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# How Odds of Winning Rounds Affect Session Prospects

12 August 2003

The gamblers' fanny pack of tricks includes ways to manipulate the chance of winning on any round. Players have opportunities not merely to shave the odds, but to flip them and be favored to win. It's done by using, not breaking, the laws of probability. But, better than a 50-50 chance doesn't mean having an edge.

The approach is especially straightforward in roulette, which therefore serves as a prime but not the sole example. Other than in casinos where 0 or 00 either lose only half or "imprison" money for the next spin on "outside" bets, the house advantage in roulette is the same on every wager regardless of the likelihood of winning. The trade-off involves balancing greater or lesser odds with smaller or larger payoffs per dollar at risk.

The idea is simple. Say you bet \$12 on a single spot; the odds are 37-to-1 against you but a win brings \$420. Bet the \$12 as \$6 on each of two spots (or \$12 on the line between two numbers); you're fighting odds of 18-to-1 and are up to net \$204. At \$4 on each of three numbers, odds are an adverse 11.67-to-1 to snatch \$132. Likewise, \$3 on each of four spots (or \$12 on a four-number corner) has you in an 8.5-to-1 battle to grab \$96. Go to \$2 on six different numbers and you're outweighed 5.33-to-1 to earn \$60. At \$1 on each of a dozen positions, it's a 2.17-to-1 ordeal looking for \$24. Carry the reasoning further, to \$6 on each of two columns; you're favored to win this bet, having put odds of 12-to-7 on your side, but you're risking \$12 for a \$6 profit. Just beyond the limits of logic, or maybe you think it's a ruse to bamboozle the bigwigs into coddling you with comps for pretending to play with what a book you bought said is negligible exposure, you could bet \$1 on each of the 12 three-number rows; you've given yourself odds of 18-to-1 to break even and not lose.

Of course, as every erudite solid citizen knows from Aesop's Fables, one swallow does not make a summer. Nor does one bet a session. Unless, that is, it happens to be something like a winning wager on a giant jackpot, but that's another fable.

The key question transcends the projected results of single rounds and involves how folks can expect to do in sessions of reasonable duration on bets having various odds. The accompanying list gives an indication of the answer. The data assume bets of \$12, as indicated, consistently for 100 spins -- about two hours at a moderately-paced table. The entries then show the range where players would have 90 percent probability of finishing. Stated differently, an individual would have under 5 percent chance of ending the session deeper in the hole than the "worst" figure and also less than 5 percent probability of quitting after the two hours with more profit than the "best" value.

 Range over which a player would have90 percent chance of finishing,with bets of \$12 distributed as shownat double-zero roulette bet worst best 1 spot -1,200 +1,074 2 spots -856 +730 3 spots -702 +576 4 spots -608 +482 6 spots -495 +369 12 spots -338 +212 2 columns -206 +80 12 rows -108 -24

You can draw several important conclusions about gambling from the data presented. 1) The odds of winning any bet can often be adjusted without necessarily changing house advantage. 2) The more conservative a strategy -- the better the odds of a smaller win on any round -- the more modest both projected session damage when a game is ugly and potential gain when it's roses. 3) Meals or other freebies you get by playing for comps can cost you a lot more than they're worth. 4) Improving your chances on individual coups by reducing the payoff ratio doesn't mean you're onto something the casino bosses have been trying to keep secret. 5) Aesop knew whereof he spoke in Fable 190, appropriately enough entitled "The Spendthrift and the Swallow."

Less eminent than Aesop, but respected in his own right, the punter's poet, Sumner A Ingmark, offered this alternate take:

Cutting back on your risk is highly commendable,
Though the profits you seek aren't nearly as spendable.