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Durango Bill's

Bingo Probabilities



Bingo Probability Statistics Analysis
Data for Four Corners and Big "X" (both diagonals)


   The 2nd column in the table below shows the single-board probability that all four corners will be filled when the "Nth" number is called. The 3rd column shows the single-board cumulative probability that all four corners will be filled on or before the "Nth" number is called.

   The 4th and 5th columns in the table show similar data, but for a large "X" (both diagonals filled). Note: these probabilities are valid for any pattern that requires 8 defined location hits in addition to the center "free" space. Examples include: A solid center, a big "+" sign, and the letter "T".

If we look at the table below we see that when the 20th number is called in a Bingo game we get the following probabilities.

1) A single board has a 0.000797236 probability of filling all 4 corners when the 20th number is called.
2) A single board has a 0.00398618 probability of filling all 4 corners on or before 20 numbers are called.
3) A single board has a 2.98665E-06 probability of filling both diagonals when the 20th number is called.
4) A single board has a 7.46663E-06 probability of filling both diagonals on or before the 20th number is called.


Computer program and data by Bill Butler

Quantity    4 Corners       Cumulative       Letter X        Cumulative
of Bingo    Probability     4 Corners        Probability     Probability
Numbers     This Turn       Probability      This Turn       Letter X
Picked      1 Board         1 Board          1 Board         1 Board
------------------------------------------------------------------------
     1      0               0                0               0
     2      0               0                0               0
     3      0               0                0               0
     4      8.22741E-07     8.22741E-07      0               0
     5      3.29096E-06     4.1137E-06       0               0
     6      8.22741E-06     1.23411E-05      0               0
     7      1.64548E-05     2.87959E-05      0               0
     8      2.87959E-05     5.75918E-05      5.92731E-11     5.92731E-11
     9      4.60735E-05     0.000103665      4.74185E-10     5.33458E-10
    10      6.91102E-05     0.000172776      2.13383E-09     2.66729E-09
    11      9.87289E-05     0.000271504      7.11277E-09     9.78006E-09
    12      0.000135752     0.000407257      1.95601E-08     2.93402E-08
    13      0.000181003     0.000588259      4.69443E-08     7.62845E-08
    14      0.000235304     0.000823563      1.01713E-07     1.77997E-07
    15      0.000299478     0.00112304       2.03425E-07     3.81423E-07
    16      0.000374347     0.00149739       3.81423E-07     7.62845E-07
    17      0.000460735     0.00195812       6.78084E-07     1.44093E-06
    18      0.000559464     0.00251759       1.15274E-06     2.59367E-06
    19      0.000671356     0.00318894       1.88631E-06     4.47998E-06
    20      0.000797236     0.00398618       2.98665E-06     7.46663E-06
    21      0.000937924     0.00492410       4.59485E-06     1.20615E-05
    22      0.00109424      0.00601835       6.89228E-06     1.89538E-05
    23      0.00126702      0.00728537       1.01087E-05     2.90624E-05
    24      0.00145707      0.00874244       1.45312E-05     4.35937E-05
    25      0.00166523      0.01040767       2.05147E-05     6.41083E-05
    26      0.00189230      0.01229997       2.84926E-05     9.26009E-05
    27      0.00213913      0.01443910       3.89899E-05     0.000131591
    28      0.00240652      0.01684561       5.26363E-05     0.000184227
    29      0.00269530      0.01954091       7.01817E-05     0.000254409
    30      0.00300629      0.02254720       9.25123E-05     0.000346921
    31      0.00334033      0.02588753       0.000120668     0.000467589
    32      0.00369822      0.02958575       0.000155863     0.000623452
    33      0.00408079      0.03366654       0.000199505     0.000822957
    34      0.00448887      0.03815542       0.000253218     0.00107617
    35      0.00492328      0.04307870       0.000318867     0.00139504
    36      0.00538484      0.04846353       0.000398583     0.00179362
    37      0.00587437      0.05433790       0.000494793     0.00228842
    38      0.00639269      0.06073059       0.000610245     0.00289866
    39      0.00694064      0.06767123       0.000748042     0.00364670
    40      0.00751903      0.07519026       0.000911676     0.00455838
    41      0.00812868      0.08331894       0.00110506      0.00566344
    42      0.00877041      0.09208935       0.00133257      0.00699602
    43      0.00944506      0.10153441       0.00159909      0.00859511
    44      0.01015344      0.11168785       0.00191002      0.01050513
    45      0.01089638      0.12258423       0.00227138      0.01277651
    46      0.01167469      0.13425892       0.00268979      0.01546630
    47      0.01248920      0.14674812       0.00317257      0.01863888
    48      0.01334074      0.16008886       0.00372778      0.02236665

    49      0.01423012      0.17431898       0.00436422      0.02673088
    50      0.01515817      0.18947715       0.00509160      0.03182247
    51      0.01612571      0.20560286       0.00592046      0.03774293
    52      0.01713357      0.22273644       0.00686235      0.04460528
    53      0.01818257      0.24091900       0.00792983      0.05253511
    54      0.01927352      0.26019252       0.00913654      0.06167165
    55      0.02040726      0.28059978       0.01049730      0.07216896
    56      0.02158460      0.30218438       0.01202816      0.08419712
    57      0.02280637      0.32499074       0.01374647      0.09794358
    58      0.02407339      0.34906413       0.01567097      0.11361456
    59      0.02538648      0.37445061       0.01782189      0.13143645
    60      0.02674647      0.40119709       0.02022099      0.15165744
    61      0.02815418      0.42935127       0.02289169      0.17454913
    62      0.02961043      0.45896170       0.02585913      0.20040826
    63      0.03111605      0.49007775       0.02915029      0.22955855
    64      0.03267185      0.52274960       0.03279408      0.26235263
    65      0.03427866      0.55702826       0.03682142      0.29917406
    66      0.03593731      0.59296557       0.04126539      0.34043944
    67      0.03764861      0.63061418       0.04616128      0.38660072
    68      0.03941339      0.67002756       0.05154676      0.43814749
    69      0.04123247      0.71126003       0.05746197      0.49560945
    70      0.04310667      0.75436670       0.06394961      0.55955906
    71      0.04503682      0.79940351       0.07105512      0.63061418
    72      0.04702374      0.84642725       0.07882677      0.70944095
    73      0.04906825      0.89549550       0.08731581      0.79675676
    74      0.05117117      0.94666667       0.09657658      0.89333333
    75      0.05333333      1                0.10666667      1



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