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Sanderson M. Smith

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KENO is an interesting numbers game. You can relaxin a chair, be served free drinks (as long as you are playing), andeven watch people who are involved in other casino games. I enjoyplaying KENO every now and then, although I know that my chances of'coming out ahead' are extremely small. It's possible to win big inKENO, but it is definitely not the game to play if you are attemptingto make money playing games of pure chance. Games of pure chance suchas roulette and craps provide opportunities to lose money at a slowerpace.

KENO is a relatively simple game. The set, S, ofthe first 80 positive integers, is involved in all versions ofKENO.

After you choose some of these numbers, the casinowill randomly select 20 number from S. (In all versions of KENO, thecasino generates a list of 20 randomly selected numbers fromS.)

Let's consider 20 SPOT KENO as played at JohnAscuaga's Nugget in Reno.

In this game, you pay to have the opportunity tochoose twenty numbers from the set S. It costs $5 to play. Afterpaying the $5 and picking your twenty numbers, the casino thengenerates its list of 20 numbers. The table below provides thepayouts for certain numbers of matches. Some examples:

• If none of your numbers are among the twenty, you win $500.
• If 1 of your numbers is among the twenty, you win $10
• If 2 of your numbers are among the twenty, you win $5.
• etc., etc., etc.
• If 19 or 20 of your numbers are among the twenty, you win $100,000.

  Note carefully that you will at least break even unless you match 4. 5, or 6 numbers. This seems to make the game almost too good to be true. Let's check it out.

The table below can be generated on the TI-83. Ifwe assume the four columns represent lists L1, L2, L3, and L4, then

L1 can be generated by highlightingthe L1 and typing seq(x,x,0,20,1).

L2 can be generated by highlighting L2 and typing(20 nCr L1)*(60 nCr (20-L1))/(80 nCr20).

This will put the probabilities in theappropriate cells. For example, the probability of matching 4numbers is (₂₀C₄)(₆₀C₁₆)/(₈₀C₂₀) = .2050318987.

You must type in the appropriate payoffs inL3.

L4 is generated by highlighting L4 and typingL2*L3

Keno 20

The sum of the last column is your expected payofffor each $5. The sum $3.45 can be easily obtained by using1-Var Stats L4on your TI-83. For each $5 'invested,' you can expect a return of$3.45. Hence, you expect to lose a total of $1.55 for each $5 youspend on 20 -SPOT KENO. You expected loss per dollar spent is this$.31, which puts the version of KENO on a par with otherversions.

Note that the only losing numbers of matches are4, 5, and 6. But the probability that you will end up matching oneof these numbers is .20503 + .23328 + .19017 = .62848. And, 2, 3, and7 are 'break even' events. The sum of these probabilities is .04971+ .12486 + .11330 = .28787. Hence, the probability that you will not'come out ahead' in a game is 1 - .62848 - .28787 = 1 - .91635 =.08365.

KENO can be fun and relaxing. Just don't expectto win much playing the game.

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