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Thread: New deck at cut

  1. 05-11-2024, 06:37 AM #105
    iCountNTrack
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    Quote Originally Posted by aceside View Post
    I believe k_c is right here. I would say, math is the enemy of success, especially in the game of blackjack.
    This is a serious discussion and continue to post nonsense after many warnings. We will try again in 4 months.
    Chance favors the prepared mind
  2. 05-11-2024, 08:34 AM #106
    toolyp
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    Quote Originally Posted by Cacarulo View Post
    Actually, they should add up to 1. For the case of 4 flips of a fair coin:

    streak of 0 heads = 0.0625
    streak of 1 heads = 0.4375
    streak of 2 heads = 0.3125
    streak of 3 heads = 0.1250
    streak of 4 heads = 0.0625

    Sincerely,
    Cac
    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.
  3. 05-11-2024, 08:36 AM #107
    toolyp
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    Code:
    Total possibilities of 10 coin tosses – 1024 elements

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  4. 05-11-2024, 10:05 AM #108
    k_c
    k_c is offline
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    Did you find this post helpful? Yes | No
    Quote Originally Posted by toolyp View Post
    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.
    I do not completely agree. It's possible to get 10 consecutive heads on the first 10 trials. That case requires a tail (fail probability = 1/2) to end the streak. Also in 1024 trials on trials 1015 to 1024 it is possible to get 10 consecutive heads. That case requires a tail (failure) on trial 1014 to begin the streak. All other cases require both a tail to begin and end the streak.

    What I do is say the trial probability for trial 1 is 1. At the end I say the trial probability for trial 1015 is the fail probability (1/2) and requires no fail probability to end the streak.

    k_c
    "Perfection is the enemy of success."
    -Elon Musk-
  5. 05-12-2024, 05:42 AM #109
    toolyp
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    Quote Originally Posted by toolyp View Post
    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 
	Line  178:  H  H  T  H  T  T  H  H  H  T 
	Line  179:  H  H  T  H  T  T  H  H  T  H 
	Line  180:  H  H  T  H  T  T  H  H  T  T 
	Line  181:  H  H  T  H  T  T  H  T  H  H 
	Line  182:  H  H  T  H  T  T  H  T  H  T 
	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 
	Line  203:  H  H  T  T  H  H  T  H  T  H 
	Line  204:  H  H  T  T  H  H  T  H  T  T 
	Line  205:  H  H  T  T  H  H  T  T  H  H 
	Line  206:  H  H  T  T  H  H  T  T  H  T 
	Line  207:  H  H  T  T  H  H  T  T  T  H 
	Line  208:  H  H  T  T  H  H  T  T  T  T 
	Line  209:  H  H  T  T  H  T  H  H  H  H 
	Line  210:  H  H  T  T  H  T  H  H  H  T 
	Line  211:  H  H  T  T  H  T  H  H  T  H 
	Line  212:  H  H  T  T  H  T  H  H  T  T 
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	Line  214:  H  H  T  T  H  T  H  T  H  T 
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	Line  216:  H  H  T  T  H  T  H  T  T  T 
	Line  217:  H  H  T  T  H  T  T  H  H  H 
	Line  218:  H  H  T  T  H  T  T  H  H  T 
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	Line  220:  H  H  T  T  H  T  T  H  T  T 
	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  223:  H  H  T  T  H  T  T  T  T  H 
	Line  224:  H  H  T  T  H  T  T  T  T  T 
	Line  231:  H  H  T  T  T  H  H  T  T  H 
	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  247:  H  H  T  T  T  T  H  T  T  H 
	Line  263:  H  T  H  H  H  H  H  T  T  H 
	Line  269:  H  T  H  H  H  H  T  T  H  H 
	Line  270:  H  T  H  H  H  H  T  T  H  T 
	Line  279:  H  T  H  H  H  T  H  T  T  H 
	Line  281:  H  T  H  H  H  T  T  H  H  H 
	Line  282:  H  T  H  H  H  T  T  H  H  T 
	Line  283:  H  T  H  H  H  T  T  H  T  H 
	Line  284:  H  T  H  H  H  T  T  H  T  T 
	Line  295:  H  T  H  H  T  H  H  T  T  H 
	Line  301:  H  T  H  H  T  H  T  T  H  H 
	Line  302:  H  T  H  H  T  H  T  T  H  T 
	Line  305:  H  T  H  H  T  T  H  H  H  H 
	Line  306:  H  T  H  H  T  T  H  H  H  T 
	Line  307:  H  T  H  H  T  T  H  H  T  H 
	Line  308:  H  T  H  H  T  T  H  H  T  T 
	Line  309:  H  T  H  H  T  T  H  T  H  H 
	Line  310:  H  T  H  H  T  T  H  T  H  T 
	Line  311:  H  T  H  H  T  T  H  T  T  H 
	Line  312:  H  T  H  H  T  T  H  T  T  T 
	Line  327:  H  T  H  T  H  H  H  T  T  H 
	Line  333:  H  T  H  T  H  H  T  T  H  H 
	Line  334:  H  T  H  T  H  H  T  T  H  T 
	Line  343:  H  T  H  T  H  T  H  T  T  H 
	Line  345:  H  T  H  T  H  T  T  H  H  H 
	Line  346:  H  T  H  T  H  T  T  H  H  T 
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	Line  348:  H  T  H  T  H  T  T  H  T  T 
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	Line  354:  H  T  H  T  T  H  H  H  H  T 
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	Line  356:  H  T  H  T  T  H  H  H  T  T 
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	Line  358:  H  T  H  T  T  H  H  T  H  T 
	Line  359:  H  T  H  T  T  H  H  T  T  H 
	Line  360:  H  T  H  T  T  H  H  T  T  T 
	Line  361:  H  T  H  T  T  H  T  H  H  H 
	Line  362:  H  T  H  T  T  H  T  H  H  T 
	Line  363:  H  T  H  T  T  H  T  H  T  H 
	Line  364:  H  T  H  T  T  H  T  H  T  T 
	Line  365:  H  T  H  T  T  H  T  T  H  H 
	Line  366:  H  T  H  T  T  H  T  T  H  T 
	Line  367:  H  T  H  T  T  H  T  T  T  H 
	Line  368:  H  T  H  T  T  H  T  T  T  T 
	Line  375:  H  T  H  T  T  T  H  T  T  H 
	Line  385:  H  T  T  H  H  H  H  H  H  H 
	Line  386:  H  T  T  H  H  H  H  H  H  T 
	Line  387:  H  T  T  H  H  H  H  H  T  H 
	Line  388:  H  T  T  H  H  H  H  H  T  T 
	Line  389:  H  T  T  H  H  H  H  T  H  H 
	Line  390:  H  T  T  H  H  H  H  T  H  T 
	Line  391:  H  T  T  H  H  H  H  T  T  H 
	Line  392:  H  T  T  H  H  H  H  T  T  T 
	Line  393:  H  T  T  H  H  H  T  H  H  H 
	Line  394:  H  T  T  H  H  H  T  H  H  T 
	Line  395:  H  T  T  H  H  H  T  H  T  H 
	Line  396:  H  T  T  H  H  H  T  H  T  T 
	Line  397:  H  T  T  H  H  H  T  T  H  H 
	Line  398:  H  T  T  H  H  H  T  T  H  T 
	Line  399:  H  T  T  H  H  H  T  T  T  H 
	Line  400:  H  T  T  H  H  H  T  T  T  T 
	Line  401:  H  T  T  H  H  T  H  H  H  H 
	Line  402:  H  T  T  H  H  T  H  H  H  T 
	Line  403:  H  T  T  H  H  T  H  H  T  H 
	Line  404:  H  T  T  H  H  T  H  H  T  T 
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	Line  406:  H  T  T  H  H  T  H  T  H  T 
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	Line  410:  H  T  T  H  H  T  T  H  H  T 
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	Line  420:  H  T  T  H  T  H  H  H  T  T 
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	Line  434:  H  T  T  H  T  T  H  H  H  T 
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	Line  436:  H  T  T  H  T  T  H  H  T  T 
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	Line  438:  H  T  T  H  T  T  H  T  H  T 
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	Line  440:  H  T  T  H  T  T  H  T  T  T 
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	Line  442:  H  T  T  H  T  T  T  H  H  T 
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	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  471:  H  T  T  T  H  T  H  T  T  H 
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	Line  474:  H  T  T  T  H  T  T  H  H  T 
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	Line  494:  H  T  T  T  T  H  T  T  H  T 
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	Line  519:  T  H  H  H  H  H  H  T  T  H 
	Line  525:  T  H  H  H  H  H  T  T  H  H 
	Line  526:  T  H  H  H  H  H  T  T  H  T 
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	Line  713:  T  H  T  T  H  H  T  H  H  H 
	Line  714:  T  H  T  T  H  H  T  H  H  T 
	Line  715:  T  H  T  T  H  H  T  H  T  H 
	Line  716:  T  H  T  T  H  H  T  H  T  T 
	Line  717:  T  H  T  T  H  H  T  T  H  H 
	Line  718:  T  H  T  T  H  H  T  T  H  T 
	Line  719:  T  H  T  T  H  H  T  T  T  H 
	Line  720:  T  H  T  T  H  H  T  T  T  T 
	Line  721:  T  H  T  T  H  T  H  H  H  H 
	Line  722:  T  H  T  T  H  T  H  H  H  T 
	Line  723:  T  H  T  T  H  T  H  H  T  H 
	Line  724:  T  H  T  T  H  T  H  H  T  T 
	Line  725:  T  H  T  T  H  T  H  T  H  H 
	Line  726:  T  H  T  T  H  T  H  T  H  T 
	Line  727:  T  H  T  T  H  T  H  T  T  H 
	Line  728:  T  H  T  T  H  T  H  T  T  T 
	Line  729:  T  H  T  T  H  T  T  H  H  H 
	Line  730:  T  H  T  T  H  T  T  H  H  T 
	Line  731:  T  H  T  T  H  T  T  H  T  H 
	Line  732:  T  H  T  T  H  T  T  H  T  T 
	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  735:  T  H  T  T  H  T  T  T  T  H 
	Line  736:  T  H  T  T  H  T  T  T  T  T 
	Line  743:  T  H  T  T  T  H  H  T  T  H 
	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  759:  T  H  T  T  T  T  H  T  T  H 
	Line  775:  T  T  H  H  H  H  H  T  T  H 
	Line  781:  T  T  H  H  H  H  T  T  H  H 
	Line  782:  T  T  H  H  H  H  T  T  H  T 
	Line  791:  T  T  H  H  H  T  H  T  T  H 
	Line  793:  T  T  H  H  H  T  T  H  H  H 
	Line  794:  T  T  H  H  H  T  T  H  H  T 
	Line  795:  T  T  H  H  H  T  T  H  T  H 
	Line  796:  T  T  H  H  H  T  T  H  T  T 
	Line  807:  T  T  H  H  T  H  H  T  T  H 
	Line  813:  T  T  H  H  T  H  T  T  H  H 
	Line  814:  T  T  H  H  T  H  T  T  H  T 
	Line  817:  T  T  H  H  T  T  H  H  H  H 
	Line  818:  T  T  H  H  T  T  H  H  H  T 
	Line  819:  T  T  H  H  T  T  H  H  T  H 
	Line  820:  T  T  H  H  T  T  H  H  T  T 
	Line  821:  T  T  H  H  T  T  H  T  H  H 
	Line  822:  T  T  H  H  T  T  H  T  H  T 
	Line  823:  T  T  H  H  T  T  H  T  T  H 
	Line  824:  T  T  H  H  T  T  H  T  T  T 
	Line  839:  T  T  H  T  H  H  H  T  T  H 
	Line  845:  T  T  H  T  H  H  T  T  H  H 
	Line  846:  T  T  H  T  H  H  T  T  H  T 
	Line  855:  T  T  H  T  H  T  H  T  T  H 
	Line  857:  T  T  H  T  H  T  T  H  H  H 
	Line  858:  T  T  H  T  H  T  T  H  H  T 
	Line  859:  T  T  H  T  H  T  T  H  T  H 
	Line  860:  T  T  H  T  H  T  T  H  T  T 
	Line  865:  T  T  H  T  T  H  H  H  H  H 
	Line  866:  T  T  H  T  T  H  H  H  H  T 
	Line  867:  T  T  H  T  T  H  H  H  T  H 
	Line  868:  T  T  H  T  T  H  H  H  T  T 
	Line  869:  T  T  H  T  T  H  H  T  H  H 
	Line  870:  T  T  H  T  T  H  H  T  H  T 
	Line  871:  T  T  H  T  T  H  H  T  T  H 
	Line  872:  T  T  H  T  T  H  H  T  T  T 
	Line  873:  T  T  H  T  T  H  T  H  H  H 
	Line  874:  T  T  H  T  T  H  T  H  H  T 
	Line  875:  T  T  H  T  T  H  T  H  T  H 
	Line  876:  T  T  H  T  T  H  T  H  T  T 
	Line  877:  T  T  H  T  T  H  T  T  H  H 
	Line  878:  T  T  H  T  T  H  T  T  H  T 
	Line  879:  T  T  H  T  T  H  T  T  T  H 
	Line  880:  T  T  H  T  T  H  T  T  T  T 
	Line  887:  T  T  H  T  T  T  H  T  T  H 
	Line  903:  T  T  T  H  H  H  H  T  T  H 
	Line  909:  T  T  T  H  H  H  T  T  H  H 
	Line  910:  T  T  T  H  H  H  T  T  H  T 
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	Line  921:  T  T  T  H  H  T  T  H  H  H 
	Line  922:  T  T  T  H  H  T  T  H  H  T 
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	Line  942:  T  T  T  H  T  H  T  T  H  T 
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	Line  946:  T  T  T  H  T  T  H  H  H  T 
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	Line  948:  T  T  T  H  T  T  H  H  T  T 
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	Line  950:  T  T  T  H  T  T  H  T  H  T 
	Line  951:  T  T  T  H  T  T  H  T  T  H 
	Line  952:  T  T  T  H  T  T  H  T  T  T 
	Line  967:  T  T  T  T  H  H  H  T  T  H 
	Line  973:  T  T  T  T  H  H  T  T  H  H 
	Line  974:  T  T  T  T  H  H  T  T  H  T 
	Line  983:  T  T  T  T  H  T  H  T  T  H 
	Line  985:  T  T  T  T  H  T  T  H  H  H 
	Line  986:  T  T  T  T  H  T  T  H  H  T 
	Line  987:  T  T  T  T  H  T  T  H  T  H 
	Line  988:  T  T  T  T  H  T  T  H  T  T 
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	Line 1006:  T  T  T  T  T  H  T  T  H  T 
	Line 1015:  T  T  T  T  T  T  H  T  T  H 


L1: Search "H  T  H" (860 hits in 1 file of 1 searched) 
	Line    3:  H  H  H  H  H  H  H  H  T  H 
	Line    5:  H  H  H  H  H  H  H  T  H  H 
	Line    6:  H  H  H  H  H  H  H  T  H  T 
	Line    9:  H  H  H  H  H  H  T  H  H  H 
	Line   10:  H  H  H  H  H  H  T  H  H  T 
	Line   11:  H  H  H  H  H  H  T  H  T  H 
	Line   12:  H  H  H  H  H  H  T  H  T  T 
	Line   17:  H  H  H  H  H  T  H  H  H  H 
	Line   18:  H  H  H  H  H  T  H  H  H  T 
	Line   19:  H  H  H  H  H  T  H  H  T  H 
	Line   20:  H  H  H  H  H  T  H  H  T  T 
	Line   21:  H  H  H  H  H  T  H  T  H  H 
	Line   22:  H  H  H  H  H  T  H  T  H  T 
	Line   23:  H  H  H  H  H  T  H  T  T  H 
	Line   24:  H  H  H  H  H  T  H  T  T  T 
	Line   27:  H  H  H  H  H  T  T  H  T  H 
	Line   33:  H  H  H  H  T  H  H  H  H  H 
	Line   34:  H  H  H  H  T  H  H  H  H  T 
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	Line   36:  H  H  H  H  T  H  H  H  T  T 
	Line   37:  H  H  H  H  T  H  H  T  H  H 
	Line   38:  H  H  H  H  T  H  H  T  H  T 
	Line   39:  H  H  H  H  T  H  H  T  T  H 
	Line   40:  H  H  H  H  T  H  H  T  T  T 
	Line   41:  H  H  H  H  T  H  T  H  H  H 
	Line   42:  H  H  H  H  T  H  T  H  H  T 
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	Line   44:  H  H  H  H  T  H  T  H  T  T 
	Line   45:  H  H  H  H  T  H  T  T  H  H 
	Line   46:  H  H  H  H  T  H  T  T  H  T 
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	Line   48:  H  H  H  H  T  H  T  T  T  T 
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	Line   53:  H  H  H  H  T  T  H  T  H  H 
	Line   54:  H  H  H  H  T  T  H  T  H  T 
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	Line   66:  H  H  H  T  H  H  H  H  H  T 
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	Line   76:  H  H  H  T  H  H  T  H  T  T 
	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   79:  H  H  H  T  H  H  T  T  T  H 
	Line   80:  H  H  H  T  H  H  T  T  T  T 
	Line   81:  H  H  H  T  H  T  H  H  H  H 
	Line   82:  H  H  H  T  H  T  H  H  H  T 
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	Line   84:  H  H  H  T  H  T  H  H  T  T 
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	Line   86:  H  H  H  T  H  T  H  T  H  T 
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	Line   90:  H  H  H  T  H  T  T  H  H  T 
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	Line   94:  H  H  H  T  H  T  T  T  H  T 
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	Line   96:  H  H  H  T  H  T  T  T  T  T 
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	Line  101:  H  H  H  T  T  H  H  T  H  H 
	Line  102:  H  H  H  T  T  H  H  T  H  T 
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	Line  106:  H  H  H  T  T  H  T  H  H  T 
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	Line  108:  H  H  H  T  T  H  T  H  T  T 
	Line  115:  H  H  H  T  T  T  H  H  T  H 
	Line  117:  H  H  H  T  T  T  H  T  H  H 
	Line  118:  H  H  H  T  T  T  H  T  H  T 
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	Line  129:  H  H  T  H  H  H  H  H  H  H 
	Line  130:  H  H  T  H  H  H  H  H  H  T 
	Line  131:  H  H  T  H  H  H  H  H  T  H 
	Line  132:  H  H  T  H  H  H  H  H  T  T 
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	Line  138:  H  H  T  H  H  H  T  H  H  T 
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	Line  140:  H  H  T  H  H  H  T  H  T  T 
	Line  141:  H  H  T  H  H  H  T  T  H  H 
	Line  142:  H  H  T  H  H  H  T  T  H  T 
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	Line  144:  H  H  T  H  H  H  T  T  T  T 
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	Line  146:  H  H  T  H  H  T  H  H  H  T 
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	Line  148:  H  H  T  H  H  T  H  H  T  T 
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	Line  150:  H  H  T  H  H  T  H  T  H  T 
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	Line  154:  H  H  T  H  H  T  T  H  H  T 
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	Line  156:  H  H  T  H  H  T  T  H  T  T 
	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  159:  H  H  T  H  H  T  T  T  T  H 
	Line  160:  H  H  T  H  H  T  T  T  T  T 
	Line  161:  H  H  T  H  T  H  H  H  H  H 
	Line  162:  H  H  T  H  T  H  H  H  H  T 
	Line  163:  H  H  T  H  T  H  H  H  T  H 
	Line  164:  H  H  T  H  T  H  H  H  T  T 
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	Line  166:  H  H  T  H  T  H  H  T  H  T 
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	Line  168:  H  H  T  H  T  H  H  T  T  T 
	Line  169:  H  H  T  H  T  H  T  H  H  H 
	Line  170:  H  H  T  H  T  H  T  H  H  T 
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	Line  172:  H  H  T  H  T  H  T  H  T  T 
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	Line  174:  H  H  T  H  T  H  T  T  H  T 
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	Line  176:  H  H  T  H  T  H  T  T  T  T 
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	Line  178:  H  H  T  H  T  T  H  H  H  T 
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	Line  180:  H  H  T  H  T  T  H  H  T  T 
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	Line  182:  H  H  T  H  T  T  H  T  H  T 
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	Line  184:  H  H  T  H  T  T  H  T  T  T 
	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 
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	Line  198:  H  H  T  T  H  H  H  T  H  T 
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	Line  210:  H  H  T  T  H  T  H  H  H  T 
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	Line  214:  H  H  T  T  H  T  H  T  H  T 
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	Line  258:  H  T  H  H  H  H  H  H  H  T 
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	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  701:  T  H  T  H  T  T  T  T  H  H 
	Line  702:  T  H  T  H  T  T  T  T  H  T 
	Line  703:  T  H  T  H  T  T  T  T  T  H 
	Line  704:  T  H  T  H  T  T  T  T  T  T 
	Line  707:  T  H  T  T  H  H  H  H  T  H 
	Line  709:  T  H  T  T  H  H  H  T  H  H 
	Line  710:  T  H  T  T  H  H  H  T  H  T 
	Line  713:  T  H  T  T  H  H  T  H  H  H 
	Line  714:  T  H  T  T  H  H  T  H  H  T 
	Line  715:  T  H  T  T  H  H  T  H  T  H 
	Line  716:  T  H  T  T  H  H  T  H  T  T 
	Line  721:  T  H  T  T  H  T  H  H  H  H 
	Line  722:  T  H  T  T  H  T  H  H  H  T 
	Line  723:  T  H  T  T  H  T  H  H  T  H 
	Line  724:  T  H  T  T  H  T  H  H  T  T 
	Line  725:  T  H  T  T  H  T  H  T  H  H 
	Line  726:  T  H  T  T  H  T  H  T  H  T 
	Line  727:  T  H  T  T  H  T  H  T  T  H 
	Line  728:  T  H  T  T  H  T  H  T  T  T 
	Line  731:  T  H  T  T  H  T  T  H  T  H 
	Line  739:  T  H  T  T  T  H  H  H  T  H 
	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  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  755:  T  H  T  T  T  T  H  H  T  H 
	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  763:  T  H  T  T  T  T  T  H  T  H 
	Line  771:  T  T  H  H  H  H  H  H  T  H 
	Line  773:  T  T  H  H  H  H  H  T  H  H 
	Line  774:  T  T  H  H  H  H  H  T  H  T 
	Line  777:  T  T  H  H  H  H  T  H  H  H 
	Line  778:  T  T  H  H  H  H  T  H  H  T 
	Line  779:  T  T  H  H  H  H  T  H  T  H 
	Line  780:  T  T  H  H  H  H  T  H  T  T 
	Line  785:  T  T  H  H  H  T  H  H  H  H 
	Line  786:  T  T  H  H  H  T  H  H  H  T 
	Line  787:  T  T  H  H  H  T  H  H  T  H 
	Line  788:  T  T  H  H  H  T  H  H  T  T 
	Line  789:  T  T  H  H  H  T  H  T  H  H 
	Line  790:  T  T  H  H  H  T  H  T  H  T 
	Line  791:  T  T  H  H  H  T  H  T  T  H 
	Line  792:  T  T  H  H  H  T  H  T  T  T 
	Line  795:  T  T  H  H  H  T  T  H  T  H 
	Line  801:  T  T  H  H  T  H  H  H  H  H 
	Line  802:  T  T  H  H  T  H  H  H  H  T 
	Line  803:  T  T  H  H  T  H  H  H  T  H 
	Line  804:  T  T  H  H  T  H  H  H  T  T 
	Line  805:  T  T  H  H  T  H  H  T  H  H 
	Line  806:  T  T  H  H  T  H  H  T  H  T 
	Line  807:  T  T  H  H  T  H  H  T  T  H 
	Line  808:  T  T  H  H  T  H  H  T  T  T 
	Line  809:  T  T  H  H  T  H  T  H  H  H 
	Line  810:  T  T  H  H  T  H  T  H  H  T 
	Line  811:  T  T  H  H  T  H  T  H  T  H 
	Line  812:  T  T  H  H  T  H  T  H  T  T 
	Line  813:  T  T  H  H  T  H  T  T  H  H 
	Line  814:  T  T  H  H  T  H  T  T  H  T 
	Line  815:  T  T  H  H  T  H  T  T  T  H 
	Line  816:  T  T  H  H  T  H  T  T  T  T 
	Line  819:  T  T  H  H  T  T  H  H  T  H 
	Line  821:  T  T  H  H  T  T  H  T  H  H 
	Line  822:  T  T  H  H  T  T  H  T  H  T 
	Line  827:  T  T  H  H  T  T  T  H  T  H 
	Line  833:  T  T  H  T  H  H  H  H  H  H 
	Line  834:  T  T  H  T  H  H  H  H  H  T 
	Line  835:  T  T  H  T  H  H  H  H  T  H 
	Line  836:  T  T  H  T  H  H  H  H  T  T 
	Line  837:  T  T  H  T  H  H  H  T  H  H 
	Line  838:  T  T  H  T  H  H  H  T  H  T 
	Line  839:  T  T  H  T  H  H  H  T  T  H 
	Line  840:  T  T  H  T  H  H  H  T  T  T 
	Line  841:  T  T  H  T  H  H  T  H  H  H 
	Line  842:  T  T  H  T  H  H  T  H  H  T 
	Line  843:  T  T  H  T  H  H  T  H  T  H 
	Line  844:  T  T  H  T  H  H  T  H  T  T 
	Line  845:  T  T  H  T  H  H  T  T  H  H 
	Line  846:  T  T  H  T  H  H  T  T  H  T 
	Line  847:  T  T  H  T  H  H  T  T  T  H 
	Line  848:  T  T  H  T  H  H  T  T  T  T 
	Line  849:  T  T  H  T  H  T  H  H  H  H 
	Line  850:  T  T  H  T  H  T  H  H  H  T 
	Line  851:  T  T  H  T  H  T  H  H  T  H 
	Line  852:  T  T  H  T  H  T  H  H  T  T 
	Line  853:  T  T  H  T  H  T  H  T  H  H 
	Line  854:  T  T  H  T  H  T  H  T  H  T 
	Line  855:  T  T  H  T  H  T  H  T  T  H 
	Line  856:  T  T  H  T  H  T  H  T  T  T 
	Line  857:  T  T  H  T  H  T  T  H  H  H 
	Line  858:  T  T  H  T  H  T  T  H  H  T 
	Line  859:  T  T  H  T  H  T  T  H  T  H 
	Line  860:  T  T  H  T  H  T  T  H  T  T 
	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  863:  T  T  H  T  H  T  T  T  T  H 
	Line  864:  T  T  H  T  H  T  T  T  T  T 
	Line  867:  T  T  H  T  T  H  H  H  T  H 
	Line  869:  T  T  H  T  T  H  H  T  H  H 
	Line  870:  T  T  H  T  T  H  H  T  H  T 
	Line  873:  T  T  H  T  T  H  T  H  H  H 
	Line  874:  T  T  H  T  T  H  T  H  H  T 
	Line  875:  T  T  H  T  T  H  T  H  T  H 
	Line  876:  T  T  H  T  T  H  T  H  T  T 
	Line  883:  T  T  H  T  T  T  H  H  T  H 
	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  891:  T  T  H  T  T  T  T  H  T  H 
	Line  899:  T  T  T  H  H  H  H  H  T  H 
	Line  901:  T  T  T  H  H  H  H  T  H  H 
	Line  902:  T  T  T  H  H  H  H  T  H  T 
	Line  905:  T  T  T  H  H  H  T  H  H  H 
	Line  906:  T  T  T  H  H  H  T  H  H  T 
	Line  907:  T  T  T  H  H  H  T  H  T  H 
	Line  908:  T  T  T  H  H  H  T  H  T  T 
	Line  913:  T  T  T  H  H  T  H  H  H  H 
	Line  914:  T  T  T  H  H  T  H  H  H  T 
	Line  915:  T  T  T  H  H  T  H  H  T  H 
	Line  916:  T  T  T  H  H  T  H  H  T  T 
	Line  917:  T  T  T  H  H  T  H  T  H  H 
	Line  918:  T  T  T  H  H  T  H  T  H  T 
	Line  919:  T  T  T  H  H  T  H  T  T  H 
	Line  920:  T  T  T  H  H  T  H  T  T  T 
	Line  923:  T  T  T  H  H  T  T  H  T  H 
	Line  929:  T  T  T  H  T  H  H  H  H  H 
	Line  930:  T  T  T  H  T  H  H  H  H  T 
	Line  931:  T  T  T  H  T  H  H  H  T  H 
	Line  932:  T  T  T  H  T  H  H  H  T  T 
	Line  933:  T  T  T  H  T  H  H  T  H  H 
	Line  934:  T  T  T  H  T  H  H  T  H  T 
	Line  935:  T  T  T  H  T  H  H  T  T  H 
	Line  936:  T  T  T  H  T  H  H  T  T  T 
	Line  937:  T  T  T  H  T  H  T  H  H  H 
	Line  938:  T  T  T  H  T  H  T  H  H  T 
	Line  939:  T  T  T  H  T  H  T  H  T  H 
	Line  940:  T  T  T  H  T  H  T  H  T  T 
	Line  941:  T  T  T  H  T  H  T  T  H  H 
	Line  942:  T  T  T  H  T  H  T  T  H  T 
	Line  943:  T  T  T  H  T  H  T  T  T  H 
	Line  944:  T  T  T  H  T  H  T  T  T  T 
	Line  947:  T  T  T  H  T  T  H  H  T  H 
	Line  949:  T  T  T  H  T  T  H  T  H  H 
	Line  950:  T  T  T  H  T  T  H  T  H  T 
	Line  955:  T  T  T  H  T  T  T  H  T  H 
	Line  963:  T  T  T  T  H  H  H  H  T  H 
	Line  965:  T  T  T  T  H  H  H  T  H  H 
	Line  966:  T  T  T  T  H  H  H  T  H  T 
	Line  969:  T  T  T  T  H  H  T  H  H  H 
	Line  970:  T  T  T  T  H  H  T  H  H  T 
	Line  971:  T  T  T  T  H  H  T  H  T  H 
	Line  972:  T  T  T  T  H  H  T  H  T  T 
	Line  977:  T  T  T  T  H  T  H  H  H  H 
	Line  978:  T  T  T  T  H  T  H  H  H  T 
	Line  979:  T  T  T  T  H  T  H  H  T  H 
	Line  980:  T  T  T  T  H  T  H  H  T  T 
	Line  981:  T  T  T  T  H  T  H  T  H  H 
	Line  982:  T  T  T  T  H  T  H  T  H  T 
	Line  983:  T  T  T  T  H  T  H  T  T  H 
	Line  984:  T  T  T  T  H  T  H  T  T  T 
	Line  987:  T  T  T  T  H  T  T  H  T  H 
	Line  995:  T  T  T  T  T  H  H  H  T  H 
	Line  997:  T  T  T  T  T  H  H  T  H  H 
	Line  998:  T  T  T  T  T  H  H  T  H  T 
	Line 1001:  T  T  T  T  T  H  T  H  H  H 
	Line 1002:  T  T  T  T  T  H  T  H  H  T 
	Line 1003:  T  T  T  T  T  H  T  H  T  H 
	Line 1004:  T  T  T  T  T  H  T  H  T  T 
	Line 1011:  T  T  T  T  T  T  H  H  T  H 
	Line 1013:  T  T  T  T  T  T  H  T  H  H 
	Line 1014:  T  T  T  T  T  T  H  T  H  T 
	Line 1019:  T  T  T  T  T  T  T  H  T  H
  6. 05-12-2024, 09:15 AM #110
    Cacarulo
    Cacarulo is offline
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    Quote Originally Posted by toolyp View Post
    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 don't think we will agree. While it is true that a streak of, for example, 2 consecutive heads must be bounded by 2 tails, it is also true that a streak of
    2 heads can be the beginning or the end of a series of n tosses.
    With all due respect to the late Warren Weaver, he probably omitted these 2 cases. Just to make sure, I also have his book.

    Let's consider an example of 4 coin tosses (2^4=16 possibilities). The lengths of the longest streaks of heads are, respectively:

    HHHH = 4
    HHHT = 3
    HHTH = 2
    HHTT = 2
    HTHH = 2
    HTHT = 1
    HTTH = 1
    HTTT = 1
    THHH = 3
    THHT = 2
    THTH = 1
    THTT = 1
    TTHH = 2
    TTHT = 1
    TTTH = 1
    TTTT = 0

    So we get the following distribution:

    exact streak length | probability
    0 | 1/16
    1 | 7/16
    2 | 5/16
    3 | 2/16
    4 | 1/16

    If we were to consider a definition as strict as the one you suggest, for a length of 2 the probability would be 1/16, which I don't think is correct.
    Also, according to your definition, in 4 coin tosses there are no streaks of 3 or 4, which is incorrect. However, I don't see anyone, not even online calculators,
    agreeing with Weaver's definition or yours.

    Sincerely,
    Cac
    Luck is what happens when preparation meets opportunity.
  7. 05-12-2024, 12:40 PM #111
    DSchles
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    Naturally, you're correct, and this is what I explained dozens of posts ago. But there's no explaining to toolyp, because he's adopted a false idol, and he's going to stick with Weaver, whose book I read decades ago. For me, the case has been closed for days because, well, I've studied all of this for ages. But, we always have newcomers who want to explain why they know everything and we know nothing. It's easy to grow tired of them after a while. Don't waste too many brain cells on this.

    Don
  8. 05-12-2024, 11:30 PM #112
    iCountNTrack
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    Quote Originally Posted by toolyp View Post
    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 
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	Line  813:  T  T  H  H  T  H  T  T  H  H 
	Line  814:  T  T  H  H  T  H  T  T  H  T 
	Line  817:  T  T  H  H  T  T  H  H  H  H 
	Line  818:  T  T  H  H  T  T  H  H  H  T 
	Line  819:  T  T  H  H  T  T  H  H  T  H 
	Line  820:  T  T  H  H  T  T  H  H  T  T 
	Line  821:  T  T  H  H  T  T  H  T  H  H 
	Line  822:  T  T  H  H  T  T  H  T  H  T 
	Line  823:  T  T  H  H  T  T  H  T  T  H 
	Line  824:  T  T  H  H  T  T  H  T  T  T 
	Line  839:  T  T  H  T  H  H  H  T  T  H 
	Line  845:  T  T  H  T  H  H  T  T  H  H 
	Line  846:  T  T  H  T  H  H  T  T  H  T 
	Line  855:  T  T  H  T  H  T  H  T  T  H 
	Line  857:  T  T  H  T  H  T  T  H  H  H 
	Line  858:  T  T  H  T  H  T  T  H  H  T 
	Line  859:  T  T  H  T  H  T  T  H  T  H 
	Line  860:  T  T  H  T  H  T  T  H  T  T 
	Line  865:  T  T  H  T  T  H  H  H  H  H 
	Line  866:  T  T  H  T  T  H  H  H  H  T 
	Line  867:  T  T  H  T  T  H  H  H  T  H 
	Line  868:  T  T  H  T  T  H  H  H  T  T 
	Line  869:  T  T  H  T  T  H  H  T  H  H 
	Line  870:  T  T  H  T  T  H  H  T  H  T 
	Line  871:  T  T  H  T  T  H  H  T  T  H 
	Line  872:  T  T  H  T  T  H  H  T  T  T 
	Line  873:  T  T  H  T  T  H  T  H  H  H 
	Line  874:  T  T  H  T  T  H  T  H  H  T 
	Line  875:  T  T  H  T  T  H  T  H  T  H 
	Line  876:  T  T  H  T  T  H  T  H  T  T 
	Line  877:  T  T  H  T  T  H  T  T  H  H 
	Line  878:  T  T  H  T  T  H  T  T  H  T 
	Line  879:  T  T  H  T  T  H  T  T  T  H 
	Line  880:  T  T  H  T  T  H  T  T  T  T 
	Line  887:  T  T  H  T  T  T  H  T  T  H 
	Line  903:  T  T  T  H  H  H  H  T  T  H 
	Line  909:  T  T  T  H  H  H  T  T  H  H 
	Line  910:  T  T  T  H  H  H  T  T  H  T 
	Line  919:  T  T  T  H  H  T  H  T  T  H 
	Line  921:  T  T  T  H  H  T  T  H  H  H 
	Line  922:  T  T  T  H  H  T  T  H  H  T 
	Line  923:  T  T  T  H  H  T  T  H  T  H 
	Line  924:  T  T  T  H  H  T  T  H  T  T 
	Line  935:  T  T  T  H  T  H  H  T  T  H 
	Line  941:  T  T  T  H  T  H  T  T  H  H 
	Line  942:  T  T  T  H  T  H  T  T  H  T 
	Line  945:  T  T  T  H  T  T  H  H  H  H 
	Line  946:  T  T  T  H  T  T  H  H  H  T 
	Line  947:  T  T  T  H  T  T  H  H  T  H 
	Line  948:  T  T  T  H  T  T  H  H  T  T 
	Line  949:  T  T  T  H  T  T  H  T  H  H 
	Line  950:  T  T  T  H  T  T  H  T  H  T 
	Line  951:  T  T  T  H  T  T  H  T  T  H 
	Line  952:  T  T  T  H  T  T  H  T  T  T 
	Line  967:  T  T  T  T  H  H  H  T  T  H 
	Line  973:  T  T  T  T  H  H  T  T  H  H 
	Line  974:  T  T  T  T  H  H  T  T  H  T 
	Line  983:  T  T  T  T  H  T  H  T  T  H 
	Line  985:  T  T  T  T  H  T  T  H  H  H 
	Line  986:  T  T  T  T  H  T  T  H  H  T 
	Line  987:  T  T  T  T  H  T  T  H  T  H 
	Line  988:  T  T  T  T  H  T  T  H  T  T 
	Line  999:  T  T  T  T  T  H  H  T  T  H 
	Line 1005:  T  T  T  T  T  H  T  T  H  H 
	Line 1006:  T  T  T  T  T  H  T  T  H  T 
	Line 1015:  T  T  T  T  T  T  H  T  T  H 


L1: Search "H  T  H" (860 hits in 1 file of 1 searched) 
	Line    3:  H  H  H  H  H  H  H  H  T  H 
	Line    5:  H  H  H  H  H  H  H  T  H  H 
	Line    6:  H  H  H  H  H  H  H  T  H  T 
	Line    9:  H  H  H  H  H  H  T  H  H  H 
	Line   10:  H  H  H  H  H  H  T  H  H  T 
	Line   11:  H  H  H  H  H  H  T  H  T  H 
	Line   12:  H  H  H  H  H  H  T  H  T  T 
	Line   17:  H  H  H  H  H  T  H  H  H  H 
	Line   18:  H  H  H  H  H  T  H  H  H  T 
	Line   19:  H  H  H  H  H  T  H  H  T  H 
	Line   20:  H  H  H  H  H  T  H  H  T  T 
	Line   21:  H  H  H  H  H  T  H  T  H  H 
	Line   22:  H  H  H  H  H  T  H  T  H  T 
	Line   23:  H  H  H  H  H  T  H  T  T  H 
	Line   24:  H  H  H  H  H  T  H  T  T  T 
	Line   27:  H  H  H  H  H  T  T  H  T  H 
	Line   33:  H  H  H  H  T  H  H  H  H  H 
	Line   34:  H  H  H  H  T  H  H  H  H  T 
	Line   35:  H  H  H  H  T  H  H  H  T  H 
	Line   36:  H  H  H  H  T  H  H  H  T  T 
	Line   37:  H  H  H  H  T  H  H  T  H  H 
	Line   38:  H  H  H  H  T  H  H  T  H  T 
	Line   39:  H  H  H  H  T  H  H  T  T  H 
	Line   40:  H  H  H  H  T  H  H  T  T  T 
	Line   41:  H  H  H  H  T  H  T  H  H  H 
	Line   42:  H  H  H  H  T  H  T  H  H  T 
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	Line   44:  H  H  H  H  T  H  T  H  T  T 
	Line   45:  H  H  H  H  T  H  T  T  H  H 
	Line   46:  H  H  H  H  T  H  T  T  H  T 
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	Line   48:  H  H  H  H  T  H  T  T  T  T 
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	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   59:  H  H  H  H  T  T  T  H  T  H 
	Line   65:  H  H  H  T  H  H  H  H  H  H 
	Line   66:  H  H  H  T  H  H  H  H  H  T 
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	Line   68:  H  H  H  T  H  H  H  H  T  T 
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	Line   70:  H  H  H  T  H  H  H  T  H  T 
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	Line   72:  H  H  H  T  H  H  H  T  T  T 
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	Line   76:  H  H  H  T  H  H  T  H  T  T 
	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   79:  H  H  H  T  H  H  T  T  T  H 
	Line   80:  H  H  H  T  H  H  T  T  T  T 
	Line   81:  H  H  H  T  H  T  H  H  H  H 
	Line   82:  H  H  H  T  H  T  H  H  H  T 
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	Line   84:  H  H  H  T  H  T  H  H  T  T 
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	Line   90:  H  H  H  T  H  T  T  H  H  T 
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	Line   92:  H  H  H  T  H  T  T  H  T  T 
	Line   93:  H  H  H  T  H  T  T  T  H  H 
	Line   94:  H  H  H  T  H  T  T  T  H  T 
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	Line   96:  H  H  H  T  H  T  T  T  T  T 
	Line   99:  H  H  H  T  T  H  H  H  T  H 
	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  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  115:  H  H  H  T  T  T  H  H  T  H 
	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  123:  H  H  H  T  T  T  T  H  T  H 
	Line  129:  H  H  T  H  H  H  H  H  H  H 
	Line  130:  H  H  T  H  H  H  H  H  H  T 
	Line  131:  H  H  T  H  H  H  H  H  T  H 
	Line  132:  H  H  T  H  H  H  H  H  T  T 
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	Line  134:  H  H  T  H  H  H  H  T  H  T 
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	Line  136:  H  H  T  H  H  H  H  T  T  T 
	Line  137:  H  H  T  H  H  H  T  H  H  H 
	Line  138:  H  H  T  H  H  H  T  H  H  T 
	Line  139:  H  H  T  H  H  H  T  H  T  H 
	Line  140:  H  H  T  H  H  H  T  H  T  T 
	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  143:  H  H  T  H  H  H  T  T  T  H 
	Line  144:  H  H  T  H  H  H  T  T  T  T 
	Line  145:  H  H  T  H  H  T  H  H  H  H 
	Line  146:  H  H  T  H  H  T  H  H  H  T 
	Line  147:  H  H  T  H  H  T  H  H  T  H 
	Line  148:  H  H  T  H  H  T  H  H  T  T 
	Line  149:  H  H  T  H  H  T  H  T  H  H 
	Line  150:  H  H  T  H  H  T  H  T  H  T 
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	Line  152:  H  H  T  H  H  T  H  T  T  T 
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	Line  154:  H  H  T  H  H  T  T  H  H  T 
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	Line  156:  H  H  T  H  H  T  T  H  T  T 
	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  159:  H  H  T  H  H  T  T  T  T  H 
	Line  160:  H  H  T  H  H  T  T  T  T  T 
	Line  161:  H  H  T  H  T  H  H  H  H  H 
	Line  162:  H  H  T  H  T  H  H  H  H  T 
	Line  163:  H  H  T  H  T  H  H  H  T  H 
	Line  164:  H  H  T  H  T  H  H  H  T  T 
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	Line  166:  H  H  T  H  T  H  H  T  H  T 
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	Line  168:  H  H  T  H  T  H  H  T  T  T 
	Line  169:  H  H  T  H  T  H  T  H  H  H 
	Line  170:  H  H  T  H  T  H  T  H  H  T 
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	Line  172:  H  H  T  H  T  H  T  H  T  T 
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	Line  174:  H  H  T  H  T  H  T  T  H  T 
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	Line  176:  H  H  T  H  T  H  T  T  T  T 
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	Line  178:  H  H  T  H  T  T  H  H  H  T 
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	Line  180:  H  H  T  H  T  T  H  H  T  T 
	Line  181:  H  H  T  H  T  T  H  T  H  H 
	Line  182:  H  H  T  H  T  T  H  T  H  T 
	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  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 
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	Line  190:  H  H  T  H  T  T  T  T  H  T 
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	Line  198:  H  H  T  T  H  H  H  T  H  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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	Line  204:  H  H  T  T  H  H  T  H  T  T 
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	Line  210:  H  H  T  T  H  T  H  H  H  T 
	Line  211:  H  H  T  T  H  T  H  H  T  H 
	Line  212:  H  H  T  T  H  T  H  H  T  T 
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	Line  214:  H  H  T  T  H  T  H  T  H  T 
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	Line  216:  H  H  T  T  H  T  H  T  T  T 
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	Line  230:  H  H  T  T  T  H  H  T  H  T 
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	Line  234:  H  H  T  T  T  H  T  H  H  T 
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	Line  246:  H  H  T  T  T  T  H  T  H  T 
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	Line  257:  H  T  H  H  H  H  H  H  H  H 
	Line  258:  H  T  H  H  H  H  H  H  H  T 
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	Line  260:  H  T  H  H  H  H  H  H  T  T 
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    You can certainly define your streak the way you want, but please keep in mind that it's not the definition accepted by many people.witj decades of experience in the field nor does it make sense in general for a streak to be narrowly defined the way you are describing it where a stream can on be when it's included between two non-events
    Chance favors the prepared mind
  9. 05-13-2024, 02:19 AM #113
    toolyp
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    Quote Originally Posted by DSchles View Post
    Naturally, you're correct, and this is what I explained dozens of posts ago. But there's no explaining to toolyp, because he's adopted a false idol, and he's going to stick with Weaver, whose book I read decades ago. For me, the case has been closed for days because, well, I've studied all of this for ages. But, we always have newcomers who want to explain why they know everything and we know nothing. It's easy to grow tired of them after a while. Don't waste too many brain cells on this.

    Don
    Don “Lucky” Vito, off the topic, I commend you for creating the Lucky Ladies sidebet. Sadly Warren Weaver, who never asked for to be an idol, didnt have the chance to analyze the LL bet streak-wise!

    Methinks the “false idol” is a Freudian slip on your part. You do want to be idolized, or else you gonna whack the perpetrator! kidding! Warren Weaver’s book is still studied in universities. Despite your claimed old-age, no university cares about your ineptitudes. You dont know the difference between probability and streak. Simply put it, probability is a fraction; streak is an integer.

    There is a human activity named sports. They gamble on sports too. There are streaks in sports. “The Eagles had an 10-game winning streak.” Remember? The Eagles lost and the streak ended. They started another streak, a losing streak this time. So the streaks were marked by a beginning and an end of the opposite outcome. According to your anti-Weaver-jealousy ineptitude, Eagles had 11 winning streaks: a streak of 0, a streak of 1, a streak of 2… a streak of 9 and a streak of 10 consecutive wins! Man oh man!

    Capisci?

    No offence, no whack, just my honest opinion.
  10. 05-13-2024, 02:20 AM #114
    toolyp
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    Quote Originally Posted by Cacarulo View Post
    I don't think we will agree. While it is true that a streak of, for example, 2 consecutive heads must be bounded by 2 tails, it is also true that a streak of
    2 heads can be the beginning or the end of a series of n tosses.
    With all due respect to the late Warren Weaver, he probably omitted these 2 cases. Just to make sure, I also have his book.

    Let's consider an example of 4 coin tosses (2^4=16 possibilities). The lengths of the longest streaks of heads are, respectively:

    HHHH = 4
    HHHT = 3
    HHTH = 2
    HHTT = 2
    HTHH = 2
    HTHT = 1
    HTTH = 1
    HTTT = 1
    THHH = 3
    THHT = 2
    THTH = 1
    THTT = 1
    TTHH = 2
    TTHT = 1
    TTTH = 1
    TTTT = 0

    So we get the following distribution:

    exact streak length | probability
    0 | 1/16
    1 | 7/16
    2 | 5/16
    3 | 2/16
    4 | 1/16

    If we were to consider a definition as strict as the one you suggest, for a length of 2 the probability would be 1/16, which I don't think is correct.
    Also, according to your definition, in 4 coin tosses there are no streaks of 3 or 4, which is incorrect. However, I don't see anyone, not even online calculators,
    agreeing with Weaver's definition or yours.

    Sincerely,
    Cac
    Don Cacarulo, my reply to Don “Lucky” Vito is also a reply to you. To summarize, probability is a fraction, streak is an integer.

    The worst part, you still believe in “a streak of 0 length”. Such thing is a chimera. Nobody will ever see “a streak of 0 length”. Life will be full of such chimeras! Speaking of sports as in my reply to Don “Lucky” Vito. Teams have winning streaks and/or losing streaks.

    But youll never hear the expression “Eagles have a 0-winning streak”. Sure they had a 10-game winning streak but it was a 1 followed by a 0; that’s not zero. According to your anti-Weaver-jealousy ineptitude, Eagles had 11 winning streaks: a streak of 0, a streak of 1, a streak of 2… a streak of 9 and a streak of 10 consecutive wins! Man oh man!

    And again the same absurdity you Don Cacarulo share with Don “Lucky” Vito. String equates probability. “Length-0 streak is equal to probability of exactly 0 successes” (in how many trials?) That’s really bad… sorry!

    Streaks are also characterized by skips. Haven’t you heard gamblers say “That goddam roulette number skipped dozens of spins! Then it hit…and had only a winning streak of 1!” It doesnt mean the number had a dozen streaks of length-0.

    Again, probability is a fraction, streak is an integer equal to or greater than +1.

    Capisci?

    No offence, no whack, just my honest opinion.
  11. 05-13-2024, 04:33 AM #115
    iCountNTrack
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    Dear Lord, thread locked
    Chance favors the prepared mind
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