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# Rethink Your Exit Strategy before Blaming Losses all on the Edge

27 September 2004

Augie and Connie relish double-zero roulette. They know the house advantage is a huge 5.26 percent. But Augie likes the high payoffs on single spot longshots, while Connie enjoys getting the odds of winning strongly in her favor by covering multiple numbers, even though the payoff is low. Further, both go to the casino for dining and entertainment as well as gambling; so their exit strategies are to hold playing sessions to an hour, less if they hit their loss limits or win goals. As a result, both believe the edge doesn't affect them enough to write home about.

For illustration's sake, pretend the pair push their proclivities to the peak with rather radical betting strategies. They each have \$1,000 loss limits. Augie puts \$33 on a single number per spin -- that's one chance in 38 of winning \$1,115 -- and quits as soon as he hits or exceeds \$2000. Connie does pretty much the opposite; she bets \$1 on each of 33 numbers, for 33 chances in 38 of netting \$3 on a spin, and quits when she reaches or tops \$50. Both stop after an hour if they haven't reached either extreme.

A typical roulette table gets 40 spins in an hour. A computer simulation involving 5,000 players betting according to these strategies shows what they can anticipate happening in practice.

Augie's method gives him probabilities of about 11 percent of reaching his \$2,000 win goal and 45 percent of going broke within the hour. Moreover, since he bets when he's just under \$2,000 and picks up \$1,115 on a win, his take may actually go above \$3,000. If he doesn't bump into either end of his range and plays out the full 40 spins, his chances are about 16 percent of winning \$1,056 and 28 percent chance of losing \$135.

Connie's style yields virtually no prospect of finishing under \$400, let alone busting out. As a winner, she has about 13 percent chance of reaching or passing her \$50 goal and 12 percent of grinding out the hour and pocketing a tidy \$12 or \$48. On the loss side, her chances are below 1 percent of dropping over \$300, about 6 percent of being \$200 to \$300 in the hole, and 20 percent of concluding \$100 to \$200 behind; at lower levels of loss, she's looking at probabilities of being down around 16 percent by \$96, 18 percent by \$60, and 15 percent by \$24.

In either case, even after only an hour, the likelihood of a loss is much greater than that of a win. For Augie's ultra aggressive action, the proportions are about 73-to-27; for Connie's quite conservative mode, they're slightly worse at 75-to-25.

As a first guess, it might appear that the loss-to-win asymmetry is due to the effect of the edge. However, with a house advantage of 5.26 percent and bets of \$33, Augie and Connie each have theoretical losses of roughly \$69. This doesn't really jibe with the results found in the simulation. A more subtle effect of edge may be at work, of course. This supposition can be tested by simulating the same betting strategies, win targets, and loss limits at single-zero roulette -- where edge is cut in half to 2.63 percent. For the aggressive strategy, the proportion of losers to winners remains nearly the same at 73-to-27. But for the conservative approach, the offset shrinks to 60-to-40. Edge impacts Connie more than Augie. This is largely because she hits her limits less often than he does, and therefore plays longer.

A further accounting for the imbalance can be found in the selection of profit objectives for the same loss tolerances. Say they're halved, to \$1,000 for the aggressive and \$25 for the conservative paradigms. Then, for 5.26 percent double-zero roulette, the ratio of aggressive winners-to-losers decreases to 68-to-32 while those of conservative bettors drops to 58-to-42.

Edge can accordingly be seen to have an effect. But the influence is not necessarily stronger in instances such as the one examined than that of a factor which solid citizens can easily control. Namely, an upside exit strategy, devised in accord with the probabilities of winning and the associated payoffs. It's reminiscent of the rhyme by the beloved bard, Sumner A Ingmark:

Those quick to make up an explanation,
May miss the crux of a situation,
And earn as witless a reputation.

Recent Articles
Best of Alan Krigman
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.