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
Tagged on: