Odds and Probabilities in Keno
There are 2 equivalent formulas using combinations to calculate probabilities for the game of Keno.
The two variables involved in the calculation are:
 n = Number of selections made by player
 k = How many of the player's selections match the drawn numbers.
1) The following formula uses the total number of combinations (i.e. denominator) from the houses point of view. There are ^{80}C_{20} ways for the house to draw 20 from 80 numbers.
Probability(n, k) =  ^{n}C_{k} x ^{(80n)}C_{(20k)} 
 
^{80}C_{20} 
2) The following formula uses the total number of combinations (i.e. denominator) from the players point of view. There are ^{80}C_{n} ways for the player to draw n from 80 numbers.
Probability(n, k) =  ^{20}C_{k} x ^{60}C_{(nk)} 
 
^{80}C_{n} 
3) Both of the above equations can be reduced to the same equation involving factorials given below.
^{a}C_{b} =  a! 
 
b! x (a  b)! 
Therefore:
Probability(n, k) =  60! x 20 ! x n! x (80  n)! 
 
80! x k! x (20  k)! x (n  k)! x (60  n + k)! 
Calculating the House Advantage in Keno
To calculate the return to the player, sum the returns (equal to probability multiplied by the payout) for each possible outcome. The house advantage is determined by subtracting the return to the player from the bet amount and is usually expressed as a percentage. The table below calculates the player's return using formula 2 above for the Spot 9 pay outs given in the example section of the Standard Rules page. The house advantage in this case is 100 x ($1  $0.669665) = 33.03%.
Result Details 

Match  Collect ($)  Frequency  Probability (%)  Return 

0  0.00  14,783,142,660  6.374783835335  0.0000000000  1  0.00  51,172,416,900  22.066559430007  0.0000000000  2  0.00  73,379,314,800  31.642613522274  0.0000000000  3  0.00  57,072,800,400  24.610921628435  0.0000000000  4  1.00  26,461,025,640  11.410518209547  0.1141051821  5  5.00  7,560,293,040  3.260148059871  0.1630074030  6  20.00  1,326,367,200  0.571955799977  0.1143911600  7  210.00  137,210,400  0.059167841377  0.1242524669  8  2,500.00  7,558,200  0.003259245500  0.0814811375  9  100,000.00  167,960  0.000072427678  0.0724276778  Total   231,900,297,200  100.000000000000  0.669665027234 
Related Pages
Keno is fast and fun. It is a lottery style card game that players can enjoy as a break from the strategy and skill needed to play poker online. If you are short on time, but want a game that offers huge potential rewards then Keno is the game to play. The best way to take advantage of Keno's chancebased platform is to know what the odds are for each selection (our Keno odds calculator can help with that). Keep this page handy while you are playing Keno so you get the best chances of winning. Start playing right now by selecting an online casino from our reviews here on ReviewPokerRooms. We list the toprated online casinos that offer the highest internet security encryption and 24/7 customer service so you always have the help you need at any time of the day or night.
Playing Keno at the online casinos listed here allows you to make the most out of all of your free time. You can play Keno and all of your favorite online casino games right in your own home. The software on our chosen sites will give you bright, sharp graphics and sound quality for a real casino feel that puts you right in the action. Start playing now and take advantage of the great signon bonuses offered by these sites to get free money added to your account right away.
