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What is the probability of this happening again?

Topic closed. 18 replies. Last post 8 years ago by truecritic.

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WIN  D's avatar - q05Q0
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Stone Mountain*Georgia
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Posted: September 30, 2009, 12:06 pm - IP Logged

                           Odds never change ......but the probabilities do.

                                   

-----------------------------------------------------------

 

                  Say ..... can you toss a coin 33 times in a row ......and never get 2 heads in a row ?

                                                  Well, Ga Eve Pick 3 game can.   

 

   Heads and Tails ..... Odd/Even  High/LOw  Bed

 

           Mostly to all High // Mostly to all Lows            500 of each out of the P3 1000 right ?

 

 Ga Eve has not had back to back Mostly to all  Low ........ since Aug 27th !   Today is Sept 30Th. !   

 

       So..... for the last 30 + draws ....... there has been NO back to back Heads (All to Mostly Low)

 

                                                            50/50 odds each day every day .......

 

                                 ......and yet......no 2 draws in a row of Mostly to All low digits.

         Whats the probability of that happening again next month?

 

 

The only real failure .....is the failure to try.                               

                              Luck is a very rare thing....... Odds not so much. 

                              Odds never change .....but probability does. 

                                                                                       Win d    

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    NY
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    Posted: October 1, 2009, 2:22 am - IP Logged

    All high/ all low isn't a 500/500 proposition. High and low each have 5 digits, so there are 125 (5*5*5) numbers that qualify. That means that you should expect all high (as well as all low, all odd, or all even) in 1 of every 8 drawings. Since the odds of having it happening again in the next drawing would also be 1 in 8, we would expect it to happen twice in a row once every 64 drawings. Compare that to once in every 4 for flipping a coin.

    The probability that it won't happen for any number of  drawings is the probability of a different outcome, raised to the nth power, where n is the number of drawings. The probability of a different outcome is 63/64, or 0.984375, so the probability that it won't happen in 31 drawings is 0.984375 to the 30th power*. That's 0.623, or 62.3%. Conversely there's a 37.7% chance that it will happen in any given month.

    I'm not sure what "mostly to all high" means. If it means 2 high and whatever the 3rd digit is, then there are 5*5*10 or 250 numbers that qualify. For that we'd expect repeats once every 16 drawings. The probability of not happening in a month would be 15/16  or 0.9375 ^ 30 or about 14.4%. That's almost two months per year.

    * I used the 30th power instead of 31st, because there can't be a repeat on the first drawings, and if there's a repeat after the 31st drawing it will be in the next month. The difference for raising to the 31st is very small anyway.

      WIN  D's avatar - q05Q0
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      Posted: October 1, 2009, 4:27 pm - IP Logged

       Hello Ky Floyd ....good to know your around.  This was a confusing term to someone not used to PICK 3 language. Sorry about that.  I used a term which is pretty well known within the Pick 3 Hobby Player community.... " Mostly to ALL HIGH" ...Mostly to ALL LOW.....  Mostly to all Even .....Mostly to all ODD.

       What this pretty commonly used  phrase indicates to mostly to ALL of us is.... LOL   The 10 pure numbers in each of those groups...... as well as the numbers which contain 2 of the named group digits.

       For example : 

        The 10 single number ALL HIGH ....... 569, 578, 579, 678, 589, 679, 689, 789, 567, 568

          Along with the remaining 50 Mostly single like numbers which contain at least 2 of the high digits

        389, 479, 056, 489, 057, 156, 058, 067, 157, 256, 059, 068, 158, 167, 257, 356, 069, 078, 159, 168, 258, 267, 357, 456, 079, 169, 178, 259, 268, 358, 367, 457, 089, 179, 269, 278, 359, 368, 458, 467, 189, 279, 369, 378, 459, 468, 289, 379, 469, 478

         All toll...... 60 singles Box numbers ....or ..... 360 straights

        Double number versions of ALL HIGH .....20 of them

        668, 677, 588, 669, 688, 778, 599, 779, 788, 699,

       799, 889, 556, 899, 557, 566, 558, 559, 577, 667

          Mostly Highs  ...... 25 doubles

      055, 299, 488, 155, 399, 066, 255, 499, 166, 355,

       077,

      266, 455, 177, 366, 088, 277, 466, 188, 377, 099, 288, 477, 199, 388

       

       Plus ......the 5 ALL HIGH Trips ....555 666 777 888 999

       

        All toll..... 45 doubles or 135 straights .......plus 5 trips

         360 singles 135 doubles .....5 trips =    500 Straights

      ===========================================

       

       All of these Box types above translate to these numbers below...... 495 of them plus the 5 trips versions for a total of500 numbers .   Of course the Mostly to ALL LOW numbers would be the other HALF .

      555 666 777 888 999 +

      055, 056, 057, 058, 059, 065, 066, 067, 068, 069, 075, 076, 077, 078, 079, 085, 086, 087, 088, 089, 095, 096, 097, 098, 099, 155, 156, 157, 158, 159, 165, 166, 167, 168, 169, 175, 176, 177, 178, 179, 185, 186, 187, 188, 189, 195, 196, 197, 198, 199, 255, 256, 257, 258, 259, 265, 266, 267, 268, 269, 275, 276, 277, 278, 279, 285, 286, 287, 288, 289, 295, 296, 297, 298, 299, 355, 356, 357, 358, 359, 365, 366, 367, 368, 369, 375, 376, 377, 378, 379, 385, 386, 387, 388, 389, 395, 396, 397, 398, 399, 455, 456, 457, 458, 459, 465, 466, 467, 468, 469, 475, 476, 477, 478, 479, 485, 486, 487, 488, 489, 495, 496, 497, 498, 499, 505, 506, 507, 508, 509, 515, 516, 517, 518, 519, 525, 526, 527, 528, 529, 535, 536, 537, 538, 539, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 605, 606, 607, 608, 609, 615, 616, 617, 618, 619, 625, 626, 627, 628, 629, 635, 636, 637, 638, 639, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 705, 706, 707, 708, 709, 715, 716, 717, 718, 719, 725, 726, 727, 728, 729, 735, 736, 737, 738, 739, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 805, 806, 807, 808, 809, 815, 816, 817, 818, 819, 825, 826, 827, 828, 829, 835, 836, 837, 838, 839, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867,868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 905, 906, 907, 908, 909, 915, 916, 917, 918, 919, 925, 926, 927, 928, 929, 935, 936, 937, 938, 939, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998

       

       The reason I highlighted the 868 is because Ga Eve last night drew another ...." Mostly to ALL HIGH" number from that half of the 1000 chart.

      Now 34 days or Coin flips...... and No back to back Tails from the  Mostly to ALL LOW half of the chart..      

                         So ..... the beat goes on for one more night without hitting 2 Heads in a row. 

       

       

       ******  One thing we do know for sure .....beyond All doubt and with 100% surity....  It will have to go on to at least draw 36 now ...before this String ends. That much is sure.

       

       

      The only real failure .....is the failure to try.                               

                                    Luck is a very rare thing....... Odds not so much. 

                                    Odds never change .....but probability does. 

                                                                                             Win d    

        WIN  D's avatar - q05Q0
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        Posted: October 1, 2009, 4:51 pm - IP Logged

                         The 500 "Mostly to ALL LOW Group"  or  The Tails side of the Coin .  50/50

         

         

          Pure ALL LOWS  ....10 singles +20 doubles and 5 trips 000 111 222 333 444  

         244, 334, 001, 344, 002, 011, 003, 012, 004, 013, 022, 112, 014, 023, 113, 122, 024, 033, 114, 123, 034, 124, 133, 223, 044, 134, 224, 233, 144, 234

         The Mostly Low Group... 375 of them

          005, 006, 007, 008, 009, 015, 016, 017, 018, 019, 025, 026, 027, 028, 029, 035, 036, 037, 038, 039, 045, 046, 047, 048, 049, 050, 051, 052, 053, 054, 060, 061, 062, 063, 064, 070, 071, 072, 073, 074, 080, 081, 082, 083, 084, 090, 091, 092, 093, 094, 105, 106, 107, 108, 109, 115, 116, 117, 118, 119, 125, 126, 127, 128, 129, 135, 136, 137, 138, 139, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 160, 161, 162, 163, 164, 170, 171, 172, 173, 174, 180, 181, 182, 183, 184, 190, 191, 192, 193, 194, 205, 206, 207, 208, 209, 215, 216, 217, 218, 219, 225, 226, 227, 228, 229, 235, 236, 237, 238, 239, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 260, 261, 262, 263, 264, 270, 271, 272, 273, 274, 280, 281, 282, 283, 284, 290, 291, 292, 293, 294, 305, 306, 307, 308, 309, 315, 316, 317, 318, 319, 325, 326, 327, 328, 329, 335, 336, 337, 338, 339, 345, 346, 347, 348, 349, 350, 351, 352, 353, 354, 360, 361, 362, 363, 364, 370, 371, 372, 373, 374, 380, 381, 382, 383, 384, 390, 391, 392, 393, 394, 405, 406, 407, 408, 409, 415, 416, 417, 418, 419, 425, 426, 427, 428, 429, 435, 436, 437, 438, 439, 445, 446, 447, 448, 449, 450, 451, 452, 453, 454, 460, 461, 462, 463, 464, 470, 471, 472, 473, 474, 480, 481, 482, 483, 484, 490, 491, 492, 493, 494, 500, 501, 502, 503, 504, 510, 511, 512, 513, 514, 520, 521, 522, 523, 524, 530, 531, 532, 533, 534, 540, 541, 542, 543, 544, 600, 601, 602, 603, 604, 610, 611, 612, 613, 614, 620, 621, 622, 623, 624, 630, 631, 632, 633, 634, 640, 641, 642, 643, 644, 700, 701, 702, 703, 704, 710, 711, 712, 713, 714, 720, 721, 722, 723, 724, 730, 731, 732, 733, 734, 740, 741, 742, 743, 744, 800, 801, 802, 803, 804, 810, 811, 812, 813, 814, 820, 821, 822, 823, 824, 830, 831, 832, 833, 834, 840, 841, 842, 843, 844, 900, 901, 902, 903, 904, 910, 911, 912, 913, 914, 920, 921, 922, 923, 924, 930, 931, 932, 933, 934, 940, 941, 942, 943, 944

         

           Now, the question is going to have to be ...... What is the probability of tossing a coin 36 times without getting 2 Tails in a row ?    At least for now....thats the question. LOL  

         

         

        The only real failure .....is the failure to try.                               

                                      Luck is a very rare thing....... Odds not so much. 

                                      Odds never change .....but probability does. 

                                                                                               Win d    

          WIN  D's avatar - q05Q0
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          Posted: October 1, 2009, 8:05 pm - IP Logged

          059 hit tonight ....... from the Mostly to ALL High group ...... again.  Mostly Odd too.

          Now the question will have to be.... What is the probability of tossing a coin 38 times without getting 2 Tails in a row? 

           

           I guess a good way to frame this is to take it as ......( 2 tosses equal = 1 event)  So far we have had 18 2 toss events .....and 18 negative outcomes. If tomorrow is also another Mostly to ALL High..... it will be 19 negative outcomes in a row.  wow... 

               Someone betting the other way would have lost 18 two game events in a row so far!  So to speak... and if tomorrow is another Mostly to all High number ....it wil. be 19 losses in a row.       

          =================================================================

           

           

          .

          All of these Box types above translate to these numbers below...... 495 of them plus the 5 trips versions for a total of 500 numbers .   Of course the Mostly to ALL LOW numbers would be the other HALF .

          555 666 777 888 999 +

          055, 056, 057, 058,059, 065, 066, 067, 068, 069, 075, 076, 077, 078, 079, 085, 086, 087, 088, 089, 095, 096, 097, 098, 099, 155, 156, 157, 158, 159, 165, 166, 167, 168, 169, 175, 176, 177, 178, 179, 185, 186, 187, 188, 189, 195, 196, 197, 198, 199, 255, 256, 257, 258, 259, 265, 266, 267, 268, 269, 275, 276, 277, 278, 279, 285, 286, 287, 288, 289, 295, 296, 297, 298, 299, 355, 356, 357, 358, 359, 365, 366, 367, 368, 369, 375, 376, 377, 378, 379, 385, 386, 387, 388, 389, 395, 396, 397, 398, 399, 455, 456, 457, 458, 459, 465, 466, 467, 468, 469, 475, 476, 477, 478, 479, 485, 486, 487, 488, 489, 495, 496, 497, 498, 499, 505, 506, 507, 508, 509, 515, 516, 517, 518, 519, 525, 526, 527, 528, 529, 535, 536, 537, 538, 539, 545, 546, 547, 548, 549, 550, 551, 552, 553, 554, 556, 557, 558, 559, 560, 561, 562, 563, 564, 565, 566, 567, 568, 569, 570, 571, 572, 573, 574, 575, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 586, 587, 588, 589, 590, 591, 592, 593, 594, 595, 596, 597, 598, 599, 605, 606, 607, 608, 609, 615, 616, 617, 618, 619, 625, 626, 627, 628, 629, 635, 636, 637, 638, 639, 645, 646, 647, 648, 649, 650, 651, 652, 653, 654, 655, 656, 657, 658, 659, 660, 661, 662, 663, 664, 665, 667, 668, 669, 670, 671, 672, 673, 674, 675, 676, 677, 678, 679, 680, 681, 682, 683, 684, 685, 686, 687, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 698, 699, 705, 706, 707, 708, 709, 715, 716, 717, 718, 719, 725, 726, 727, 728, 729, 735, 736, 737, 738, 739, 745, 746, 747, 748, 749, 750, 751, 752, 753, 754, 755, 756, 757, 758, 759, 760, 761, 762, 763, 764, 765, 766, 767, 768, 769, 770, 771, 772, 773, 774, 775, 776, 778, 779, 780, 781, 782, 783, 784, 785, 786, 787, 788, 789, 790, 791, 792, 793, 794, 795, 796, 797, 798, 799, 805, 806, 807, 808, 809, 815, 816, 817, 818, 819, 825, 826, 827, 828, 829, 835, 836, 837, 838, 839, 845, 846, 847, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 858, 859, 860, 861, 862, 863, 864, 865, 866, 867,868, 869, 870, 871, 872, 873, 874, 875, 876, 877, 878, 879, 880, 881, 882, 883, 884, 885, 886, 887, 889, 890, 891, 892, 893, 894, 895, 896, 897, 898, 899, 905, 906, 907, 908, 909, 915, 916, 917, 918, 919, 925, 926, 927, 928, 929, 935, 936, 937, 938, 939, 945, 946, 947, 948, 949, 950, 951, 952, 953, 954, 955, 956, 957, 958, 959, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 970, 971, 972, 973, 974, 975, 976, 977, 978, 979, 980, 981, 982, 983, 984, 985, 986, 987, 988, 989, 990, 991, 992, 993, 994, 995, 996, 997, 998

           

           

          The only real failure .....is the failure to try.                               

                                        Luck is a very rare thing....... Odds not so much. 

                                        Odds never change .....but probability does. 

                                                                                                 Win d    

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            Posted: October 2, 2009, 1:16 am - IP Logged

            What is the probability of tossing a coin 38 times without getting 2 Tails in a row?

            I guess a good way to frame this is to take it as ......( 2 tosses equal = 1 event)  So far we have had 18 2 toss events

            Nope. Tossing a coin 38 times gives you 37 "2 toss events." Each  event starts with the first of 2 consecutive tosses, and ends with the following toss. Toss 1 starts the first event and toss 2 finishes it, but #2 is also the start of the 2nd event:
            1 & 2
            2 & 3
            3 & 4
            .
            .
            .
            37 & 38

            Toss 38 won't become a 2 toss event until toss 39 occurs.

            The probability of a result other than two tails in any event is .75. Just as the probability ot two tails is .5 x .5, the probability of two events both being something other than two tails is .75 x .75.  For n consecutive events it's .756^n.  For the 37 events *ending* with toss 38 it would be .75^37, which is .000024 or 1 in 41,950.

              JADELottery's avatar - AMeOn 02.png
              The Quantum Master
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              Posted: October 2, 2009, 10:14 am - IP Logged

              It's not quite that simple an equation. The progression of No Back-to-Back and Back-to-Back Bit Flips or Coin Tosses is as follows:

               

              Bit Flips orPossible OutcomesOddsProbability ofProbability of
              Coin TossesNo Back-to-BackBack-to-BackNBB : BBNo Back-to-BackBack-to-Back
              2311 : 0.3375.0000%25.0000%
              3531 : 0.6062.5000%37.5000%
              4881 : 1.0050.0000%50.0000%
              513191 : 1.4640.6250%59.3750%
              621431 : 2.0532.8125%67.1875%
              734941 : 2.7626.5625%73.4375%
              8552011 : 3.6521.4844%78.5156%
              9894231 : 4.7517.3828%82.6172%
              101448801 : 6.1114.0625%85.9375%
              1123318151 : 7.7911.3770%88.6230%
              1237737191 : 9.869.2041%90.7959%
              1361075821 : 12.437.4463%92.5537%
              14987153971 : 15.606.0242%93.9758%
              151597311711 : 19.524.8737%95.1263%
              162584629521 : 24.363.9429%96.0571%
              1741811268911 : 30.353.1898%96.8102%
              1867652553791 : 37.752.5806%97.4194%
              19109465133421 : 46.902.0878%97.9122%
              201771110308651 : 58.201.6891%98.3109%
              212865720684951 : 72.181.3665%98.6335%
              224636841479361 : 89.461.1055%98.8945%
              237502583135831 : 110.810.8944%99.1056%
              24121393166558231 : 137.210.7236%99.2764%
              25196418333580141 : 169.830.5854%99.4146%
              26317811667910531 : 210.160.4736%99.5264%
              275142291337034991 : 260.010.3831%99.6169%
              288320402676034161 : 321.620.3100%99.6900%
              2913462695355246431 : 397.780.2508%99.7492%
              30217830910715635151 : 491.920.2029%99.7971%
              31352457821439590701 : 608.290.1641%99.8359%
              32570288742892644091 : 752.120.1328%99.8672%
              33922746585807071271 : 929.910.1074%99.8926%
              3414930352171649388321 : 1149.670.0869%99.9131%
              3524157817343355805511 : 1421.300.0703%99.9297%
              3639088169686803885671 : 1757.060.0569%99.9431%
              37632459861373757074861 : 2172.090.0460%99.9540%
              381023341552747755727891 : 2685.080.0372%99.9628%
              391655801415495902337471 : 3319.180.0301%99.9699%
              4026791429610992437134801 : 4102.970.0244%99.9756%
              4143349443721985897611151 : 5071.780.0197%99.9803%
              4270140873343973451023711 : 6269.300.0159%99.9841%
              43113490317087949581190381 : 7749.520.0129%99.9871%
              441836311903175903497325131 : 9579.170.0104%99.9896%
              452971215073351814008737591 : 11840.750.0084%99.9916%
              464807526976703639366506881 : 14636.200.0068%99.9932%
              4777787420491407297096132791 : 18091.580.0055%99.9945%
              48125862690252814623904416311 : 22362.650.0045%99.9955%
              49203650110745629295884102381 : 27642.000.0036%99.9964%
              503295128009911258669555625201 : 34167.620.0029%99.9971%

              Presented 'AS IS' and for Entertainment Purposes Only.
              Any gain or loss is your responsibility.
              Use at your own risk.

              Order is a Subset of Chaos
              Knowledge is Beyond Belief
              Wisdom is Not Censored
              Douglas Paul Smallish
              Jehocifer

                Avatar
                NY
                United States
                Member #23835
                October 16, 2005
                3621 Posts
                Offline
                Posted: October 2, 2009, 2:56 pm - IP Logged

                It is that simple. What you've done is list all possible outcomes and the ratio between two types of outcomes, and assumed that the ratio  can be used to determine the probabilty of one unlikely set of possible outcomes. That works for the possible outcomes of a single event, but not multiple iterations, as in this case. In essence you're using each new flip to change the probability of previous flips.

                Let's  start from flip # 2 and then look at what happens with flip # 3. As you correctly note, after flip # 2 there are 4 possible outcomes, and there's a 75% chance that we've had one of the 3 results that didn't already give us back to back tails. Since we're looking at the probability of not having any back to back tails, we're only concerned with outcomes where that's the result we've gotten, and that 4th possible result is no longer relevant. If it happened it happened, and it's now a certainty rather than a probability. Therefore we've conducted the 2nd flip, and it was either heads or tails, with a 50% chance of each. We now make flip # 3, and there is a 50% chance it will be heads and a 50% chance it will be tails. That means that when we see the result of flip #3 there is a 75% chance that we will have ended our streak with no back to back tails and a 25% chance that it will remain unbroken.

                That means that after flip #3 the chance that we still don't have back to back tails is 75% of what it was after flip #2. 75% of 75% is 56.25%, not the 62.5% you've shown.

                As we move down the chart we'll have the same pattern. Each succeeding flip may increase the total number of possible outcomes that could have happened by a factor of two, but it only adds 4 new possibilities to the results we've actually had. Each time we reduce the possibility of no back to back tails to 75% of the previous possibility. Your figures consistently show a figure that is close to 80%, but varies a bit.

                BTW, in # 50 you're missing 5 possible outcomes in the no back to back column.

                  JADELottery's avatar - AMeOn 02.png
                  The Quantum Master
                  West Concord, MN
                  United States
                  Member #21
                  December 7, 2001
                  3954 Posts
                  Offline
                  Posted: October 2, 2009, 4:24 pm - IP Logged

                  It is that simple. What you've done is list all possible outcomes and the ratio between two types of outcomes, and assumed that the ratio  can be used to determine the probabilty of one unlikely set of possible outcomes. That works for the possible outcomes of a single event, but not multiple iterations, as in this case. In essence you're using each new flip to change the probability of previous flips.

                  Let's  start from flip # 2 and then look at what happens with flip # 3. As you correctly note, after flip # 2 there are 4 possible outcomes, and there's a 75% chance that we've had one of the 3 results that didn't already give us back to back tails. Since we're looking at the probability of not having any back to back tails, we're only concerned with outcomes where that's the result we've gotten, and that 4th possible result is no longer relevant. If it happened it happened, and it's now a certainty rather than a probability. Therefore we've conducted the 2nd flip, and it was either heads or tails, with a 50% chance of each. We now make flip # 3, and there is a 50% chance it will be heads and a 50% chance it will be tails. That means that when we see the result of flip #3 there is a 75% chance that we will have ended our streak with no back to back tails and a 25% chance that it will remain unbroken.

                  That means that after flip #3 the chance that we still don't have back to back tails is 75% of what it was after flip #2. 75% of 75% is 56.25%, not the 62.5% you've shown.

                  As we move down the chart we'll have the same pattern. Each succeeding flip may increase the total number of possible outcomes that could have happened by a factor of two, but it only adds 4 new possibilities to the results we've actually had. Each time we reduce the possibility of no back to back tails to 75% of the previous possibility. Your figures consistently show a figure that is close to 80%, but varies a bit.

                  BTW, in # 50 you're missing 5 possible outcomes in the no back to back column.

                  You're right about the 50 Back-to-Back flips; it's an Excel computation issue. It actually should be 1125866955562525. It’s caused by the fact that Excel tunicates the number after a certain number of digits; in this case 15 digits and the 5 was dropped.

                  Buuut... you are wrong about the calculation of probability; in this case, the probability of No Back-to-Back. Where you went wrong is not considering ALL possibilities. That's what the table shows. So, let's go through the progression. We'll use 1's and 0's to represent the flip; where 1 is outcome occurred and 0 is the outcome did not. Since this is a succession of flips, we'll start at 2 flips and look at ALL the possible outcomes. Now, by definition, a No Back-to-Back flip is when there are no consecutive 1’s; i.e. (1 1). The following is the total possible outcomes for 2 flips.

                   

                  Flip #

                   

                  Outcome #

                  1

                  2

                  No Back-To-Back

                  1

                  0

                  0

                  TRUE

                  2

                  0

                  1

                  TRUE

                  3

                  1

                  0

                  TRUE

                  4

                  1

                  1

                  FALSE

                  From this we can see there are 3 possible outcomes where there are No Back-to-Back flips. Given that the total number of outcomes is 4, the probability of having a No Back-to-Back flip is 3 / 4, or 75%. Continuing this progression, we can go to 3 flips as follows:

                   

                  Flip #

                   

                  Outcome #

                  1

                  2

                  3

                  No Back-To-Back

                  1

                  0

                  0

                  0

                  TRUE

                  2

                  0

                  0

                  1

                  TRUE

                  3

                  0

                  1

                  0

                  TRUE

                  4

                  0

                  1

                  1

                  FALSE

                  5

                  1

                  0

                  0

                  TRUE

                  6

                  1

                  0

                  1

                  TRUE

                  7

                  1

                  1

                  0

                  FALSE

                  8

                  1

                  1

                  1

                  FALSE

                  The table shows there are 5 possible outcomes where there is No Back-to-Back flip. This becomes 5 / 8, or 62.5% probability of having a No Back-to-Back flip. The progression continues...

                   

                  Flip #

                   

                  Outcome #

                  1

                  2

                  3

                  4

                  No Back-To-Back

                  1

                  0

                  0

                  0

                  0

                  TRUE

                  2

                  0

                  0

                  0

                  1

                  TRUE

                  3

                  0

                  0

                  1

                  0

                  TRUE

                  4

                  0

                  0

                  1

                  1

                  FALSE

                  5

                  0

                  1

                  0

                  0

                  TRUE

                  6

                  0

                  1

                  0

                  1

                  TRUE

                  7

                  0

                  1

                  1

                  0

                  FALSE

                  8

                  0

                  1

                  1

                  1

                  FALSE

                  9

                  1

                  0

                  0

                  0

                  TRUE

                  10

                  1

                  0

                  0

                  1

                  TRUE

                  11

                  1

                  0

                  1

                  0

                  TRUE

                  12

                  1

                  0

                  1

                  1

                  FALSE

                  13

                  1

                  1

                  0

                  0

                  FALSE

                  14

                  1

                  1

                  0

                  1

                  FALSE

                  15

                  1

                  1

                  1

                  0

                  FALSE

                  16

                  1

                  1

                  1

                  1

                  FALSE

                  In the case of 4 flips, there are 8 out of 16 possible outcomes for a probability of 50%. Moving along...

                   

                  Flip #

                   

                  Outcome #

                  1

                  2

                  3

                  4

                  5

                  No Back-To-Back

                  1

                  0

                  0

                  0

                  0

                  0

                  TRUE

                  2

                  0

                  0

                  0

                  0

                  1

                  TRUE

                  3

                  0

                  0

                  0

                  1

                  0

                  TRUE

                  4

                  0

                  0

                  0

                  1

                  1

                  FALSE

                  5

                  0

                  0

                  1

                  0

                  0

                  TRUE

                  6

                  0

                  0

                  1

                  0

                  1

                  TRUE

                  7

                  0

                  0

                  1

                  1

                  0

                  FALSE

                  8

                  0

                  0

                  1

                  1

                  1

                  FALSE

                  9

                  0

                  1

                  0

                  0

                  0

                  TRUE

                  10

                  0

                  1

                  0

                  0

                  1

                  TRUE

                  11

                  0

                  1

                  0

                  1

                  0

                  TRUE

                  12

                  0

                  1

                  0

                  1

                  1

                  FALSE

                  13

                  0

                  1

                  1

                  0

                  0

                  FALSE

                  14

                  0

                  1

                  1

                  0

                  1

                  FALSE

                  15

                  0

                  1

                  1

                  1

                  0

                  FALSE

                  16

                  0

                  1

                  1

                  1

                  1

                  FALSE

                  17

                  1

                  0

                  0

                  0

                  0

                  TRUE

                  18

                  1

                  0

                  0

                  0

                  1

                  TRUE

                  19

                  1

                  0

                  0

                  1

                  0

                  TRUE

                  20

                  1

                  0

                  0

                  1

                  1

                  FALSE

                  21

                  1

                  0

                  1

                  0

                  0

                  TRUE

                  22

                  1

                  0

                  1

                  0

                  1

                  TRUE

                  23

                  1

                  0

                  1

                  1

                  0

                  FALSE

                  24

                  1

                  0

                  1

                  1

                  1

                  FALSE

                  25

                  1

                  1

                  0

                  0

                  0

                  FALSE

                  26

                  1

                  1

                  0

                  0

                  1

                  FALSE

                  27

                  1

                  1

                  0

                  1

                  0

                  FALSE

                  28

                  1

                  1

                  0

                  1

                  1

                  FALSE

                  29

                  1

                  1

                  1

                  0

                  0

                  FALSE

                  30

                  1

                  1

                  1

                  0

                  1

                  FALSE

                  31

                  1

                  1

                  1

                  1

                  0

                  FALSE

                  32

                  1

                  1

                  1

                  1

                  1

                  FALSE

                  5 flips, there are 13 out of 32 possible, this works to 40.625% probability of having No Back-to-Back flips. And, one more to establish the proper sequence.

                   

                  Flip #

                   

                  Outcome #

                  1

                  2

                  3

                  4

                  5

                  6

                  No Back-To-Back

                  1

                  0

                  0

                  0

                  0

                  0

                  0

                  TRUE

                  2

                  0

                  0

                  0

                  0

                  0

                  1

                  TRUE

                  3

                  0

                  0

                  0

                  0

                  1

                  0

                  TRUE

                  4

                  0

                  0

                  0

                  0

                  1

                  1

                  FALSE

                  5

                  0

                  0

                  0

                  1

                  0

                  0

                  TRUE

                  6

                  0

                  0

                  0

                  1

                  0

                  1

                  TRUE

                  7

                  0

                  0

                  0

                  1

                  1

                  0

                  FALSE

                  8

                  0

                  0

                  0

                  1

                  1

                  1

                  FALSE

                  9

                  0

                  0

                  1

                  0

                  0

                  0

                  TRUE

                  10

                  0

                  0

                  1

                  0

                  0

                  1

                  TRUE

                  11

                  0

                  0

                  1

                  0

                  1

                  0

                  TRUE

                  12

                  0

                  0

                  1

                  0

                  1

                  1

                  FALSE

                  13

                  0

                  0

                  1

                  1

                  0

                  0

                  FALSE

                  14

                  0

                  0

                  1

                  1

                  0

                  1

                  FALSE

                  15

                  0

                  0

                  1

                  1

                  1

                  0

                  FALSE

                  16

                  0

                  0

                  1

                  1

                  1

                  1

                  FALSE

                  17

                  0

                  1

                  0

                  0

                  0

                  0

                  TRUE

                  18

                  0

                  1

                  0

                  0

                  0

                  1

                  TRUE

                  19

                  0

                  1

                  0

                  0

                  1

                  0

                  TRUE

                  20

                  0

                  1

                  0

                  0

                  1

                  1

                  FALSE

                  21

                  0

                  1

                  0

                  1

                  0

                  0

                  TRUE

                  22

                  0

                  1

                  0

                  1

                  0

                  1

                  TRUE

                  23

                  0

                  1

                  0

                  1

                  1

                  0

                  FALSE

                  24

                  0

                  1

                  0

                  1

                  1

                  1

                  FALSE

                  25

                  0

                  1

                  1

                  0

                  0

                  0

                  FALSE

                  26

                  0

                  1

                  1

                  0

                  0

                  1

                  FALSE

                  27

                  0

                  1

                  1

                  0

                  1

                  0

                  FALSE

                  28

                  0

                  1

                  1

                  0

                  1

                  1

                  FALSE

                  29

                  0

                  1

                  1

                  1

                  0

                  0

                  FALSE

                  30

                  0

                  1

                  1

                  1

                  0

                  1

                  FALSE

                  31

                  0

                  1

                  1

                  1

                  1

                  0

                  FALSE

                  32

                  0

                  1

                  1

                  1

                  1

                  1

                  FALSE

                  33

                  1

                  0

                  0

                  0

                  0

                  0

                  TRUE

                  34

                  1

                  0

                  0

                  0

                  0

                  1

                  TRUE

                  35

                  1

                  0

                  0

                  0

                  1

                  0

                  TRUE

                  36

                  1

                  0

                  0

                  0

                  1

                  1

                  FALSE

                  37

                  1

                  0

                  0

                  1

                  0

                  0

                  TRUE

                  38

                  1

                  0

                  0

                  1

                  0

                  1

                  TRUE

                  39

                  1

                  0

                  0

                  1

                  1

                  0

                  FALSE

                  40

                  1

                  0

                  0

                  1

                  1

                  1

                  FALSE

                  41

                  1

                  0

                  1

                  0

                  0

                  0

                  TRUE

                  42

                  1

                  0

                  1

                  0

                  0

                  1

                  TRUE

                  43

                  1

                  0

                  1

                  0

                  1

                  0

                  TRUE

                  44

                  1

                  0

                  1

                  0

                  1

                  1

                  FALSE

                  45

                  1

                  0

                  1

                  1

                  0

                  0

                  FALSE

                  46

                  1

                  0

                  1

                  1

                  0

                  1

                  FALSE

                  47

                  1

                  0

                  1

                  1

                  1

                  0

                  FALSE

                  48

                  1

                  0

                  1

                  1

                  1

                  1

                  FALSE

                  49

                  1

                  1

                  0

                  0

                  0

                  0

                  FALSE

                  50

                  1

                  1

                  0

                  0

                  0

                  1

                  FALSE

                  51

                  1

                  1

                  0

                  0

                  1

                  0

                  FALSE

                  52

                  1

                  1

                  0

                  0

                  1

                  1

                  FALSE

                  53

                  1

                  1

                  0

                  1

                  0

                  0

                  FALSE

                  54

                  1

                  1

                  0

                  1

                  0

                  1

                  FALSE

                  55

                  1

                  1

                  0

                  1

                  1

                  0

                  FALSE

                  56

                  1

                  1

                  0

                  1

                  1

                  1

                  FALSE

                  57

                  1

                  1

                  1

                  0

                  0

                  0

                  FALSE

                  58

                  1

                  1

                  1

                  0

                  0

                  1

                  FALSE

                  59

                  1

                  1

                  1

                  0

                  1

                  0

                  FALSE

                  60

                  1

                  1

                  1

                  0

                  1

                  1

                  FALSE

                  61

                  1

                  1

                  1

                  1

                  0

                  0

                  FALSE

                  62

                  1

                  1

                  1

                  1

                  0

                  1

                  FALSE

                  63

                  1

                  1

                  1

                  1

                  1

                  0

                  FALSE

                  64

                  1

                  1

                  1

                  1

                  1

                  1

                  FALSE

                  Based on 6 flips there is 21 out of 64 for a probability of 32.8125%. With the progression we have we can find an equation or equation process to find the next sequence and then verify it by actually doing all the outcomes. The current progression is shown below.

                  Flips

                  No Back-to-Back Outcomes

                  2

                  3

                  3

                  5

                  4

                  8

                  5

                  13

                  6

                  21

                  If you know this sequence, you should be able to see it's a Fibonacci Sequence; where the previous 2 outcomes summed together become the next outcome total.

                  3 + 5 = 8

                  5 + 8 = 13

                  8 + 13 = 21

                  So, where does this lead? Well, by this understanding the next No Back-to-Back outcome count should be 13 + 21, or 34; you verify it in the table below.

                   

                  Flip #

                   

                  Outcome #

                  1

                  2

                  3

                  4

                  5

                  6

                  7

                  No Back-To-Back

                  1

                  0

                  0

                  0

                  0

                  0

                  0

                  0

                  TRUE

                  2

                  0

                  0

                  0

                  0

                  0

                  0

                  1

                  TRUE

                  3

                  0

                  0

                  0

                  0

                  0

                  1

                  0

                  TRUE

                  4

                  0

                  0

                  0

                  0

                  0

                  1

                  1

                  FALSE

                  5

                  0

                  0

                  0

                  0

                  1

                  0

                  0

                  TRUE

                  6

                  0

                  0

                  0

                  0

                  1

                  0

                  1

                  TRUE

                  7

                  0

                  0

                  0

                  0

                  1

                  1

                  0

                  FALSE

                  8

                  0

                  0

                  0

                  0

                  1

                  1

                  1

                  FALSE

                  9

                  0

                  0

                  0

                  1

                  0

                  0

                  0

                  TRUE

                  10

                  0

                  0

                  0

                  1

                  0

                  0

                  1

                  TRUE

                  11

                  0

                  0

                  0

                  1

                  0

                  1

                  0

                  TRUE

                  12

                  0

                  0

                  0

                  1

                  0

                  1

                  1

                  FALSE

                  13

                  0

                  0

                  0

                  1

                  1

                  0

                  0

                  FALSE

                  14

                  0

                  0

                  0

                  1

                  1

                  0

                  1

                  FALSE

                  15

                  0

                  0

                  0

                  1

                  1

                  1

                  0

                  FALSE

                  16

                  0

                  0

                  0

                  1

                  1

                  1

                  1

                  FALSE

                  17

                  0

                  0

                  1

                  0

                  0

                  0

                  0

                  TRUE

                  18

                  0

                  0

                  1

                  0

                  0

                  0

                  1

                  TRUE

                  19

                  0

                  0

                  1

                  0

                  0

                  1

                  0

                  TRUE

                  20

                  0

                  0

                  1

                  0

                  0

                  1

                  1

                  FALSE

                  21

                  0

                  0

                  1

                  0

                  1

                  0

                  0

                  TRUE

                  22

                  0

                  0

                  1

                  0

                  1

                  0

                  1

                  TRUE

                  23

                  0

                  0

                  1

                  0

                  1

                  1

                  0

                  FALSE

                  24

                  0

                  0

                  1

                  0

                  1

                  1

                  1

                  FALSE

                  25

                  0

                  0

                  1

                  1

                  0

                  0

                  0

                  FALSE

                  26

                  0

                  0

                  1

                  1

                  0

                  0

                  1

                  FALSE

                  27

                  0

                  0

                  1

                  1

                  0

                  1

                  0

                  FALSE

                  28

                  0

                  0

                  1

                  1

                  0

                  1

                  1

                  FALSE

                  29

                  0

                  0

                  1

                  1

                  1

                  0

                  0

                  FALSE

                  30

                  0

                  0

                  1

                  1

                  1

                  0

                  1

                  FALSE

                  31

                  0

                  0

                  1

                  1

                  1

                  1

                  0

                  FALSE

                  32

                  0

                  0

                  1

                  1

                  1

                  1

                  1

                  FALSE

                  33

                  0

                  1

                  0

                  0

                  0

                  0

                  0

                  TRUE

                  34

                  0

                  1

                  0

                  0

                  0

                  0

                  1

                  TRUE

                  35

                  0

                  1

                  0

                  0

                  0

                  1

                  0

                  TRUE

                  36

                  0

                  1

                  0

                  0

                  0

                  1

                  1

                  FALSE

                  37

                  0

                  1

                  0

                  0

                  1

                  0

                  0

                  TRUE

                  38

                  0

                  1

                  0

                  0

                  1

                  0

                  1

                  TRUE

                  39

                  0

                  1

                  0

                  0

                  1

                  1

                  0

                  FALSE

                  40

                  0

                  1

                  0

                  0

                  1

                  1

                  1

                  FALSE

                  41

                  0

                  1

                  0

                  1

                  0

                  0

                  0

                  TRUE

                  42

                  0

                  1

                  0

                  1

                  0

                  0

                  1

                  TRUE

                  43

                  0

                  1

                  0

                  1

                  0

                  1

                  0

                  TRUE

                  44

                  0

                  1

                  0

                  1

                  0

                  1

                  1

                  FALSE

                  45

                  0

                  1

                  0

                  1

                  1

                  0

                  0

                  FALSE

                  46

                  0

                  1

                  0

                  1

                  1

                  0

                  1

                  FALSE

                  47

                  0

                  1

                  0

                  1

                  1

                  1

                  0

                  FALSE

                  48

                  0

                  1

                  0

                  1

                  1

                  1

                  1

                  FALSE

                  49

                  0

                  1

                  1

                  0

                  0

                  0

                  0

                  FALSE

                  50

                  0

                  1

                  1

                  0

                  0

                  0

                  1

                  FALSE

                  51

                  0

                  1

                  1

                  0

                  0

                  1

                  0

                  FALSE

                  52

                  0

                  1

                  1

                  0

                  0

                  1

                  1

                  FALSE

                  53

                  0

                  1

                  1

                  0

                  1

                  0

                  0

                  FALSE

                  54

                  0

                  1

                  1

                  0

                  1

                  0

                  1

                  FALSE

                  55

                  0

                  1

                  1

                  0

                  1

                  1

                  0

                  FALSE

                  56

                  0

                  1

                  1

                  0

                  1

                  1

                  1

                  FALSE

                  57

                  0

                  1

                  1

                  1

                  0

                  0

                  0

                  FALSE

                  58

                  0

                  1

                  1

                  1

                  0

                  0

                  1

                  FALSE

                  59

                  0

                  1

                  1

                  1

                  0

                  1

                  0

                  FALSE

                  60

                  0

                  1

                  1

                  1

                  0

                  1

                  1

                  FALSE

                  61

                  0

                  1

                  1

                  1

                  1

                  0

                  0

                  FALSE

                  62

                  0

                  1

                  1

                  1

                  1

                  0

                  1

                  FALSE

                  63

                  0

                  1

                  1

                  1

                  1

                  1

                  0

                  FALSE

                  64

                  0

                  1

                  1

                  1

                  1

                  1

                  1

                  FALSE

                  65

                  1

                  0

                  0

                  0

                  0

                  0

                  0

                  TRUE

                  66

                  1

                  0

                  0

                  0

                  0

                  0

                  1

                  TRUE

                  67

                  1

                  0

                  0

                  0

                  0

                  1

                  0

                  TRUE

                  68

                  1

                  0

                  0

                  0

                  0

                  1

                  1

                  FALSE

                  69

                  1

                  0

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                  Presented 'AS IS' and for Entertainment Purposes Only.
                  Any gain or loss is your responsibility.
                  Use at your own risk.

                  Order is a Subset of Chaos
                  Knowledge is Beyond Belief
                  Wisdom is Not Censored
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                  Jehocifer

                    Raven62's avatar - binary
                    New Jersey
                    United States
                    Member #17843
                    June 28, 2005
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                    Posted: October 2, 2009, 4:29 pm - IP Logged

                    "Now, the question is going to have to be ...... What is the probability of tossing a coin 36 times without getting 2 Tails in a row?    At least for now....thats the question. LOL "

                    It really doesn't matter: Heads They Win, Tails You Lose! LOL!!!

                    A mind once stretched by a new idea never returns to its original dimensions!

                      Avatar
                      NY
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                      Member #23835
                      October 16, 2005
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                      Posted: October 3, 2009, 1:08 pm - IP Logged

                      "Where you went wrong is not considering ALL possibilities."

                       I was dismissing some of the possibilities, albeit indirectly, and it took a while to find the fault in my logic.

                      I'm glad to see that the number of  outcomes with no back to back flips follows the Fibonacci sequence. If it wasn't for that saving grace I'd be completely dismayed at seeing  the calculations. Most math is fairly elegant, and most probability follows a fairly direct path of factorials or squares, and simple arithmetic. Even calculating as the remainder of  the probability of the opposite outcome seems perfectly simple and straighforward. For this exercise I'm still not seeing anything simple and direct in calculating the probabilities, and I find it extremely counterintuitive that the differences between the probability at n flips and n+1 don't change by the same factor.

                      Any chance the excel formual you used can essily do a list for not having any 3 in a row occcurrences? I'd be curious to see if there's an part of that that has a simple pattern.

                        JADELottery's avatar - AMeOn 02.png
                        The Quantum Master
                        West Concord, MN
                        United States
                        Member #21
                        December 7, 2001
                        3954 Posts
                        Offline
                        Posted: October 3, 2009, 2:28 pm - IP Logged

                        "Where you went wrong is not considering ALL possibilities."

                         I was dismissing some of the possibilities, albeit indirectly, and it took a while to find the fault in my logic.

                        I'm glad to see that the number of  outcomes with no back to back flips follows the Fibonacci sequence. If it wasn't for that saving grace I'd be completely dismayed at seeing  the calculations. Most math is fairly elegant, and most probability follows a fairly direct path of factorials or squares, and simple arithmetic. Even calculating as the remainder of  the probability of the opposite outcome seems perfectly simple and straighforward. For this exercise I'm still not seeing anything simple and direct in calculating the probabilities, and I find it extremely counterintuitive that the differences between the probability at n flips and n+1 don't change by the same factor.

                        Any chance the excel formual you used can essily do a list for not having any 3 in a row occcurrences? I'd be curious to see if there's an part of that that has a simple pattern.

                        It's just a matter of setting up the proper testing IF statements; you can use the same set of outcomes and reform the testing IF condition. To understand this correctly, you are looking for a condition when there are no 1's in a triple consecutive sequence, i.e. ( 1 1 1 )?

                        Presented 'AS IS' and for Entertainment Purposes Only.
                        Any gain or loss is your responsibility.
                        Use at your own risk.

                        Order is a Subset of Chaos
                        Knowledge is Beyond Belief
                        Wisdom is Not Censored
                        Douglas Paul Smallish
                        Jehocifer

                          JADELottery's avatar - AMeOn 02.png
                          The Quantum Master
                          West Concord, MN
                          United States
                          Member #21
                          December 7, 2001
                          3954 Posts
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                          Posted: October 3, 2009, 4:13 pm - IP Logged

                          Well, OK... here is the expansion and more than just a 3 non-consecutive flips. I've expanded it to 5 non-consecutive flips. Below is a table with just the counts. You can figure the Probability by taking the count and dividing by the value, 2n, where n is the number of flips; to get the percentage, multiply by 100. Also, I have found that the counts are related to the number of non-consecutives in determining the progression sequence. It's a play on the basic idea of the Fibonacci Sequence by expanding the sum from the last 2 values to increase the sum set by one more value. The non-consecutive count for 3 is the sum of the last 3 values; the non-consecutive count for 4 is the sum of the last 4 values and so on. The numbers highlighted in each column are the starting Fibonacci numbers.

                           

                            No Back-to-Back Counts
                          Non-Consecutive Flips Threshold->2345
                          Fibonacci Sum Pattern ->fn-1 + fn-2 = fnfn-1 + fn-2 + fn-3 = fnfn-1 + fn-2 + fn-3 + fn-4 = fnfn-1 + fn-2 + fn-3 + fn-4 + fn-5 = fn
                          n Number of Flips       
                          23---
                          357--
                          481315-
                          513242931
                          621445661
                          73481108120
                          855149208236
                          989274401464
                          10144504773912
                          1123392714901793
                          12377170528723525
                          13610313655366930
                          1498757681067113624
                          151597106092056926784
                          162584195133964852656
                          1741813589076424103519
                          18676566012147312203513
                          1910946121415283953400096
                          2017711223317547337786568
                          212865741074410550261546352
                          224636875547620336283040048
                          2375025138953739199445976577
                          241213932555757755593511749641
                          2519641847007701456453323099186
                          2631781186460642807404045411804
                          27514229159025915411445289277256
                          2883204029249425104308960175514464
                          29134626953798080201061985345052351
                          30217830998950096387559437678355061
                          3135245781819976017470448341333610936
                          32570288733474577714399752162621810068
                          33922746561569347427756414725154342880
                          34149303521132436852535022095910133171296
                          352415781720828761031031288248119921290241
                          363908816938310064291987872012839164225421
                          376324598670463193843831746504076994839906
                          381023341551296020191673859288608151367869744
                          3916558014123837527729142368356257297581396608
                          4026791429643844049029274423830033585029621920
                          41433494437806417786745289689399381150137953599
                          4270140873314832335543210196204148362261111681777
                          43113490317027280918313519653815410644445228523648
                          44183631190350177431724137883947258718739089177552
                          452971215073922906855808730236562170917180596958496
                          46480752697616974903561841407576230348033776164295072
                          47777874204931221715292332713190419212466402190636545
                          4812586269025574256874122552298426843184130543269591313
                          492036501107410562230626642100808458960497256641310658978
                          503295128009919426970897100194314552299285504543532140404

                          Presented 'AS IS' and for Entertainment Purposes Only.
                          Any gain or loss is your responsibility.
                          Use at your own risk.

                          Order is a Subset of Chaos
                          Knowledge is Beyond Belief
                          Wisdom is Not Censored
                          Douglas Paul Smallish
                          Jehocifer

                            truecritic's avatar - PirateTreasure
                            Michigan
                            United States
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                            September 24, 2005
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                            Posted: October 4, 2009, 12:09 am - IP Logged

                            @ KY Floyd

                            @ JADELottery

                            Not that I ever needed those particular questions answered but glad you guys are around for all the statistics/probabilities/math!  Thank you.

                              CARBOB's avatar - ga lottery.png.gif
                              COLUMBUS,GA.
                              United States
                              Member #4924
                              June 3, 2004
                              6124 Posts
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                              Posted: October 4, 2009, 10:35 am - IP Logged

                              @ KY Floyd

                              @ JADELottery

                              Not that I ever needed those particular questions answered but glad you guys are around for all the statistics/probabilities/math!  Thank you.

                              How right you are! It's nice to know, for questions like these, we have brilliant minds that will come forward with the solution. Thanks to both of them.