T H
Line 481: H T T T T H H H H H
Line 482: H T T T T H H H H T
Line 483: H T T T T H H H T H
Line 484: H T T T T H H H T T
Line 485: H T T T T H H T H H
Line 486: H T T T T H H T H T
Line 487: H T T T T H H T T H
Line 488: H T T T T H H T T T
Line 489: H T T T T H T H H H
Line 490: H T T T T H T H H T
Line 491: H T T T T H T H T H
Line 492: H T T T T H T H T T
Line 493: H T T T T H T T H H
Line 494: H T T T T H T T H T
Line 495: H T T T T H T T T H
Line 496: H T T T T H T T T T
Line 543: T H H H H T T T T H
Line 573: T H H H T T T T H H
Line 574: T H H H T T T T H T
Line 607: T H H T H T T T T H
Line 633: T H H T T T T H H H
Line 634: T H H T T T T H H T
Line 635: T H H T T T T H T H
Line 636: T H H T T T T H T T
Line 671: T H T H H T T T T H
Line 701: T H T H T T T T H H
Line 702: T H T H T T T T H T
Line 735: T H T T H T T T T H
Line 753: T H T T T T H H H H
Line 754: T H T T T T H H H T
Line 755: T H T T T T H H T H
Line 756: T H T T T T H H T T
Line 757: T H T T T T H T H H
Line 758: T H T T T T H T H T
Line 759: T H T T T T H T T H
Line 760: T H T T T T H T T T
Line 799: T T H H H T T T T H
Line 829: T T H H T T T T H H
Line 830: T T H H T T T T H T
Line 863: T T H T H T T T T H
Line 889: T T H T T T T H H H
Line 890: T T H T T T T H H T
Line 891: T T H T T T T H T H
Line 892: T T H T T T T H T T
Line 927: T T T H H T T T T H
Line 957: T T T H T T T T H H
Line 958: T T T H T T T T H T
Line 991: T T T T H T T T T H
L3: Search "H T T T H" (188 hits in 1 file of 1 searched)
Line 15: H H H H H H T T T H
Line 29: H H H H H T T T H H
Line 30: H H H H H T T T H T
Line 47: H H H H T H T T T H
Line 57: H H H H T T T H H H
Line 58: H H H H T T T H H T
Line 59: H H H H T T T H T H
Line 60: H H H H T T T H T T
Line 79: H H H T H H T T T H
Line 93: H H H T H T T T H H
Line 94: H H H T H T T T H T
Line 111: H H H T T H T T T H
Line 113: H H H T T T H H H H
Line 114: H H H T T T H H H T
Line 115: H H H T T T H H T H
Line 116: H H H T T T H H T T
Line 117: H H H T T T H T H H
Line 118: H H H T T T H T H T
Line 119: H H H T T T H T T H
Line 120: H H H T T T H T T T
Line 143: H H T H H H T T T H
Line 157: H H T H H T T T H H
Line 158: H H T H H T T T H T
Line 175: H H T H T H T T T H
Line 185: H H T H T T T H H H
Line 186: H H T H T T T H H T
Line 187: H H T H T T T H T H
Line 188: H H T H T T T H T T
Line 207: H H T T H H T T T H
Line 221: H H T T H T T T H H
Line 222: H H T T H T T T H T
Line 225: H H T T T H H H H H
Line 226: H H T T T H H H H T
Line 227: H H T T T H H H T H
Line 228: H H T T T H H H T T
Line 229: H H T T T H H T H H
Line 230: H H T T T H H T H T
Line 231: H H T T T H H T T H
Line 232: H H T T T H H T T T
Line 233: H H T T T H T H H H
Line 234: H H T T T H T H H T
Line 235: H H T T T H T H T H
Line 236: H H T T T H T H T T
Line 237: H H T T T H T T H H
Line 238: H H T T T H T T H T
Line 239: H H T T T H T T T H
Line 240: H H T T T H T T T T
Line 271: H T H H H H T T T H
Line 285: H T H H H T T T H H
Line 286: H T H H H T T T H T
Line 303: H T H H T H T T T H
Line 313: H T H H T T T H H H
Line 314: H T H H T T T H H T
Line 315: H T H H T T T H T H
Line 316: H T H H T T T H T T
Line 335: H T H T H H T T T H
Line 349: H T H T H T T T H H
Line 350: H T H T H T T T H T
Line 367: H T H T T H T T T H
Line 369: H T H T T T H H H H
Line 370: H T H T T T H H H T
Line 371: H T H T T T H H T H
Line 372: H T H T T T H H T T
Line 373: H T H T T T H T H H
Line 374: H T H T T T H T H T
Line 375: H T H T T T H T T H
Line 376: H T H T T T H T T T
Line 399: H T T H H H T T T H
Line 413: H T T H H T T T H H
Line 414: H T T H H T T T H T
Line 431: H T T H T H T T T H
Line 441: H T T H T T T H H H
Line 442: H T T H T T T H H T
Line 443: H T T H T T T H T H
Line 444: H T T H T T T H T T
Line 449: H T T T H H H H H H
Line 450: H T T T H H H H H T
Line 451: H T T T H H H H T H
Line 452: H T T T H H H H T T
Line 453: H T T T H H H T H H
Line 454: H T T T H H H T H T
Line 455: H T T T H H H T T H
Line 456: H T T T H H H T T T
Line 457: H T T T H H T H H H
Line 458: H T T T H H T H H T
Line 459: H T T T H H T H T H
Line 460: H T T T H H T H T T
Line 461: H T T T H H T T H H
Line 462: H T T T H H T T H T
Line 463: H T T T H H T T T H
Line 464: H T T T H H T T T T
Line 465: H T T T H T H H H H
Line 466: H T T T H T H H H T
Line 467: H T T T H T H H T H
Line 468: H T T T H T H H T T
Line 469: H T T T H T H T H H
Line 470: H T T T H T H T H T
Line 471: H T T T H T H T T H
Line 472: H T T T H T H T T T
Line 473: H T T T H T T H H H
Line 474: H T T T H T T H H T
Line 475: H T T T H T T H T H
Line 476: H T T T H T T H T T
Line 477: H T T T H T T T H H
Line 478: H T T T H T T T H T
Line 479: H T T T H T T T T H
Line 480: H T T T H T T T T T
Line 495: H T T T T H T T T H
Line 527: T H H H H H T T T H
Line 541: T H H H H T T T H H
Line 542: T H H H H T T T H T
Line 559: T H H H T H T T T H
Line 569: T H H H T T T H H H
Line 570: T H H H T T T H H T
Line 571: T H H H T T T H T H
Line 572: T H H H T T T H T T
Line 591: T H H T H H T T T H
Line 605: T H H T H T T T H H
Line 606: T H H T H T T T H T
Line 623: T H H T T H T T T H
Line 625: T H H T T T H H H H
Line 626: T H H T T T H H H T
Line 627: T H H T T T H H T H
Line 628: T H H T T T H H T T
Line 629: T H H T T T H T H H
Line 630: T H H T T T H T H T
Line 631: T H H T T T H T T H
Line 632: T H H T T T H T T T
Line 655: T H T H H H T T T H
Line 669: T H T H H T T T H H
Line 670: T H T H H T T T H T
Line 687: T H T H T H T T T H
Line 697: T H T H T T T H H H
Line 698: T H T H T T T H H T
Line 699: T H T H T T T H T H
Line 700: T H T H T T T H T T
Line 719: T H T T H H T T T H
Line 733: T H T T H T T T H H
Line 734: T H T T H T T T H T
Line 737: T H T T T H H H H H
Line 738: T H T T T H H H H T
Line 739: T H T T T H H H T H
Line 740: T H T T T H H H T T
Line 741: T H T T T H H T H H
Line 742: T H T T T H H T H T
Line 743: T H T T T H H T T H
Line 744: T H T T T H H T T T
Line 745: T H T T T H T H H H
Line 746: T H T T T H T H H T
Line 747: T H T T T H T H T H
Line 748: T H T T T H T H T T
Line 749: T H T T T H T T H H
Line 750: T H T T T H T T H T
Line 751: T H T T T H T T T H
Line 752: T H T T T H T T T T
Line 783: T T H H H H T T T H
Line 797: T T H H H T T T H H
Line 798: T T H H H T T T H T
Line 815: T T H H T H T T T H
Line 825: T T H H T T T H H H
Line 826: T T H H T T T H H T
Line 827: T T H H T T T H T H
Line 828: T T H H T T T H T T
Line 847: T T H T H H T T T H
Line 861: T T H T H T T T H H
Line 862: T T H T H T T T H T
Line 879: T T H T T H T T T H
Line 881: T T H T T T H H H H
Line 882: T T H T T T H H H T
Line 883: T T H T T T H H T H
Line 884: T T H T T T H H T T
Line 885: T T H T T T H T H H
Line 886: T T H T T T H T H T
Line 887: T T H T T T H T T H
Line 888: T T H T T T H T T T
Line 911: T T T H H H T T T H
Line 925: T T T H H T T T H H
Line 926: T T T H H T T T H T
Line 943: T T T H T H T T T H
Line 953: T T T H T T T H H H
Line 954: T T T H T T T H H T
Line 955: T T T H T T T H T H
Line 956: T T T H T T T H T T
Line 975: T T T T H H T T T H
Line 989: T T T T H T T T H H
Line 990: T T T T H T T T H T
Line 1007: T T T T T H T T T H
L2: Search "H T T H" (417 hits in 1 file of 1 searched)
Line 7: H H H H H H H T T H
Line 13: H H H H H H T T H H
Line 14: H H H H H H T T H T
Line 23: H H H H H T H T T H
Line 25: H H H H H T T H H H
Line 26: H H H H H T T H H T
Line 27: H H H H H T T H T H
Line 28: H H H H H T T H T T
Line 39: H H H H T H H T T H
Line 45: H H H H T H T T H H
Line 46: H H H H T H T T H T
Line 49: H H H H T T H H H H
Line 50: H H H H T T H H H T
Line 51: H H H H T T H H T H
Line 52: H H H H T T H H T T
Line 53: H H H H T T H T H H
Line 54: H H H H T T H T H T
Line 55: H H H H T T H T T H
Line 56: H H H H T T H T T T
Line 71: H H H T H H H T T H
Line 77: H H H T H H T T H H
Line 78: H H H T H H T T H T
Line 87: H H H T H T H T T H
Line 89: H H H T H T T H H H
Line 90: H H H T H T T H H T
Line 91: H H H T H T T H T H
Line 92: H H H T H T T H T T
Line 97: H H H T T H H H H H
Line 98: H H H T T H H H H T
Line 99: H H H T T H H H T H
Line 100: H H H T T H H H T T
Line 101: H H H T T H H T H H
Line 102: H H H T T H H T H T
Line 103: H H H T T H H T T H
Line 104: H H H T T H H T T T
Line 105: H H H T T H T H H H
Line 106: H H H T T H T H H T
Line 107: H H H T T H T H T H
Line 108: H H H T T H T H T T
Line 109: H H H T T H T T H H
Line 110: H H H T T H T T H T
Line 111: H H H T T H T T T H
Line 112: H H H T T H T T T T
Line 119: H H H T T T H T T H
Line 135: H H T H H H H T T H
Line 141: H H T H H H T T H H
Line 142: H H T H H H T T H T
Line 151: H H T H H T H T T H
Line 153: H H T H H T T H H H
Line 154: H H T H H T T H H T
Line 155: H H T H H T T H T H
Line 156: H H T H H T T H T T
Line 167: H H T H T H H T T H
Line 173: H H T H T H T T H H
Line 174: H H T H T H T T H T
Line 177: H H T H T T H H H H
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Line 183: H H T H T T H T T H
Line 184: H H T H T T H T T T
Line 193: H H T T H H H H H H
Line 194: H H T T H H H H H T
Line 195: H H T T H H H H T H
Line 196: H H T T H H H H T T
Line 197: H H T T H H H T H H
Line 198: H H T T H H H T H T
Line 199: H H T T H H H T T H
Line 200: H H T T H H H T T T
Line 201: H H T T H H T H H H
Line 202: H H T T H H T H H T
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