Durango Bill's
Bingo Probabilities
Bingo Probability Statistics Analysis and Graphs
Data and Graphs for Single Board and 50 Board Games
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.
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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