# Doin’ the math for Caribbean Stud poker

Nov 27, 2001 2:27 AM

What could exasperate a Caribbean Stud stalwart more than playing for hours without ever seeing a respectable hand? How about finally receiving a lollapaloosa, only to have the dealer not qualify? Or, perish the thought, to qualify with better cards?

Picture the predicament. Make believe you start with \$10 on Ante and pull three-of-a-kind. You eagerly plop another \$20 on Bet. You’re mentally tallying your take: \$10 for the Ante and \$60 for the Bet, \$70 in all. Drat! The dealer doesn’t qualify so the Bet pushes and all you earn is \$10 for the Ante. Or, double drat! The dealer qualifies with higher triplets, a straight, or whatnot and you lose \$30. Had you begun with a straight instead of trips, an analogous situation turns your imagined \$90 gain into the same \$10 win or \$30 loss.

What’s the likelihood of such a scenario? The odds you have to overcome to get three-of-a-kind at Caribbean Stud are over 46-to-1. When you have this hand, the probability of a dealer not qualifying, leaving you with even money for the Ante and zip for the Bet, is almost 42.5 percent. Not all that far from 50-50. A qualifying dealer doesn’t let you completely off the hook, either. You can’t tie three-of-a-kind, but have over 3.3 percent chance of losing to a straight or better, or, depending on the rank of your hand, to higher triplets.

Similarly, the odds against your pulling a straight are about 254-to-1. Assuming you do line ”˜em up, the chance of a dealer failing to qualify is 43.43 percent. If the dealer does overcome the ace-king barrier, you’re sitting reasonably pretty but still have roughly one chance in 102 of losing to a higher-ranked hand and one in 3,585 of pushing against an equal-valued straight.

The wicket isn’t as sticky when bettors are blessed with hands ranking above straights. This, because most Caribbean Stud buffs put \$1 on the progressive jackpot. Consequently, when a dealer doesn’t qualify (or does, with an equal or better hand), flushes, full houses, and quads at least pay consolation prizes ”” typically of \$50, \$75, and \$100, respectively. And straight flushes and royals can represent big bucks, at 10 and 100 percent of sums that often rise into the \$200,000-or-more realm.

Consider the amounts and probabilities for flushes, however. Say you’re a \$10 bettor. Beating a dealer with a flush is worth \$10 on the Ante, \$20 x 5 = \$110 on the Bet, and \$50 from the jackpot. That’s \$160. If a dealer doesn’t qualify, you net \$60. Tie the dealer and you’re left with \$50. Losing to the dealer drops your gain to \$20. A \$25 bettor is looking at a range from profits of \$310 for a sweep, \$75 if a dealer doesn’t qualify, and \$50 for a tie, to losses of \$25 if a dealer has the upper hand.

Further, flushes are expected to pop only once in every 507 or so tries. When they appear, a dealer has nearly 44 percent prospects of not qualifying. And although flushes are tough to tie or beat, doing so is hardly impossible. Chances are a scant one in 286,124 of the former, but not excessive at one in 194 for the latter.

Solid citizens busting their buttons with straight flushes and royals are often more cavalier about the dealer’s hand because they’re thinking mainly about the progressive jackpot. Chances of getting into the position to worry about this issue are low, to be sure. One out of 72,192 for a straight flush and one out of 649,739 for a royal. But the probability a dealer won’t qualify in these cases is about 43 and 45 percent, respectively.

And the sacrifice is \$20 x 50 = \$1,000 and \$20 x 100 = \$2,000 for a \$10 ante. Chump change compared with the 10 and 100 percent of the jackpot? Maybe, if that jackpot is \$200,000 or \$300,000. Some people, though, gamble wherever the bus happens to stop, or where they’re treated “real good,” despite a paltry \$15,000 or \$20,000 on the payoff meter. These folks, apparently, ignored this cogent counsel of punterdom’s pet poetic pen pusher, Sumner A Ingmark:

By focusing on petty purse,
A gambler’s lot too oft gets worse.