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Best of Alan Krigman

Gaming Guru

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Should you avoid keno just because the gurus rail against it?

28 May 2012

In the standard version of casino keno, 20 numbers – called “spots” – are drawn from a set between 1 and 80. Players bet by marking as many choices as they wish – forming a “pick” – on a card showing all 80 possibilities. Some establishments limit pick sizes, for example between four and 10 numbers; other operators accept as few as one or as many as 15 or 20 selections. Winners are those whose picks “catch” designated complements of the spots drawn.

Credible gaming gurus advise casino buffs to avoid keno. Their argument is that house advantage is too high – between 25.0 and 28.6 percent depending on the number of spots in a pick and the pay schedule at a particular casino. For comparison, slot machines typically have 6 to 10 percent edge. And table games like blackjack and craps can be played with edge under 0.5 percent.

Many solid citizens flout this caveat. They like the high “utility” of gambles that offer big bucks for small bets. The slow speed at which bets are typically resolved, once in 10 or 15 minutes, is another attractive feature because losing doesn’t hurt much despite how often it occurs and the total sacrificed to house edge doesn’t mount vary fast. Action is also promoted by ubiquity in joints where keno bets can be made in restaurants, rest rooms, elevators, and everywhere else.

The parameters of a keno wager depend on the number of spots in a pick. Bettors accordingly have strategic options for tailoring the game somewhat to meet their personal preferences.
Overall hit rate, the theoretical frequency of returns regardless of amount, varies with how many spots are selected. It also hinges on the number of catches which have payouts for each pick. To illustrate, say a player chooses five spots. The probability is 22.72 percent of no catches, 40.57 percent of one, 27.05 percent of two, 8.40 percent of three, 1.21 percent of four, and 0.06 percent of five. A pick of five should accordingly average at least one correct spot in 77.28 percent of all rounds. But on picks of five, one or two catches lose; players only win on three, four, and five catches, dropping the productive hit rate for this selection from 77.28 to 9.67 percent.

Players who relish wins, regardless of how much they collect, might want to make their bets based on hit rate. Picks of four spots are best by this criterion, at 25.89 percent. These are followed by picks of one spot at 25.00 percent, six spots at 16.16 percent, three spots at 15.26 percent, and 14 spots at 10.20 percent. The lowest hit rates are on picks of eight spots at 2.08 percent and 11 spots at 2.43 percent.

Individuals more eager to toss a buck on a longshot at the biggest possible payday might be inclined to make large picks and hope for lots of catches. With a representative payoff schedule, picking and catching 14 spots returns $100,000 for $1 bet. Chance is one out of 38,910,016,282. Those who pick 14 spots but miss the sweep are still eligible for consolation returns of $50,000 with 13 catches (one out of 324,250,136), $25,000 with 12 catches (one out of 6,764,018), $8,000 with 11 catches (one out of 262,397), $1,100 with 10 catches (one out of 16,740), $310 with nine catches (one out of 1,644), $42 with eight catches (one out of 239), $9 with seven catches (one out of 50), or $1 – their money back for a push – with six catches (one out of 13).
A third criterion for selecting numbers of spots is house advantage, a consequence of the offset between returns and the odds surmounted to win. The lowest edge is 25.0 percent on a pick of one spot, paying 2-to-1 on a hit with adverse odds of 3-to-1. Next lowest is 25.1 percent on a pick of nine which returns $4, $50, $280, $4,000, and $50,000 – including the initial bet – for five through nine catches respectively. Overall hit rate on a pick of nine is 3.89 percent, though, and the $50,000 return isn’t exactly an everyday occurrence at a chance of one out of 1,380,666.

Enquiring minds might want to know how keno compares with state lotteries. In the New Jersey Pick 6, for instance, six numbers are drawn from a set of 1 to 49; players also pick six. Jackpots start at $2,000,000 and grow until they’re won, but are split among multiple winners and are awarded as annuities with cash options of 60 to 65 percent of nominal value. Jackpots require catching all six, the chance being one out of 13,983,816. Five, four, and three catches also win. Amounts for five and four are pari-mutuel – based on sales and how many tickets are winners; averages are $2,700 and $56, corresponding to prospects of one out of 54,201 and one out of 1,032, respectively. Matching three returns $3 for $1, a $2 profit, and has a chance of one out of 57. Across all its lotteries, New Jersey estimates it gives 57 percent of ticket sales to back to players. This constitutes a 43 percent edge for the state, worse than what casinos keep for keno. There’s a moral dilemma, however, in deciding between social services supported by the state versus the salaries of the grunts and bonuses of the bosses who bring you the casino’s thrills and chills. Both situations were mulled by the muse, Sumner A Ingmark, when he muttered:
A gambler noble always should,
Try doing well by doing good.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.