Side bets: cheap at the price or expensive in the end?

Many casino table games now feature “side bets.” These long shots usually give the bosses a big edge. But they tempt players with huge progressive jackpots. And wagers are small relative to what must be risked for lower-edge, more regularly hit, smaller returns on the primary action.

Caribbean Stud Poker affords a classic illustration. Here’s how it works.

The main game requires players to begin with an ante of at least the table minimum. Say it’s $5. After the deal, players can fold and lose the $5, or add twice the ante – $10 in this instance – to call the dealer. Winning after a call can pay from $5 if the dealer doesn’t “qualify” with ace-king or better, up to $1,005 if the player has an uncontested royal. For bettors who follow the game’s optimum strategy, chances are about 38.5 percent of earning something along this range, 47.8 percent of sacrificing $5 by folding, and 13.7 percent of losing $15 with a hand ranked below that of the dealer. An almost insignificant proportion of hands push. Edge for optimal play is 5.2 percent of the ante – equivalent to 26 cents for $5 bet at the start of a round.

The side bet costs $1, regardless of the nominal table minimum. Most Caribbean Stud buffs dismiss a buck as chicken feed, if not relative to an ante such as $5, then compared to the $15 needed for a called bet and certainly with respect to their session bankrolls. Payoffs are generally $50 for a flush, $75 for a full house, $100 for four-of-a-kind, 10 percent of the progressive jackpot for a non-royal straight flush, and 100 percent of the jackpot for a royal. Jackpots are normally seeded at $10,000 but players rarely have to look far to find tables where the prize has risen to $100,000, $200,000, or more. Of course, it doesn’t take a math whiz to realize that 100,000-to-1 payoffs are infrequent or that progressive jackpots wouldn’t grow from $10,000 to this level on rakes from $1 bets were they hit and reset very often. In fact, chances of any joy are so low they’re best grasped when stated, not as percentages, but as one out of 649,740 for a royal, one out of 72,193 for a non-royal straight flush, one out of 4,165 for four-of-a-kind, one out of 694 for a full house, and one out of 508 for a flush. Edge for this auxiliary gamble depends on the current size of the jackpot but averages about 26.5 cents on the dollar.

The majority of casino aficionados are acutely aware how much of a cushion they have from which to draw bets. Players seldom hesitate to put small fractions of this nest egg up for grabs because they’re not worried about a few losses busting them out. Under such circumstances, the adverse impact of high edge and low success rate may easily go unnoticed. This is typically the case with side bets. The same solid citizens who’d change tables, break for lunch, go to the cash machine in the lobby, or even head home after five or ten straight misses in the main game at Caribbean Stud are apt to keep making $1 side bets round after fruitless round.

Series of $1 side bet losses can add up, however. Consider a situation in which Billy and Millie partner at Caribbean Stud. Each starts with $100. Billy bets on the main game, sliding out a $5 ante on each round. Millie fronts the $1 side bet.
Billy’s prospects for being in the fray after 100 rounds are close to 55 percent. The probability Millie won’t exhaust her stake by losing 100 bets in a row is under 31 percent. Those $1 side bets are accordingly more apt to spell disaster than the $5-ante plus $10-call at risk in the primary game. Not that the chance of 55 percent average survival in the main game is especially good.

Say, instead, that Billy and Millie bet the same way on $200 stakes. Now Millie’s chance of at least one hit in 200 tries and still having money in the end rises to 52 percent; Billy’s likelihood of lasting at least this many rounds is 70 percent. Higher bankroll-to-bet ratios give both brighter outlooks but, again, Billy’s are better than Millie’s. Another alternative with $200 budgets is that Millie puts her $1 per round on the side bet while Billy is full of himself and bets $10 as ante and another $20 to call. Millie’s chance of avoiding bankruptcy stays at 52 percent; Billy is over betting his $200 bankroll at $10 and $20 if he expects it to carry him through the normal downswings of a 200-round session, and has only 34 percent chance of making it.

The bottom line is that the utility principle, tossing what you consider chump change on an admittedly faint hope of a big bounty, may be fine for an occasional fling. When done repeatedly, though, for instance every round at a casino table game, it can be at least as hazardous to your financial health as larger bets on propositions with lower house advantage that pay less but win more often. As the venerated versifier, Sumner A Ingmark, noted in this memorable maxim:
A proposition nickel-dime,
May promise a reward sublime,
But prove disastrous, given time.