Bingo Bet
Introduction
Calculating bingo odds is similar to calculating keno odds. From a probability standpoint, bingo is basically a game of keno where you don't win anything for partial matches. Of course, I am solely talking about the probability of matching a particular pattern as opposed to winning a game of bingo because the probability of winning a bingo game is dependent on how many other people you are competing against.
Calculating bingo odds
Bingo Bethlehem Pa
Here is the equation for calculating the probability (p) of matching a particular pattern made up of (x) numbers when (y) numbers were drawn out of (z) total numbers (i.e. - 'What is the probability of hitting a pattern made up of 4 particular numbers (e.g. 'corners') when 20 numbers are drawn out of 75?').
- BINGO.BET last sold for $3,250 on 2020-05-10 at Afilias. Historical Sales. No historical sales found. Odds.market at $21.88 ends Jan 13th @ 10:37am ยป.
- Jan 11, 2016 Prizes in bingo are fixed. Your odds are inversely proportional to the number of competing cards in the room. Of course you won't know exactly how many cards you are up against, but the more you play the better you will be at estimating the competition. Here are some ways to estimate the number the competing cards in the room.
- Online bingo emerged in the US in the mid-1990s, while we have witnessed the appearance of the first online bingo sites in the early 2000s. Since then, online bingo has changed for the better, and players can now enjoy a quick game of bingo on the go.
p(x,n) = (((combin(x,(x-x)))*combin(z-x,y-x))/combin(z,y))
To calculate different bingo odds, you can download my odds spreadsheet by right-clicking and selecting 'Save target as' to calculate the casino's edge of the keno game you play.
Bingo Odds Table
Just like any other type of betting game, bingo has odds. In bingo, the caller will traditionally choose from balls numbered 1 through 75. When the first call is made, the odds of a specific number on your card is 1 in 75. As the game progresses, with each ball selected, those odds increase.
| # of Calls | Cover All | Four corners | 'X' pattern |
| 1 | - | - | - |
| 2 | - | - | - |
| 3 | - | - | - |
| 4 | - | 0.00008% | - |
| 5 | - | 0.00041% | - |
| 6 | - | 0.00123% | - |
| 7 | - | 0.00288% | - |
| 8 | - | 0.00576% | 0.000000006% |
| 9 | - | 0.01037% | 0.000000053% |
| 10 | - | 0.01728% | 0.000000267% |
| 11 | - | 0.02715% | 0.000000978% |
| 12 | - | 0.04073% | 0.000002934% |
| 13 | - | 0.05883% | 0.000007628% |
| 14 | - | 0.08236% | 0.000017800% |
| 15 | - | 0.11230% | 0.000038142% |
| 16 | - | 0.14974% | 0.000076285% |
| 17 | - | 0.19581% | 0.000144093% |
| 18 | - | 0.25176% | 0.000259367% |
| 19 | - | 0.31889% | 0.000447998% |
| 20 | - | 0.39862% | 0.000746663% |
| 21 | - | 0.49241% | 0.001206149% |
| 22 | - | 0.60183% | 0.001895377% |
| 23 | - | 0.72854% | 0.002906244% |
| 24 | 0.000000000000000004% | 0.87424% | 0.004359366% |
| 25 | 0.000000000000000097% | 1.04077% | 0.006410833% |
| 26 | 0.000000000000001261% | 1.23000% | 0.009260091% |
| 27 | 0.000000000000011347% | 1.44391% | 0.013159077% |
| 28 | 0.000000000000079426% | 1.68456% | 0.018422708% |
| 29 | 0.000000000000460671% | 1.95409% | 0.025440883% |
| 30 | 0.000000000002303355% | 2.25472% | 0.034692113% |
| 31 | 0.000000000010200573% | 2.58875% | 0.046758935% |
| 32 | 0.000000000040802291% | 2.95858% | 0.062345246% |
| 33 | 0.000000000149608400% | 3.36665% | 0.082295725% |
| 34 | 0.000000000508668560% | 3.81554% | 0.107617487% |
| 35 | 0.000000001618490874% | 4.30787% | 0.139504149% |
| 36 | 0.000000004855472621% | 4.84635% | 0.179362478% |
| 37 | 0.000000013819422074% | 5.43379% | 0.228841782% |
| 38 | 0.000000037509859915% | 6.07306% | 0.289866257% |
| 39 | 0.000000097525635779% | 6.76712% | 0.364670453% |
| 40 | 0.000000243814089448% | 7.51903% | 0.455838066% |
| 41 | 0.000000588022215727% | 8.33189% | 0.566344264% |
| 42 | 0.000001372051836696% | 9.20893% | 0.699601738% |
| 43 | 0.000003105169946207% | 10.15344% | 0.859510706% |
| 44 | 0.000006831373881656% | 11.16879% | 1.050513085% |
| 45 | 0.000014638658317834% | 12.25842% | 1.277651050% |
| 46 | 0.000030608103755472% | 13.42589% | 1.546630218% |
| 47 | 0.000062546994630747% | 14.67481% | 1.863887699% |
| 48 | 0.000125093989261493% | 16.00889% | 2.236665238% |
| 49 | 0.000245184218952526% | 17.43190% | 2.673087724% |
| 50 | 0.000471508113370243% | 18.94771% | 3.182247290% |
| 51 | 0.000890626436366014% | 20.56029% | 3.774293298% |
| 52 | 0.001654020524679740% | 22.27364% | 4.460528443% |
| 53 | 0.003022865096828490% | 24.09190% | 5.253511277% |
| 54 | 0.005441157174291290% | 26.01925% | 6.167165412% |
| 55 | 0.009653665954387760% | 28.05998% | 7.216895695% |
| 56 | 0.016893915420178600% | 30.21844% | 8.419711644% |
| 57 | 0.029180399362126600% | 32.49907% | 9.794358443% |
| 58 | 0.049778328323627800% | 34.90641% | 11.361455794% |
| 59 | 0.083912039174115500% | 37.44506% | 13.143644939% |
| 60 | 0.139853398623526000% | 40.11971% | 15.165744160% |
| 61 | 0.230569116649597000% | 42.93513% | 17.454913090% |
| 62 | 0.376191716638816000% | 45.89617% | 20.040826140% |
| 63 | 0.607694311493471000% | 49.00777% | 22.955855397% |
| 64 | 0.972310898389554000% | 52.27496% | 26.235263310% |
| 65 | 1.541468497446850000% | 55.70283% | 29.917405529% |
| 66 | 2.422307638845060000% | 59.29656% | 34.043944223% |
| 67 | 3.774293297735320000% | 63.06142% | 38.660072253% |
| 68 | 5.832998732863680000% | 67.00276% | 43.814748554% |
| 69 | 8.943931390390970000% | 71.12600% | 49.560945086% |
| 70 | 13.610330376681900000% | 75.43667% | 55.955905742% |
| 71 | 20.560286313711000000% | 79.94035% | 63.061417582% |
| 72 | 30.840429470566500000% | 84.64272% | 70.944094780% |
| 73 | 45.945945945945900000% | 89.54955% | 79.675675676% |
| 74 | 68.000000000000000000% | 94.66667% | 89.333333333% |
| 75 | 100.000000000000000000% | 100.00000% | 100.000000000% |
COMMENTS:
Hey! Thanks for all this great info! I'm a fan.
I have a question, what would be the equation if I needed to make it dynamic in a way where the odds react to the number of real players in the room and the # of bingo cards they each have keeping in mind that I want a balance between AI odds of winning and player odds.
I have a question, what would be the equation if I needed to make it dynamic in a way where the odds react to the number of real players in the room and the # of bingo cards they each have keeping in mind that I want a balance between AI odds of winning and player odds.
dandan on September 7, 2016
How would this formula change if the number chosen was put back into the hopper instead of kept out (ie with replacement)
DaveG44131 on September 11, 2014
Bingo Bet It All Beaver
HPG ADMIN on February 27, 2013
Bingo Betty
Quantity Bingo Cumulative Bingo Cumulativeof Bingo Probability Probability Probability Probability
Numbers This Turn of Bingo This Turn of Bingo
Picked 1Board 1Board 50Boards 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