Bingomania UK Bingo.net abcBingo.co.uk JackpotCity Bingo LiveFreeBingo BingoFunland BingoFunland FreeBingo.co.uk Kiss My Bingo ZingoBingo BingoBingo Bingo Gala WOWBingo

Which bingo game do you prefer?  Patterns  Crazy Patterns (rotating)  Speed Bingo  Coverall  Lines   View Results Previous Polls

The following statistics were calculated and compiled by The Wizard of Odds. The Wizard of Odds is Michael Shackleford, A.S.A., a professional actuary who has made a career of analyzing casino games. You can find further details of his work at http://wizardofodds.com

The following table shows the probability of getting a single line, cover-all, or four corners within a specified number of calls on any one card. For example the probability of a single player forming a bingo within 25 calls is 0.06396106, or about 6.4%.

It's important to note that these statistics reflect the probability of achieving a result on any one (singular) bingo card. These are not the odds of winning bingo in a bingo hall or room.

Probabilties in Bingo
Number of Calls	Single Line	Cover-all	Four Corners
1	0.00000000	0.00000000	0.00000000
2	0.00000000	0.00000000	0.00000000
3	0.00000000	0.00000000	0.00000000
4	0.00000329	0.00000000	0.00000082
5	0.00001692	0.00000000	0.00000411
6	0.00005215	0.00000000	0.00001234
7	0.00012492	0.00000000	0.00002880
8	0.00025632	0.00000000	0.00005759
9	0.00047305	0.00000000	0.00010367
10	0.00080783	0.00000000	0.00017278
11	0.00129986	0.00000000	0.00027150
12	0.00199521	0.00000000	0.00040726
13	0.00294715	0.00000000	0.00058826
14	0.00421648	0.00000000	0.00082356
15	0.00587167	0.00000000	0.00112304
16	0.00798905	0.00000000	0.00149739
17	0.01065272	0.00000000	0.00195812
18	0.01395440	0.00000000	0.00251759
19	0.01799309	0.00000000	0.00318894
20	0.02287445	0.00000000	0.00398618
21	0.02871003	0.00000000	0.00492410
22	0.03561614	0.00000000	0.00601835
23	0.04371249	0.00000000	0.00728537
24	0.05312045	0.00000000	0.00874244
25	0.06396106	0.00000000	0.01040767
26	0.07635261	0.00000000	0.01229997
27	0.09040799	0.00000000	0.01443910
28	0.10623163	0.00000000	0.01684561
29	0.12391628	0.00000000	0.01954091
30	0.14353947	0.00000000	0.02254720
31	0.16515993	0.00000000	0.02588753
32	0.18881391	0.00000000	0.02958575
33	0.21451154	0.00000000	0.03366654
34	0.24223348	0.00000000	0.03815542
35	0.27192783	0.00000000	0.04307870
36	0.30350759	0.00000000	0.04846353
37	0.33684876	0.00000000	0.05433790
38	0.37178933	0.00000000	0.06073059
39	0.40812916	0.00000000	0.06767123
40	0.44563111	0.00000000	0.07519026
41	0.48402328	0.00000001	0.08331894
42	0.52300269	0.00000001	0.09208935
43	0.56224021	0.00000003	0.10153441
44	0.60138685	0.00000007	0.11168785
45	0.64008123	0.00000015	0.12258423
46	0.67795818	0.00000031	0.13425892
47	0.71465810	0.00000063	0.14674812
48	0.74983686	0.00000125	0.16008886
49	0.78317588	0.00000245	0.17431898
50	0.81439191	0.00000472	0.18947715
51	0.84324614	0.00000891	0.20560286
52	0.86955207	0.00001654	0.22273644
53	0.89318170	0.00003023	0.24091900
54	0.91406974	0.00005441	0.26019252
55	0.93221528	0.00009654	0.28059978
56	0.94768080	0.00016894	0.30218438
57	0.96058846	0.00029180	0.32499074
58	0.97111353	0.00049778	0.34906413
59	0.97947539	0.00083912	0.37445061
60	0.98592639	0.00139853	0.40119709
61	0.99073928	0.00230569	0.42935127
62	0.99419379	0.00376192	0.45896170
63	0.99656346	0.00607694	0.49007775
64	0.99810354	0.00972311	0.52274960
65	0.99904080	0.01541468	0.55702826
66	0.99956626	0.02422308	0.59296557
67	0.99983122	0.03774293	0.63061418
68	0.99994699	0.05832999	0.67002756
69	0.99998812	0.08943931	0.71126003
70	0.99999861	0.13610330	0.75436670
71	1.00000000	0.20560286	0.79940351
72	1.00000000	0.30840429	0.84642725
73	1.00000000	0.45945946	0.89549550
74	1.00000000	0.68000000	0.94666667
75	1.00000000	1.00000000	1.00000000

The Wizard of Odds' method of analysis is entirely mathematical. The probability of x marks on the card given y calls is easily calculated as combin(24,x)*combin(51,y-x)/combin(75,y). The probability that x marks will form a bingo (five in a row) is more compicated and necessitated a computer program to run through all possible combinations and tabulate the results.

by Editor - 10/11/05

Back to archive