PLAYING IT SMART by ALAN KRIGMAN

Which do you want: a better chance or a greater profit?

Mary and Gary enjoy roulette. They each start with $180. Mary bets $5 on a single spot per spin; she quits as soon as she scores. Gary also bets $5 straight-up per spin, but he runs his bankroll once-through -- 36 spins -- hoping for multiple hits.

Neither approach is inherently superior to the other. Because either may perform better in any given session, the results of one or more specific games don't prove anything. The likelihoods of various outcomes, however, differ for playing in the respective modes. And these may suggest which alternative resonates more strongly with your own personal preferences.

The worst-case scenario, no hits in 36 spins, is a wash. In either case, the chance of such a run of bad luck is 38.3 percent and the monetary consequence is a loss of 36 x $5 or $180.

The best Mary can do is score on her first spin. She'll then pick up 35 x $5 or $175; having not previously lost, the $175 is pure profit. The chance this will happen is just over 2.6 percent. Mary's next best scenario is a miss on the first spin and a hit on the second. She'll again pick up $175, but will have already lost $5 so her net gain is $170. The likelihood of a miss followed by a hit is slightly below 2.6 percent. Probabilities and amounts continue to fall gradually for more misses followed by a hit. At 35 losses then a win, the probability of which is 1.0 percent, she was $175 down then jumps back up to break even.

Mary should actually be interested in cumulative rather than individual probabilities. For instance the chance of hitting within the first six tries and earning at least $150 is 14.8 percent, that of winning within 16 rounds and netting at least $100 is 34.7 percent, and the promise of scoring within the first 26 spins and quitting with at least $50 is 50.0%. none are huge paydays, but the odds of beating the house are decent.

Gary can make a tidy sum, although any profit at all is a longshot. In the extreme, he might be one of those solid citizens who sees a butterfly on his way out the door and takes it as an omen that this will be his lucky day. Say, 36 hits out of 36, for a grand total of $6,300 -- assuming he keeps betting $5 a pop rather than starts pressing his bet so he can really teach the bosses a lesson and bring the casino to its knees.

The probability of a 36-hit streak is so small that, expressed as a percentage, the number wouldn't mean anything. Think of it like this. All the casinos in the United States with roulette tables might get a total of 100 to 200 million visits per year. Suppose that on each trip, each patron plays three or four full 36-spin roulette sessions -- about three hours of ecstasy or agony. The time required before the casinos, collectively, would expect to encounter this streak once is substantially more than the 15 billion or so years scientists peg as the age of the universe.

Returning to planet Earth, if Gary hits once in 36 spins, he breaks even. He'll have lost 35 x $5 or $175, and won $175 on his single success. Prospects this will happen are 37.2 percent. He's home free if he hits twice; the profit is $180 (34 losses at $5 each for $170 and two wins at $175 each for $350). The chance of two hits is low but reasonable -- 17.6 percent. Three hits nets him $360, a 5.4 percent possibility. Four hits puts $540 into his fanny pack, but chances are down to 1.2 percent. Odds fall precipitously as the number of hits continues to rise.

Which of these betting strategies would you prefer? The downsides are the same -- 38.3 percent chance of busting out. The outlook for breaking exactly even is 1.0 percent quitting after one win; it's 37.2 percent plowing ahead, come what may. Mary's hope of any gain at all is brighter than Gary's, 60.7 percent versus 24.5 percent. In terms of revenue, Mary has a gradually increasing probability of earning slowly decreasing amounts; Gary has a sharply falling likelihood of grabbing rapidly escalating rewards. A tough call? Well, as the poet, Sumner A Ingmark noted:

Folks seeking plans which satisfy them're
Oft caught on the horns of a puzzling dilemma.

(c) 2008, ICON/Information Concepts Inc

To view more columns, click here

English Harbour is one of the finest casinos online. They offer you your own personalized start page, $35 free with a minimum first purchase of $35 and first rate software.The software must be downloaded, but the wait is well worth it.The largest slot machine jackpots on the internet.