Casinos let you win more often than you lose. But there's a catch.

It isn't the difference between the odds of the house or the player winning particular bets that fills a casino's coffers. Urban myth aside, bettors can win more often than they lose. The rest of the story is that payoffs upon success are less than losses upon failure. And the bosses make their dough on the gap between the odds of winning and the payoff ratio, regardless of who the statistics say will win wagers more frequently.

Most casino patrons today prefer propositions on which they can score big multiples of the money at risk. It's the essence of utility theory and the allure of the slots. Sow a little, hoping to reap a lot. Then, defeat isn't bitter but victory is sweet. Minor setbacks, however, are far more likely than major gains.

Some gamblers fancy the opposite approach, high probabilities of collecting small amounts, at the peril of occasionally getting bludgeoned. Roulette affords both types of action. For instance, at double-zero tables, the odds are a steep 37-to-1 that the house will prevail over folks who bet $10 on any number, but they get a $350 payday. Alternately, punters may split $10 between two columns, to have favorable 24-to-14 (roughly 1.7-to-1) odds of winning, but they can only earn $5.

Enquiring minds will surely want to know how these two types of bets affect their outlook for whole sessions or casino visits. The auxiliary "Free Odds" bets on Pass and Don't Pass for points of four at craps offer good examples for purposes of comparison.

Assume, arguendo, the flat portion of the wager is $10 and the maximum Odds multiple is 5X. Pass is expected to lose twice as often as it wins, and $50 in Free Odds earns $100 if a four pops before a seven. Don't Pass is expected to win twice as often as it loses, but $100 in Free Odds only earns $50 if a seven shows before a four. Edge on these bets is zero because fighting 2-to-1 pays 2-to-1 while having a 2-to-1 upper hand pays 1-to-2; there's no margin between the odds of winning and the payoff either way.

Given enough decisions for the law of averages to be reliably applied, zero edge means that players should come out even with either bet. How about the short term that characterizes almost everybody's play? Are there disparities between fewer but larger and more but smaller wins in a normal gambling time frame?

Computer simulations are handy tools to answer these questions. Pretend that a million pairs of solid citizens wager the full 5X Free Odds on $10 flat bets with points of four. One of each pair is on Pass and the other on Don't Pass. Supposing nobody busts out early, and recognizing that even after a million trials the results will still show a margin of error, here are the findings.

If each player goes for 25 decisions then stops, the tallies are 463,000 Pass bettors with winning sessions averaging $307 up and 537,000 with losing sessions averaging $264 down. The exact reverse holds for the Don't Pass bettors.
If each goes for 100 decisions then quits, the tallies are 480,821 Pass bettors relishing ecstasy, averaging $587 ahead and 519,179 suffering agony, averaging $544 behind. The exact reverse holds for the Don't Pass bettors.

Because the 25 and 100 coups simulated weren't integrally divisible by three, nobody broke exactly even. Bettors as a group, though, averaged close to zero. (Numbers of winners times the average won minus numbers of losers times the average lost, divided by a million equalled under $1 per player.)

The simulations demonstrate that sessions follow the same trends as individual coups. If you have a greater chance of winning than losing your bets, but get paid less than the amount wagered, expect more successful sessions but with lower earnings when they happen. Con-versely, if you're more apt to lose than win each bet but the payoff exceeds what's at risk, your prospects are for fewer fruitful sessions but higher profits when they occur. Play long enough, though, and it all comes out in the wash. As the beloved bard, Sumner A Ingmark, enigmatically expressed it:
If more is less and less is more,
Trust time to even up the score.