Rec.Gambling. Keno Odds

Keno Odds

Copyright (C) 1995 John C. Hallyburton, Jr.

Page last modified: 1-15-96
Page cleanup: 7-03-17

Here are all possible keno outcomes. For every possible number of spots played you can see both the probability of each outcome and the odds against that outcome happening. This shows, for example, that you have roughly a 71-1 shot at hitting a 3-spot, while you are almost 85% likely to catch only 0 or 1 on the same ticket.

For very large or very small numbers, scientific notation is used. The term “e+nnn” means move the decimal point nnn places to the right, adding zeroes as appropriate. Similarly, “e-nnn” means to move the decimal point nnn places to the left, padding with zeroes. Thus, 1.42e-09 is shorthand for .00000000142, while 2.71e+6 is another way of writing 2710000.

Keno outcome probabilities

Play 1 spot

Catch probability odds-to-1 against

0 0.7500 0.3333
1 0.2500 3.0000

Play 2 spots

Catch probability odds-to-1 against

0 0.5601 0.7853
1 0.3797 1.6333
2 0.0601 15.6316

Play 3 spots

Catch probability odds-to-1 against

0 0.4165 1.4009
1 0.4309 1.3209
2 0.1388 6.2070
3 0.0139 71.0702

Play 4 spots

Catch probability odds-to-1 against

0 0.3083 2.2434
1 0.4327 1.3109
2 0.2126 3.7029
3 0.0432 22.1225
4 0.003063 325.44

Play 5 spots

Catch probability odds-to-1 against

0 0.2272 3.4017
1 0.4057 1.4650
2 0.2705 2.6974
3 0.0839 10.9140
4 0.0121 81.6970
5 0.000645 1549.57

Play 6 spots

Catch probability odds-to-1 against

0 0.1666 5.0023
1 0.3635 1.7511
2 0.3083 2.2434
3 0.1298 6.7030
4 0.0285 34.0411
5 0.003096 322.04
6 0.000129 7751.84

Play 7 spots

Catch probability odds-to-1 against

0 0.1216 7.2254
1 0.3152 2.1727
2 0.3267 2.0613
3 0.1750 4.7145
4 0.0522 18.1604
5 0.008639 114.76
6 0.000732 1364.98
7 0.00002440 40978

Play 8 spots

Catch probability odds-to-1 against

0 0.0883 10.3294
1 0.2665 2.7529
2 0.3281 2.0474
3 0.2148 3.6558
4 0.0815 11.2694
5 0.0183 53.6371
6 0.002367 421.53
7 0.000160 6231.27
8 0.00000435 230114

Play 9 spots

Catch probability odds-to-1 against

0 0.0637 14.6868
1 0.2207 3.5317
2 0.3164 2.1603
3 0.2461 3.0632
4 0.1141 7.7638
5 0.0326 29.6735
6 0.005720 173.84
7 0.000592 1689.11
8 0.00003259 30681
9 7.2428e-007 1.3807e+006

Play 10 spots

Catch probability odds-to-1 against

0 0.0458 20.8385
1 0.1796 4.5688
2 0.2953 2.3869
3 0.2674 2.7397
4 0.1473 5.7880
5 0.0514 18.4448
6 0.0115 86.1126
7 0.001611 619.68
8 0.000135 7383.47
9 0.00000612 163380
10 1.1221e-007 8.9117e+006

Play 11 spots

Catch probability odds-to-1 against

0 0.0327 29.5739
1 0.1439 5.9486
2 0.2681 2.7303
3 0.2784 2.5921
4 0.1786 4.5995
5 0.0741 12.4989
6 0.0202 48.4958
7 0.003608 276.18
8 0.000411 2429.62
9 0.00002837 35243
10 0.00000106 945180
11 1.6030e-008 6.2382e+007

Play 12 spots

Catch probability odds-to-1 against

0 0.0232 42.0530
1 0.1138 7.7900
2 0.2378 3.2057
3 0.2797 2.5749
4 0.2058 3.8600
5 0.0994 9.0616
6 0.0322 30.0474
7 0.007027 141.30
8 0.001020 979.78
9 0.00009540 10481
10 0.00000543 184229
11 1.6727e-007 5.9783e+006
12 2.0909e-009 4.7826e+008

Play 13 spots

Catch probability odds-to-1 against

0 0.0164 59.9918
1 0.0888 10.2600
2 0.2066 3.8398
3 0.2727 2.6665
4 0.2273 3.3998
5 0.1259 6.9442
6 0.0475 20.0521
7 0.0123 80.2008
8 0.002183 457.06
9 0.000260 3846.67
10 0.00002006 49844
11 9.4337e-007 1.0600e+006
12 2.3984e-008 4.1695e+007
13 2.4599e-010 4.0652e+009

Play 14 spots

Catch probability odds-to-1 against

0 0.0115 85.9458
1 0.0685 13.5945
2 0.1763 4.6723
3 0.2590 2.8603
4 0.2422 3.1287
5 0.1520 5.5801
6 0.0658 14.2074
7 0.0199 49.3746
8 0.004182 238.14
9 0.000608 1643.09
10 0.00005974 16739
11 0.00000381 262396
12 1.4784e-007 6.7640e+006
13 3.0840e-009 3.2425e+008
14 2.5700e-011 3.8910e+010

Play 15 spots

Catch probability odds-to-1 against

0 0.008016 123.75
1 0.0523 18.1281
2 0.1479 5.7595
3 0.2404 3.1597
4 0.2502 2.9966
5 0.1762 4.6770
6 0.0863 10.5810
7 0.0299 32.4563
8 0.007331 135.40
9 0.001267 788.16
10 0.000152 6575.37
11 0.00001234 81020
12 6.4960e-007 1.5394e+006
13 2.0677e-008 4.8363e+007
14 3.5046e-010 2.8534e+009
15 2.3364e-012 4.2801e+011

Play 16 spots

Catch probability odds-to-1 against

0 0.005550 179.19
1 0.0395 24.3395
2 0.1223 7.1798
3 0.2185 3.5768
4 0.2515 2.9762
5 0.1971 4.0738
6 0.1084 8.2251
7 0.0425 22.5240
8 0.0120 82.6408
9 0.002406 414.59
10 0.000343 2913.53
11 0.00003403 29387
12 0.00000228 438862
13 9.8402e-008 1.0162e+007
14 2.5449e-009 3.9295e+008
15 3.4507e-011 2.8980e+010
16 1.7972e-013 5.5641e+012

Play 17 spots

Catch probability odds-to-1 against

0 0.003815 261.10
1 0.0295 32.9185
2 0.0996 9.0417
3 0.1948 4.1324
4 0.2467 3.0542
5 0.2138 3.6779
6 0.1309 6.6405
7 0.0576 16.3649
8 0.0183 53.4990
9 0.004234 235.16
10 0.000703 1421.34
11 0.00008285 12069
12 0.00000678 147516
13 3.7247e-007 2.6848e+006
14 1.3069e-008 7.6517e+007
15 2.7039e-010 3.6983e+009
16 2.8643e-012 3.4912e+011
17 1.1233e-014 8.9026e+013

Play 18 spots

Catch probability odds-to-1 against

0 0.002604 383.00
1 0.0218 44.8670
2 0.0800 11.4963
3 0.1707 4.8576
4 0.2366 3.2267
5 0.2255 3.4342
6 0.1527 5.5490
7 0.0748 12.3710
8 0.0267 36.4013
9 0.006990 142.06
10 0.001331 750.43
11 0.000183 5475.01
12 0.00001775 56324
13 0.00000119 839002
14 5.3209e-008 1.8794e+007
15 1.4936e-009 6.6952e+008
16 2.4142e-011 4.1421e+010
17 1.9256e-013 5.1932e+012
18 5.3489e-016 1.8695e+015

Play 19 spots

Catch probability odds-to-1 against

0 0.001764 565.86
1 0.0160 61.6531
2 0.0635 14.7549
3 0.1471 5.7962
4 0.2223 3.4975
5 0.2320 3.3101
6 0.1728 4.7879
7 0.0936 9.6853
8 0.0372 25.8502
9 0.0109 90.5347
10 0.002356 423.39
11 0.000371 2696.22
12 0.00004197 23824
13 0.00000335 298668
14 1.8263e-007 5.4756e+006
15 6.5224e-009 1.5332e+008
16 1.4304e-010 6.9912e+009
17 1.7408e-012 5.7445e+011
18 9.8350e-015 1.0168e+014
19 1.7254e-017 5.7956e+016

Play 20 spots

Catch probability odds-to-1 against

0 0.001186 842.38
1 0.0116 85.4464
2 0.0497 19.1150
3 0.1249 7.0087
4 0.2050 3.8773
5 0.2333 3.2867
6 0.1902 4.2583
7 0.1133 7.8265
8 0.0499 19.0554
9 0.0163 60.4198
10 0.003940 252.80
11 0.000702 1422.82
12 0.00009117 10968
13 0.00000847 118084
14 5.4888e-007 1.8219e+006
15 2.3951e-008 4.1751e+007
16 6.6828e-010 1.4964e+009
17 1.1035e-011 9.0624e+010
18 9.5126e-014 1.0512e+013
19 3.3943e-016 2.9461e+015
20 2.8286e-019 3.5353e+018

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