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Best of Alan Krigman
How Should You Size Your Bets for Let It Ride?9 August 1999
Players tend to approach Let It Ride as they do the slots. Not having in mind win goals at which they'll happily color-up and count their blessings. Rather, meaning to persist until they hit a big payoff, their time runs out, or their spouse's nagging to go to the all-you-can-eat buffet exceeds human endurance limits.
Typically, on the machines, only jackpots suffice. At Let It Ride, most solid citizens would be content to quit after hitting any of the top three hands -- quads (50-to-1), straight flushes (200-to-1), or royals (1000-to-1). With optimum strategy, four of a kind would be resolved with at least two and sometimes three active wagers, so the return with a $5 base bet would be $500 or $750. A straight flush or royal would have three active wagers so $5 bettors would grab $3,000 or $15,000, respectively.
Determining a wagering level involves some give and take. Bigger bets pay proportionally more when one of the hot hands happens. But extra money at risk can also fade at a faster rate, and makes any given well more likely to run dry before reasonable playing time has elapsed. The compromise for each player is a point of personal preference. Surviving a session may be small consolation to punters who won't be pleased with the promised payoffs. And big potential returns are useless to the vast majority of those who can't take a licking and keep on ticking.
Ability to survive a session is the usual starting point to determine the most appropriate bet size. Imagine that players want to be fairly confident of continuing for four hours on their original bankrolls if they don't hit any of the top three hands. How many rounds they can expect during that period depends on factors like the number of players at the table, whether cards are shuffled and dealt manually or by machine, and the dealer's speed. A good average at Let It Ride is 55 rounds per hour, so a normal four-hour session would involve 220 rounds.
Maximum bet size can be found from a "risk of ruin" analysis. Assume that players will accept 85 percent confidence they won't exhaust their bankrolls during 220 rounds if they don't hit four of a kind, a straight flush, or a royal. Following the optimum strategy for the first two decisions, the math shows that the bet on each spot should not exceed 1.6 percent of the initial stake. At this rate, a $300 bankroll would mean betting $4.80 per spot.
Rounding up to $5 per spot with a $300 bankroll trims session length with 85 percent chance of survival to about 200 rounds. This might be ample at a crowded table where under 50 hands were dealt per hour. Fewer players or a faster dealer might inject too much chance of early retirement.
Conversely, $5 per spot on $500 bankrolls (1 percent) would stretch an 85 percent chance of survival over 400 rounds. This is enough to expect four hours, alone, against a fast dealer with a shuffling machine. And, even the weakest of the three big payoffs would bring bettors back to break even from their bottom dollars. Oh yes, about players who think $500 pokes put them in the majors with $10 or $15 per spot (2 or 3 percent). They should have a plan "B" for free time at the casino, because they'll only be 85 percent sure of surviving 150 and 75 rounds, respectively.
Reducing bets to survive longer sessions in high-payoff games has a benefit beyond avoiding the let-down of going belly-up. The probability of receiving any of the three top hands is always 0.026 percent, 26 chances out of 100,000. But playing more rounds raises the likelihood of hitting during a session. Folks with the cash cushion and self control to last for 400 rounds have 9.7 percent chance of hitting during such a game -- an average of once in about 10 sessions. At a ceiling of 150 rounds, the chance of hitting drops to 3.75 percent during a game -- an average of once in about 27 such sessions. Betting twice as much, possible returns double but prospects fall because players are more apt to tap out earlier without a hit. It's as the poet, Sumner A Ingmark, noted about life imitating gambling:
Their goals are frequently elusive,
While seasoned masters of the trade-off,
More oft find gains from chance effusive.
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