Poker News

Richard Burke

Years ago the casinos called it Racehorse Keno, and I suppose some still do. We call the game Keno at my local casino. Anyway, on a Friday afternoon in spring Patrick O’Flaherty, a middle-aged Dubliner on holiday, sat on my left at my $4-8 Hold’Em game. He had signed up for all the larger-stake Hold’Em games and while he was waiting to be called, he played low-stakes poker and big-bet Keno.

His Keno tactic was to select two numbers and bet that both ping-pong balls with those numbers would arise, paying him $1200 for $100. He had plenty of Franklins for his endeavors: he counted them and while I didn’t actually watch, I could hear the bills being counted, sluff-sluff-sluff, and I guessed that he had thirty Benjamins. Patrick wasn’t shy about his Keno bets; he informed everyone at the table that he wanted both “17″ and “29″ to hit. His opinion was that those two numbers appeared more often than any other two.

After three or four unsuccessful Keno plays, he won a $100+ Hold’Em pot, so he doubled up on his Keno bet. Sure enough, his “17″ and “29″ were among the twenty numbers selected, for a payout of $2400!

Had he found El Dorado? Of course, “17″ and “29″ weren’t any more likely than any other pair, but was the Keno payout table in error? Patrick said he always played those two numbers and was way ahead.

Between hands I figured his chances. The probability that those two would be among the twenty ping-pong balls randomly drawn from the eighty is C(78,18)/C(80,20), which simplifies to 20*19/80/79, or once in 16.63 games.

The expectation is the payoff times its probability minus its cost, $1200/16.63 - $100, which obtains -$27.85. Since Patrick’s expected “win” is negative, on average he pays the casino $27.85 per $100 to see if both his numbers appear in lights. (The hold for every Keno bet at my local casino is between 25% and 35%.) The Two-Spot payout table was correct, and I sincerely doubted that Patrick was ahead in his campaign.

Paradoxically there’s a 50-50 chance that Patrick would hit his two numbers within 11 games. The catch is that it’s always the next 11 games, no matter how many times he had been unsuccessful in the past. Patrick was taking the worst of it not only because of his negative expectation, but also because of the fine print. At my casino, the fine print limits the Keno payout to $25,000. In the admittedly unlikely event of two or more big winners, they must divide the max payout. Since most people pick their birthdates, spouse’s birthdates, children’s birthdates, etc., the popular numbers chosen by the players.

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