Keno in association with thewizardofodds.com

Keno is a simple game that is played the same way as most lottery tickets. A card of video screen features every number from 1 to 80. The player chooses some numbers, usually from 1 to 10 of them. Then 20 numbers will be drawn at random, either with numbered ping pong balls or electronically. If enough of the random numbers fall on the player's picks then the player will win.

There are three main forums for keno, state lotteries, keno lounges, and video keno. The return on state lottery keno is about 50%, in keno lounges is about 70%, and in video keno is about 90%.

State run keno is usually played during certain hours in bars and restaurants licenses to play keno. A new game will be played about every five minutes. Players fill out cards that are read through a machine to provide a receipt. Then the random picks will be shown on a television monitor. With a return of only about 50% (at least this is the case in Maryland) state lottery keno is absolutely to be avoided.

Many casinos have a keno lounge where players can make their picks and watch the numbers drawn from a ping pong ball chamber. A game is played about every five minutes. Although the return is poor at about 70% it can be a good way to kill time on a low budget.

The best return in keno can be found in video keno. These games are mixed among the slots and video poker. With a rod the player touches the desired numbers on the screen and presses a button to begin displaying the computer's picks. Although the return is much better at about 90% the pace is also much faster than lounge keno. The player should avoid the pick-1 in video keno, which only pays 3 for 1, for a return of 75%.

The following table shows the expected return according to the number of picks for 8 video poker games in Las Vegas. Table 1 is from a keno lounge, the other seven are from video keno machines. The specific locations follow the table.

• Table 1: Las Vegas Hilton
• Table 2: Regent - $2 machine
• Table 3: Regent - 5 cent machine
• Table 4: Horseshoe - 25 cent machine
• Table 5: Suncoast - 5 cent machine
• Table 6: Suncoast - 5 cent machine
• Table 7: Suncoast - 5c, 10c, 25c machines
• Table 8: Suncoast - 25c, 50c, $2 machines

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 CityTropicana, 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

Computation of Probabilities

The probability of matching x numbers, given that y were chosen, is the number of ways to select x out of y, multiplied by the number of ways to select 20-x out of 80-y, divided by the number of ways to select 20 out of 80.

The "number of ways to select x out of y" means the number of ways, without regard to order, you can select x items out of y to choose from. I shall represent this function as combin(y,x) which you can use in Excel.

For the general case combin(y,x) is y!/(x!*(y-x)!). For those of you unfamiliar with the factorial function n! is defined as 1*2*3*...*n. For example 5!=120. The number of possible five card poker hands would thus be 52!/(47!*5!) = 2,598,960.

As an example let's find the probability of getting 4 matches given that 7 were chosen. This would be the product of combin(7,4) and combin(73,16) divided by combin(80,20). combin(7,4) = 7!/(4!*3!)= 35. combin(73,16) = 73!/(16!*57!)=5271759063474610. combin(80,20) = 3535316142212170000. The probability is thus (35*5271759063474610)/3535316142212170000 =~ 0.052190967 .