How To Play Keno

In general the easier a game is to understand the greater the house advantage, and keno is a perfect example of this. Played in a lounge or at your restaurant table, keno involves the player choosing from 1 to 15 (sometimes 20) numbers from 1 to 80. Every five minutes or so the casino will choose 20 numbers ranging from 1 to 80. If enough of your chosen numbers match those drawn by the casino then you will win, depending on exactly how many match and the payoff table at your particular casino.While the payoff tables will vary from one casino to another the expected return seems to always range from 70 to 80 cents per dollar bet, making keno among the worst bets in the casino. Many states outside Nevada offer keno as an alternative to lottery tickets. While I can’t speak for every state Maryland keno has an expected return of about 50 cents per dollar bet. I believe other state run keno to be just as bad.

Below are 15 tables, according to the number of numbers chosen, and the probability of matching any given number, the payoff table at the Atlantic City Tropicana, the contribution toward the expected return, and the total expected return for all possible matches. Following the tables is an explanation of how the probabilities were calculated.

Tables and Probabilities
Pick 1
Catches Pays Probability Return
0 0 0.75000000000000 0.00000000000000
1 3 0.25000000000000 0.75000000000000
Total 1.00000000000000 0.75000000000000


Pick 2
Catches Pays Probability Return
0 0 0.56012658227848 0.00000000000000
1 0 0.37974683544304 0.00000000000000
2 12 0.06012658227848 0.72151898734177
Total 1.00000000000000 0.72151898734177


Pick 3
Catches Pays Probability Return
0 0 0.41650438169426 0.00000000000000
1 0 0.43086660175268 0.00000000000000
2 1 0.13875365141188 0.13875365141188
3 43 0.01387536514119 0.59664070107108
Total 1.00000000000000 0.73539435248296


Pick 4
Catches Pays Probability Return
0 0 0.30832142541003 0.00000000000000
1 0 0.43273182513689 0.00000000000000
2 1 0.21263546580002 0.21263546580002
3 3 0.04324789134916 0.12974367404747
4 130 0.00306339230390 0.39824099950682
Total 1.00000000000000 0.74062013935432


Pick 5
Catches Pays Probability Return
0 0 0.22718420819687 0.00000000000000
1 0 0.40568608606583 0.00000000000000
2 0 0.27045739071056 0.00000000000000
3 1 0.08393505228948 0.08393505228948
4 10 0.01209233804171 0.12092338041705
5 800 0.00064492469556 0.51593975644609
Total 1.00000000000000 0.72079818915262


Pick 6
Catches Pays Probability Return
0 0 0.16660175267770 0.00000000000000
1 0 0.36349473311499 0.00000000000000
2 0 0.30832142541003 0.00000000000000
3 1 0.12981954754107 0.12981954754107
4 4 0.02853791777842 0.11415167111370
5 95 0.00309563853868 0.29408566117427
6 1500 0.00012898493911 0.19347740866728
Total 1.00000000000000 0.73153428849631
Pick 7
Catches Pays Probability Return
0 0 0.12157425195400 0.00000000000000
1 0 0.31519250506592 0.00000000000000
2 0 0.32665405070468 0.00000000000000
3 0 0.17499324144894 0.00000000000000
4 1 0.05219096674793 0.05219096674793
5 25 0.00863850484104 0.21596262102591
6 350 0.00073207668144 0.25622683850532
7 8000 0.00002440255605 0.19522044838501
Total 1.00000000000000 0.71960087466417
Pick 8
Catches Pays Probability Return
0 0 0.08826623772003 0.00000000000000
1 0 0.26646411387178 0.00000000000000
2 0 0.32814562171247 0.00000000000000
3 0 0.21478622512089 0.00000000000000
4 0 0.08150370149677 0.00000000000000
5 9 0.01830258559927 0.16472327039346
6 90 0.00236671365508 0.21300422895706
7 1500 0.00016045516306 0.24068274458425
8 25000 0.00000434566067 0.10864151665261
Total 1.00000000000000 0.72705176058740
Pick 9
Catches Pays Probability Return
0 0 0.06374783835335 0.00000000000000
1 0 0.22066559430007 0.00000000000000
2 0 0.31642613522274 0.00000000000000
3 0 0.24610921628435 0.00000000000000
4 0 0.11410518209547 0.00000000000000
5 4 0.03260148059871 0.13040592239483
6 50 0.00571955799977 0.28597789998865
7 280 0.00059167841377 0.16566995585549
8 4000 0.00003259245500 0.13036981998314
9 50000 0.00000072427678 0.03621383888420
Total 1.00000000000000 0.74863743710631
Pick 10
Catches Pays Probability Return
0 0 0.04579070078903 0.00000000000000
1 0 0.17957137564325 0.00000000000000
2 0 0.29525678110572 0.00000000000000
3 0 0.26740236779386 0.00000000000000
4 0 0.14731889707162 0.00000000000000
5 1 0.05142768770500 0.05142768770500
6 22 0.01147939457701 0.25254668069420
7 150 0.00161114309853 0.24167146477914
8 1000 0.00013541935526 0.13541935526417
9 5000 0.00000612064883 0.03060324412750
10 100000 0.00000011221190 0.01122118951342
Total 1.00000000000000 0.72288962208343
Pick 11
Catches Pays Probability Return
0 0 0.03270764342073 0.00000000000000
1 0 0.14391363105123 0.00000000000000
2 0 0.26807441078170 0.00000000000000
3 0 0.27838496504254 0.00000000000000
4 0 0.17858658134804 0.00000000000000
5 0 0.07408035967030 0.00000000000000
6 8 0.02020373445554 0.16162987564429
7 80 0.00360780972420 0.28862477793623
8 400 0.00041141689837 0.16456675934961
9 2500 0.00002837357920 0.07093394799552
10 25000 0.00000105799787 0.02644994671019
11 100000 0.00000001603027 0.00160302707335
Total 1.00000000000000 0.71380833470919
Pick 12
Catches Pays Probability Return
0 0 0.02322716706690 0.00000000000000
1 0 0.11376571624603 0.00000000000000
2 0 0.23777034695421 0.00000000000000
3 0 0.27972981994613 0.00000000000000
4 0 0.20576280024883 0.00000000000000
5 0 0.09938731483717 0.00000000000000
6 5 0.03220885203057 0.16104426015283
7 32 0.00702738589758 0.22487634872249
8 200 0.00101959840032 0.20391968006364
9 1000 0.00009540101991 0.09540101991282
10 5000 0.00000542798906 0.02713994532003
11 25000 0.00000016727239 0.00418180975655
12 100000 0.00000000209090 0.00020909048783
Total 1.00000000000000 0.71677215441618
Pick 13
Catches Pays Probability Return
0 1 0.01639564734134 0.01639564734134
1 0 0.08880975643226 0.00000000000000
2 0 0.20661861700566 0.00000000000000
3 0 0.27273657444747 0.00000000000000
4 0 0.22728047870623 0.00000000000000
5 0 0.12587841897576 0.00000000000000
6 1 0.04750129017953 0.04750129017953
7 20 0.01231514930580 0.24630298611609
8 80 0.00218314010421 0.17465120833686
9 600 0.00025989763145 0.15593857887220
10 3500 0.00002006227331 0.07021795656818
11 10000 0.00000094336708 0.00943367083316
12 50000 0.00000002398391 0.00119919544489
13 100000 0.00000000024599 0.00002459888092
Total 1.00000000000000 0.72166513257318
Pick 14
Catches Pays Probability Return
0 1 0.01150142425437 0.01150142425437
1 0 0.06851912321754 0.00000000000000
2 0 0.17629399411180 0.00000000000000
3 0 0.25904423624590 0.00000000000000
4 0 0.24220636088992 0.00000000000000
5 0 0.15197261859760 0.00000000000000
6 1 0.06575738304704 0.06575738304704
7 9 0.01985128544816 0.17866156903346
8 42 0.00418163651802 0.17562873375666
9 310 0.00060823803898 0.18855379208507
10 1100 0.00005973766454 0.06571143099739
11 8000 0.00000381101528 0.03048812225484
12 25000 0.00000014784111 0.00369602775180
13 50000 0.00000000308404 0.00015420194010
14 100000 0.00000000002570 0.00000257003234
Total 1.00000000000000 0.72015525515306
Pick 15
Catches Pays Probability Return
0 1 0.00801614417729 0.00801614417729
1 0 0.05227920115624 0.00000000000000
2 0 0.14793901603787 0.00000000000000
3 0 0.24040090106154 0.00000000000000
4 0 0.25021318273752 0.00000000000000
5 0 0.17615008064721 0.00000000000000
6 0 0.08634807874863 0.00000000000000
7 10 0.02988971956684 0.29889719566835
8 25 0.00733144064847 0.18328601621172
9 100 0.00126716258122 0.12671625812169
10 300 0.00015205950975 0.04561785292381
11 2800 0.00001234249267 0.03455897948773
12 25000 0.00000064960488 0.01624012193972
13 50000 0.00000002067708 0.00103385391659
14 100000 0.00000000035046 0.00003504589548
15 100000 0.00000000000234 0.00000023363930
Total 1.00000000000000 0.71440170198168
How To Play Keno
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