Side Action Usually Means Sucker Bets, Unless You Win

17 June 2003

By Alan Krigman

Longshots offer big returns for small bets, with odds often so steep that gamblers know their chances are remote and don't worry about how much. Statistically, they're usually sucker bets. But the high payoffs draw lots of folks to the slots and the lotteries. And they encourage side action at casino tables as well. Both the formal kind -- like bets on the Caribbean Stud progressive jackpot or the Let It Ride bonus, and less extreme do-it-yourself types -- such as a buck on a one-roll proposition at craps, or a nickel on Tie at baccarat.

Some solid citizens make side bets purely by whim or hunch. Others use them for hedges; $4 on the Horn at craps to "protect" $25 on the line during the come-out roll is one common example, $1 apiece on 10 odd numbers to offset $10 on Even at roulette is another. An alternate strategy is to allocate a fraction of a bankroll during the course of a session, for instance an amount equal to a single "regular" bet, for a shot at an earnings spike. Maybe in the hopes of a quick recovery after a series of cold rounds, or to put the icing on the cake of a successful game.

Assume you want to try for an earnings boost at craps with an occasional bet on the 11, a 17-to-1 wager that pays 15-to-1. If you normally have about $25 at risk per shooter on Pass and Place bets, you might mentally set aside an equal amount to bet on this proposition in $5 increments. Say you're considering two options: 1) bet the $5 five times regardless of what happens on each try, 2) bet $5 up to five times, but stop as soon as you win. Either way, the probability is 75.14 percent you'll be sending your $25 into the dreaded abyss from which no money has ever been known to return. But the upside prospects differ for the two cases.

The first of the accompanying tables shows the chances of winning various amounts if you bet $5 on the 11 in each of five rounds, regardless of what happens. The second indicates the chances and amounts associated with betting $5 on the 11 in up to five rounds, but quitting as soon as you win once.

Both methods offer the same risk of losing the entire $25 -- just over 75.14 percent. And, inversely, the likelihood of winning at least once is 24.86 percent one way or the other. The most evident differences are in the amounts it's possible to win.

Betting every time, regardless of intermediate results, the net is as high as $375 with five wins, although the chance is only 0.0001 percent or one in a million. A single win during the "cycle" returns $55 and has over 22 percent chance of occurrence. Maximum earnings with the strategy of stopping after a win is $75. The probability of reaching this point with a success on the first attempt is 5.56 percent.

There are seasoned players to whom going for the full five bets seems more desirable than quitting after a hit. They'd prefer settling for $55 after a win on the first round and four subsequent losses, taking the opportunity to go for up to $375. Others would opt to pocket the $75 and not press their luck.

The laws of probability favor the win-and-quit method. This, because the casino earns slightly less from the bettors. However, the difference in expectation is a function of the average bet totaling $22.30 rather than the full $25, and not of the edge on what's placed at risk. Utility theory asks whether a player is willing to sacrifice part of a profit already earned, and go for more. Either is legitimate, it being left to individuals to decide that weighty matter themselves. For, as the Chaucer of choice and chance, Sumner A Ingmark, charmingly chanted:

Though dollars, odds, and payoffs seem objective,
Each person views them from his own perspective.