Keno Strategies
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.
Basically, any sort of Keno Strategies are based simply on mathematical computations, such as those below.
Tables
|
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< | |