## Keno

Keno is everywhere nowadays. It is kind of a middle class Bingo. It is the easy way to gamble. In Vegas, you sit down to buy a meal, at the Pizza Hut in your hotel, and there are keno tickets and crayons for your use. In your home town, you will find keno machines. A few of the options will change. But the main difference is in the payoffs. Vegas has bigger payoffs, but it is still a poor bet. Bigger hotels probably have bigger payoffs. And your home town keno machine probably has very small payoffs.

Above, you see a typical keno ticket. There are 80 numbers to choose from. Just draw an X over every number that you choose. More complicated options will be described later. You can choose from one to 15 numbers. Also choose how much money your want to pay; the more you pay, the more you can win. You can play the same ticket for several games. Then the casino chooses 20 numbers (shuffled balls or computer chosen) and then pays you if you had a winning ticket. The payoffs come from predetermined (and freely available) charts like this one:

 Mark 12 Spots Winning Spots Play \$1 Play \$3 Play \$5 6 pays \$5 \$15 \$25 7 pays \$30 \$90 \$150 8 pays \$240 \$720 \$1200 9 pays \$600 \$1800 \$3000 10 pays \$1480 \$4440 \$7400 11 pays \$12,000 \$36,000 \$60,000 12 pays \$36,000 \$100,000 \$100,000

If you marked 12 spots, then the house would use this table. If you payed \$3, then nine winning spots will pay you \$1800. Notice that two of the payoffs are the same, \$100,000 for 12 winning spots. Of course 12 for 12 is very very rare. But the large payoff makes this outcome important for your chances. This \$100,000 payoff limit (which the casino brags about on their ticket, and on their marquee) makes betting \$5 a worse bet than betting \$3 (which in this case is a worse bet than the \$1 bet).

What kind of bet is keno? Well, it is a bad bet. To begin, I will play a single game for \$1 and choose one number. Here is the chart for that:

 Mark 1 Spot Winning Spots Play \$1 Play \$15 Play \$100 1 pays \$3 \$45 \$300

That's my kinda chart (simple). I chose one spot (number 37), and the casino chose 20 numbers at random. My chance of winning is 1/4. My expected payoff on a dollar is \$0.75. That is better odds than my state lottery. But it is still a sucker bet (bad bet) for Las Vegas. Well, I suppose there are better bets on this ticket, because of all of the more complicated tables and ways to play. Don't bet on it (a gambling joke there). Yes there are better and perhaps worse bets available for the keno player, at my casino. But the bets are never much better than \$0.75 return on your dollar bet.

What about the 12 spot chart, above? It is more difficult to calculate the expected return. It turns out that the expected return is about \$0.71, worse than the one spot ticket.

There are more complicated options. You can play a combination ticket, which works like writing two or more separate tickets. You are essentially playing two or more games simultaneously on the same ticket. I won't show how to mark such a ticket. You can also choose to play a "way ticket," which is rather complicated (like playing many many keno games simultaneously). I won't describe these. None of these options changes the expected return on your bet very much.