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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