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From the perspective of profit motive, casino games fall into two types. One group appeals to gamblers who set target earnings, either dollar amounts or fractional or integral multipliers of their bankrolls, at which they're happy to quit. Examples include blackjack, craps, baccarat, roulette, and pai gow -- which mainly involve short-odds wagers with payoffs comparable in magnitude to what's bet. The second category attracts bettors who won't be satisfied other than by a score big enough to change their lifestyles. Illustrations are slot machines and table games like Caribbean Stud and Let It Ride, in which a small bet can yield anything from a push or even money to a gigantic jackpot.

Sizing bets when the objective is to achieve some win goal involves a trade-off. Bets that are small relative to players' bankrolls reduce the chance of normal downswings leading to wipeouts during sessions of reasonable length. Conversely, large bets raise the likelihood of reaching any particular profit levels. Sizing bets when the purpose is to keep pursuing the pot of platinum only involves the first of these factors. The sole objective is to survive for the time allocated to play, on a bankroll that made sense on the way into the casino and will still seem prudent if it's gone by the end of the visit.

Make believe you enjoy playing Caribbean Stud. And assume you'd like to get four hours of tries at a hefty haul. You're undoubtedly not only going to play the main game, but also make the $1 side bet on the progressive jackpot. You'll surrender your seat ahead of schedule under just three conditions: a) you hit a royal flush paying 100-to-1 on your hand and 100 percent of the jackpot; b) you hit a straight flush returning 50-to-1 on your hand and 10 percent of the jackpot; c) you go bust.

The number of rounds you can anticipate experiencing in four hours depends on the speed of the dealer and how many solid citizens join you at the table. A good average is 60 rounds per hour, 240 rounds in a four-hour session. Bet sizing for Caribbean Stud then comes down to the question: what fraction of your bankroll should you wager as ante on each round to have a high degree of confidence you won't go belly-up in 240 rounds if you don't hit a royal or straight flush? To get an answer, picture your bankroll as comprising two segments, one for the ante and "bet" on the main game and the other for the $1 jackpot try.

Analysis based on "risk of ruin" suggests what to ante as a fraction of your main-game bankroll. (You'll have to trust that I really did the math on this.) You can be 85 percent sure of surviving the normal downswings of a 240-round session, with no royals or straight flushes, betting under 1.6 percent of your bankroll as the ante per round. This would be a $5 outlay on a main-game bankroll just over $300. To be 95 percent confident of exhausting no poke before its time, the ante shouldn't exceed 1.2 percent. This is $4.80, close enough to $5, starting with $400.

For the side bet, based on chances of occurrence, you can expect to hit either a flush, full house, or four-of-a-kind once every 275 rounds. As a ballpark estimate for 240 rounds, if you don't hit a royal or straight flush, figure on putting out $240 and getting back $75. So you need a stake of $240 - $75 or $165 for the side bets.

What's the bottom line? Say you start with $500. You set aside $165 for the side bet. You have $335 for the main game. At the 85 percent confidence level, 1.6 percent of $335 means you can wager $5 on the ante. What if, instead, you start with $1,000? You'll still set aside $165 for the side bets, leaving $835 for the main game. To be 85 percent sure this bankroll will last for four hours, you should limit the ante to 1.6 percent of $835 or $15