Durango Bill's
Bingo Probabilities



Bingo Probability Statistics Analysis and Graphs
Data and Graphs for Single Board and 50 Board Games


Graph showing the Bingo hit probabilities for a single board.

   The red line in the above graph shows the probability that a single board will score a Bingo exactly when the “Nth” number is called. The blue line shows the cumulative single-board probability that a Bingo will hit on or before the “Nth” number is called.

   The same statistical data is shown in the table below. The 2nd column in the table shows the single-board probability that a "Bingo" will hit exactly when the "Nth" number is called. The 3rd column shows the cumulative single-board probability that a "Bingo" will hit on or before the "Nth" number is called.



Graph showing the Bingo hit probabilities in a 50 board game.

   The red line in the above graph shows the probability that at least one Bingo board will score a Bingo exactly when the “Nth” number is called in a game where 50 boards are in play. The blue line shows the cumulative 50-board probability that a Bingo will hit on or before the “Nth” number is called.

   The 4th and 5th columns in the table show similar statistical data for a 50-board Bingo Game. 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 0.00488136 probability of producing a Bingo when the 20th number is called.
2) A single board has a 0.0228745 probability of producing a Bingo on or before the 20th number is called.
3) In a 50 board game there is a 0.088966 probability someone will get a Bingo when the 20th number is called.
4) In a 50 board game there is a 0.685574 probability someone will get a Bingo on or before the 20th number is called.

Quantity    Bingo           Cumulative        Bingo           Cumulative
of Bingo    Probability     Probability       Probability     Probability
Numbers     This Turn       of Bingo          This Turn       of Bingo
Picked      1 Board         1 Board           50 Boards       50 Boards
-------------------------------------------------------------------------
     1      0               0                 0               0            
     2      0               0                 0               0            
     3      0               0                 0               0            
     4      3.29096E-06     3.29096E-06       0.000164535     0.000164535  
     5      1.36274E-05     1.69183E-05       0.000681031     0.000845566  
     6      3.52272E-05     5.21455E-05       0.00175838      0.00260395   
     7      7.2772E-05      0.000124918       0.00362285      0.0062268    
     8      0.000131405     0.000256322       0.00650917      0.012736     
     9      0.000216726     0.000473048       0.0106444       0.0233803    
    10      0.000334778     0.000807826       0.0162218       0.0396021    
    11      0.000492032     0.00129986        0.0233634       0.0629655    
    12      0.00069535      0.00199521        0.0320704       0.0950359    
    13      0.000951947     0.00294715        0.0421666       0.137203     
    14      0.00126932      0.00421648        0.0532417       0.190444     
    15      0.0016552       0.00587167        0.0646138       0.255058     
    16      0.00211738      0.00798905        0.0753299       0.330388     
    17      0.00266367      0.0106527         0.0842316       0.414619     
    18      0.00330168      0.0139544         0.0901015       0.504721     
    19      0.00403869      0.0179931         0.0918871       0.596608     
    20      0.00488136      0.0228745         0.088966        0.685574     
    21      0.00583558      0.02871           0.0813781       0.766952     
    22      0.00690611      0.0356161         0.0699319       0.836884     
    23      0.00809634      0.0437125         0.056106        0.89299      
    24      0.00940796      0.0531204         0.0417365       0.934727     
    25      0.0108406       0.0639611         0.028571        0.963297     
    26      0.0123916       0.0763526         0.0178526       0.98115      
    27      0.0140554       0.090408          0.0100934       0.991243     
    28      0.0158236       0.106232          0.00511529      0.996359     
    29      0.0176846       0.123916          0.0023007       0.998659     
    30      0.0196232       0.143539          0.000908658     0.999568     
    31      0.0216205       0.16516           0.000311613     0.99988      
    32      0.023654        0.188814          9.16944E-05     0.999971     
    33      0.0256976       0.214512          2.28629E-05     0.999994     
    34      0.0277219       0.242233          4.76674E-06     0.999999     
    35      0.0296943       0.271928          8.19471E-07     1            
    36      0.0315798       0.303508          1.14456E-07     1            
    37      0.0333412       0.336849          1.2786E-08      1            
    38      0.0349406       0.371789          1.12361E-09     1            
    39      0.0363398       0.408129          7.63153E-11     1            
    40      0.0375019       0.445631          3.9316E-12      1            
    41      0.0383922       0.484023          1.50581E-13     1            
    42      0.0389794       0.523003          4.19631E-15     1            
    43      0.0392375       0.56224           8.31411E-17     1            
    44      0.0391466       0.601387          1.14225E-18     1            
    45      0.0386944       0.640081          1.05911E-20     1            
    46      0.037877        0.677958          6.43502E-23     1            
    47      0.0366999       0.714658          2.48078E-25     1            
    48      0.0351788       0.749837          5.85697E-28     1            
    49      0.033339        0.783176          8.14376E-31     1            
    50      0.031216        0.814392          6.38553E-34     1            
    51      0.0288542       0.843246          2.69E-37        1            
    52      0.0263059       0.869552          5.7659E-41      1            
    53      0.0236296       0.893182          5.91344E-45     1            
    54      0.020888        0.91407           2.70567E-49     1            
    55      0.0181455       0.932215          5.09686E-54     1            
    56      0.0154655       0.947681          3.60239E-59     1            
    57      0.0129077       0.960588          8.57142E-65     1            
    58      0.0105251       0.971114          6.04182E-71     1            
    59      0.00836186      0.979475          1.08323E-77     1            
    60      0.00645101      0.985926          4.10912E-85     1            
    61      0.00481289      0.990739          2.6319E-93      1            
    62      0.00345451      0.994194          2.149E-102      1            
    63      0.00236968      0.996563          1.56547E-112    1            
    64      0.00154008      0.998104          6.39794E-124    1            
    65      0.00093726      0.999041          7.89187E-137    1            
    66      0.00052546      0.999566          1.24578E-151    1            
    67      0.000264961     0.999831          7.26872E-169    1            
    68      0.000115769     0.999947          2.32208E-189    1            
    69      4.11308E-05     0.999988          1.65168E-214    1            
    70      1.04887E-05     0.999999          5.48842E-247    1            
    71      1.39055E-06     1                 1.44308E-293    1            
    72      0               1                 0               1            
    73      0               1                 0               1            
    74      0               1                 0               1            
    75      0               1                 0               1


(Note: After line 34, the value for the last column on row "R" is equal to the quantity:  1.000 minus the sum of all values in column 4 below row "R". These results are all very close to 1.000. For example, on row 70 the result would be: .9999 etc. for 292 "9's" followed by "855692".)

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