Probabilities For Bingo.

Every Bingo player wishes to know their chances of winning with one or several cards, with different numbers of competitors and so on... Unfortunately, the answer is not an easy one; this is because it depends on a number of factors including the type of Bingo being played.

To give you a general idea of the probabilities you can expect in a round of Bingo, imagine that there are 900 cards in a game, and that you are playing with only 9 of these cards, your chance of winning is only 1 per-cent.

On this page you can find a table of probabilities regarding your chance of having a winning card according to the number of numbers called. The table does not show your chance of winning, but gives you a probability of having a winning card from the number of numbers called. For example, after 30 calls, there is a 14 per-cent chance that a winner will claim a one-line win and a 2 per-cent chance that the four corners of the card are filled.

We hope the following table will be of benefit to you:

No. of Calls    One Line        The Full Card  4 Corners
1                   0.00000000    0.00000000   0.00000000
2                   0.00000000    0.00000000   0.00000000
3                   0.00000000    0.00000000   0.00000000
4                   0.0000033      0.00000000   0.0000008
5                   0.000017        0.00000000   0.000004
6                   0.00005          0.00000000   0.00001
7                   0.000124        0.00000000   0.00003
8                   0.000260        0.00000000   0.00006
9                   0.000470        0.00000000   0.00010
10                 0.00081          0.00000000   0.0001 
11                 0.00130          0.00000000   0.0003 
12                 0.002              0.00000000   0.0004
13                 0.003              0.00000000   0.0006
14                 0.004              0.00000000   0.0008
15                 0.006              0.00000000   0.0011
16                 0.008              0.00000000   0.0015
17                 0.0106            0.00000000   0.0020
18                 0.014              0.00000000   0.0025
19                 0.018              0.00000000   0.0032
20                 0.022              0.00000000   0.0040
21                 0.03                0.00000000   0.0050
22                 0.04                0.00000000   0.0060
23                 0.044              0.00000000   0.0072
24                 0.05                0.00000000   0.0087
25                 0.06                0.00000000   0.0104
26                 0.08                0.00000000   0.0123
27                 0.09                0.00000000   0.0140
28                 0.11                0.00000000   0.0170
29                 0.12                0.00000000   0.0200
30                 0.14                0.00000000   0.0230
31                 0.17                0.00000000   0.0260
32                 0.19                0.00000000   0.0300
33                 0.21                0.00000000   0.0340
34                 0.24                0.00000000   0.0381
35                 0.27                0.00000000   0.0431
36                 0.30                0.00000000   0.0485
37                 0.336              0.00000000   0.0543
38                 0.37                0.00000000   0.0607
39                 0.41                0.00000000   0.0673
40                 0.45                0.00000000   0.075
41                 0.50                0.00000001   0.083
42                 0.523              0.00000001   0.092
43                 0.57                0.00000003   0.102
44                 0.60                0.00000007   0.112
45                 0.64                0.00000015   0.122
46                 0.68                0.00000031   0.134
47                 0.71                0.00000063   0.150
48                 0.75                0.00000125   0.160
49                 0.79                0.00000245   0.174
50                 0.81                0.00000472   0.190
51                 0.84                0.00000891   0.210
52                 0.87                0.00001654   0.222
53                 0.90                0.00003023   0.241
54                 0.91                0.00005441   0.260
55                 0.93                0.00009654   0.281
56                 0.95                0.00016894   0.302
57                 0.96                0.00029180   0.324
58                 0.97                0.00049778   0.350
59                 0.98                0.00083912   0.374
60                 0.989              0.00139853   0.400
61                 0.991              0.00230569   0.429
62                 0.995              0.00376192   0.459
63                 0.997              0.00607694   0.490
64                 0.998              0.00972311   0.522
65                 0.999              0.01541468   0.55702826
66                 0.9996            0.02422308   0.59296557
67                 0.9998            0.03774293   0.63061418
68                 0.9999            0.05832999   0.67002756
69                 0.99998          0.08943931   0.71126003
70                 0.99999          0.13610330   0.75436670
71                 1.000              0.20560286   0.79940351
72                 1.000              0.30840429   0.84642725
73                 1.000              0.45945946   0.89549550
74                 1.000              0.68000000   0.94666667
75                 1.000              1.00000000   1.00000000