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# What Are the Pros and Cons of Longshots versus Parlays?

20 April 2005

Joe puts \$5 each on 17 and 24 at single-zero roulette. With luck, he'll win \$175 (at 35-to-1) on the spot that hit. He'll also get his \$5 back so he has \$180. But he began with \$10, so his net is \$170. His chance of winning is two out of 37 or 5.4 percent.

Jane comes by and bets \$10 on Red. This pays even money. She plans to add any winnings to the total and bet it all for up to three more spins, making a four-bet parlay. If she reaches the fourth spin and wins, she'll have wagered \$10, \$20, \$40, and \$80 ?? all based on her original \$10. The last spin will pay \$80 and return the \$80 on the table, giving her \$160. She began with \$10 so her net profit is \$150. Her chance on any spin is 18 out of 37 or 48.6 percent; the likelihood she'll win four in a row is 48.6 percent multiplied by itself four times, or 5.6 percent.

The details differ slightly, 5.4 or 5.6 percent and \$170 or \$150. Do the discrepancies simply trade-off lesser prospects of higher gain and the converse? Or, is it a case of "more things on heaven and earth, Horatio, Than are dreamt of in your philosophy."

There are psychological contrasts. Joe and Jane may each consider \$10 as chump change. And neither may distinguish between the utilities of \$170 and \$150, regarding either amount well worth a 5 or 6 percent longshot for a \$10 investment.

The approaches diverge in the perceptions of what's at risk. Joe sees only \$10 and is comfortable with it. Jane is aware that with mounting success she's betting \$20, then \$40, then \$80. Despite her original intent, after the first win she knows she can lock up a profit and may be uneasy hazarding the greater amounts.

Another psychological element is the gambling time \$10 buys. Joe has a good chance of being KO'd on one spin. This may be OK, for instance if he's heading home anyway and prefers a shot at \$170 to waiting in line for the cashier to redeem his last two red chips. For her money, Jane has at least reasonable prospects of a longer game ?? if not a win at the end.

Another factor some solid citizens find important is the house advantage on the action, and the effective bite the bosses take from their bankrolls. Joe, betting \$10 with 5.4 percent chance of winning \$170, gives the house 2.7 percent edge. In essence, the casino figures it earns \$0.27 on the coup. Jane's wager, \$10 with 5.6 percent chance of winning \$150, gives the house an edge of 10.4 percent. The bosses figure this is worth \$1.04 to them.

Why the disparity? Good gamblers know that every bet made at single-zero roulette is docked a merely outrageous 2.7 percent. This is just what Joe pays. Jane, though, is hit for a usurious 10.4 percent. How is this possible?

The answer is that the 2.7 percent edge on Joe's action is applied to the original \$10. He bets it once, win or lose, and the casino pencils in \$0.27. Not so for Jane. She bets \$10 on the first spin and the house's theoretical take is \$0.27. If she wins, which will happen on the average of 18 times out of 37, she bets \$20 and the house gets 2.7 percent of this ?? or \$0.54; multiply \$0.54 by the 18/38 of the time it actually applies and the second bet accounts for over \$0.26. Similar reasoning adds more than \$0.25 for the \$40 and almost \$0.25 for the \$80 wagers.

Another way to envision the effect of the edge on the alternate bets would involve Joe's and Jane's earnings were they to have 5.4 and 5.6 percent chances of winning \$10 bets with no advantage for either the house or the player. In Joe's case, the profit would be \$175.00; in Jane's, \$168.53. So the edge has cut \$5.00 from Joe's earnings while it's lopped \$18.53 from Jane's.

Which strategy is best to get a decent payoff for a small bet at the tables? You'll have to weigh the kinds of considerations presented and decide for yourself. After all, wasn't it the memorable muse, Sumner A Ingmark, who reminded us all that: