Keno Odds

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

Please send corrections or additions to john@hideaway.mv.com.

Page last modified: 01-15-96

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

rec.gambling Keno FAQ