Why Players Love Bets that Earn Big Bucks for the Bosses

22 July 2003

By Alan Krigman

Side bets for progressive jackpots and consolation prizes at Caribbean Stud are big profit items for the casinos. But, when the jackpot exceeds $218,047, players have an effective edge. You'll encounter this situation occasionally, especially if you're in a venue with multiple casinos and check around for the best payouts rather than simply stay where the bus happens to drop you. Computer simulations of 100 "cycles" from a $10,000 "seed" to the payoff on a royal, with $0.70 added to the jackpot per dollar bet, show that about 14 percent of all starts get to the level where they're statistically advantageous for players.

The bettors' edge under these conditions comes courtesy of contributions from customers who've taken a chance and missed, because the casinos continue to make money, too. In fact, the operators tend to clear more per dollar bet as the jackpot grows. This, because the gravy train gets its momentum and keeps rolling once the seed is covered. The bosses' share is derived from the $0.30 per dollar not added to the jackpot, minus the seed. If a royal hits early, the casino can actually go into the hole.

To illustrate the effect, in one of the simulated cycles, the royal popped on the 20,008th hand. At that point, the casino had taken in $20,008 in bets; it forked over $12,135 for the royal and had previously distributed a total of $11,874 for secondary payoffs. So $20,008 total came in and $24,009 went out. The loss was $4,001 on $20,008 or 20 percent. In another short cycle, a jackpot at the 17,398th hand paid $14,881 after having disbursed $7,300. Here the deficit was $4,783 on $17,398 or 27.5 percent.

Usually, as you'd surely guess, cycles are longer and the casinos do quite well. The 100 simulations showed the joints taking an average of 28 percent of the handle. In contrast, players using the A-K-8-J-3 strategy give the house an edge in the primary game of 5.3 percent of the ante. So the casinos pocket nearly as much on the $1 side bets as on expert play of hands with $5 antes.

Say that you find a game with a jackpot over $218,047. Do you jump right in and start a marathon session, figuring that on the side bet, at least, you've got an advantage? A wager that probability theory says favors the player isn't guaranteed to win. And it may not be especially attractive if the cost of losing is too high or the chance of success too low.

The side bet on the Caribbean Stud progressive is only a buck. This is normally perceived as peanuts by the punting public. Still, solid citizens ought to consider how often those dollars are dropped into the slots during a session, and the premium the quest for the mother lode adds to the ante in the main game.

As for prospects of winning, the likelihood of scoring with a royal is one out of 649,740. Secondary wins brighten the picture. Chances are one out of 72,193 for 10 percent of the jackpot with a non-royal straight flush, one out of 4,165 for $500 with four of a kind, one out of 694 for $100 with a full house, and one out of 509 for $50 with a non-straight flush. All told, the side bet should return something on the average of once every 273 tries.

What about playing for a jackpot well below $218,047? The laws of probability aren't all there is to gambling. Utility theory is also a factor. This holds that bettors will risk sums they won't lament losing, reaching for riches they realize they're never apt to amass the proverbial hard way, regardless of the odds of success or their relationship with the payoff. The popularity of Caribbean Stud side bets suggests that many players perceive the utility of a dollar bet several times to be less than the same number of remote shots at enough to pay off the car or the house.

So, should you run to or from the Caribbean Stud tables? If you have to ask, you didn't get the message about utility being what the loss, the gain, and the order of magnitude of the odds mean psychologically to each individual. Or, perhaps you didn't pause to ponder the puzzle posed by that precocious poet, Sumner A Ingmark:

Is your incentive to gamble in the main for the fun of it,
Or are you after the money, because work's made you none of it?