BONUS BETS AT BLACKJACK
by Alan Krigman
Alan Krigman, and his poetic sidekick Sumner A. Ingmark, have been illuminating the dark recesses of casino gambling for more than a dozen years. Mr. Krigman is especially well known for sharing his insights into the mathematics underlying the various games (including blackjack), the influence of volatility and skewness as well as edge on bankroll during the course of a session, and the impact of betting as well as decision strategies on expected performance. A searchable archive of Mr. Krigman's prose and Mr. Ingmark's muse is online athttp://www.iconworldwide.com/winningways/search.php.
Some table games offer side (aka bonus) bets, ancillary to the primary action. These bets typically dangle the bait of rich rewards for moderate amounts of risk – often as little as $1 when the nominal table minimum may be $5, $10, $25, or more. Gambling gurus tend to pooh-pooh such propositions because they generally have usurious house advantages. Not only are the percentages raked by the casinos high when the side action is appraised on its own, they elevate what may otherwise be a modest edge on the main bet when the combined wagers are evaluated.
As an example, make believe you play blackjack with basic strategy. Edge would be about 0.5 percent – equivalent to $0.025 on a $5 wager. "Lucky Ladies," a side bet available in some joints, wins if your first two cards total 20, and the amount you win depends on how the sum is formed. A version paying the amounts below gives the casino roughly a 25 percent edge – $0.25 on $1 at risk.
Two queens of hearts when the dealer has blackjack: 1000-to-1
Two queens of hearts when the dealer doesn’t have blackjack: 125-to-1
Any suited 10-valued pair other than queens (e.g., two jacks): 19-to-1
Any suited unpaired 20 (e.g., 10-jack or ace-nine): 9-to-1
Any unsuited 20: 4-to-1
Any non-20: lose
Say you bet $5 on the main blackjack game and $1 on Lucky Ladies, $6 total for the round. The bosses earn $0.025 on your principal action and $0.25 on your side bet, $0.275 in all. Edge on the whole $6 at risk is 0.275/6 or 4.6 percent, which is over nine-times greater than the 0.5 percent for blackjack without the gee-gaws.
With $10 on the fundamental bet and $1 on the side bets, effective edge on the $11 net is 0.30/11 or 2.7 percent. Go for $25 on what may seem like the cake and $1 on the icing, and the overall edge on your $26 would be 0.375/26 or 1.4 percent.
Considering edge alone, side bets are most deleterious for low-stakes players. This has two relevant implications: 1) Gamblers at low-limit tables, those hit proportionately hardest by excess edge, are the most apt to make the secondary bets; this, especially in games that normally pay close to even-money because players see the side bet as their sole path to copious cash. 2) Bosses have the strongest incentives to offer these wagers at their lowest-limit tables since the take from the normal edge on small bets can’t cover the house’s overhead, let alone yield a profit.
If edge was the sole consideration in gambling, no rational argument could be advanced to support side bets. Of course, in this case, nobody would gamble in the face of any edge at all because there’d be no way to win. People patronize their friendly, neighborhood dens of iniquity because the games are characterized by volatility as well as edge. And the former overwhelms the latter – for better or worse as the simultaneously revered and feared fickle-finger-of-fate might decree – during the statistically short span of a session, stay, or even series of visits.
Picture the effect of the volatility by positing an even-money bet having 49.5 percent chance of success versus 50.5 percent of failure. The 1 percent (50.5 - 49.5) offset in probabilities gives the house its edge. If you bet $5 on a proposition with 1 percent edge, the bosses figure you for $0.05 – which is the average you’d lose per hand if you repeat the bet millions of times; however, in one round, the $0.05 gets buried because you’ll either be ahead or behind by $5. After two rounds, the house figures you for $0.10 but you’d actually be $10 ahead, even, or $10 in the hole. After three rounds, the casino calculates that it’s squeezed $0.15 from your poke, but you’re actually either $15 or $5 up, or $5 or $15 down. Where’d the $0.05, $0.10, or $0.15 go?
The appeal of Lucky Ladies and most other side bets is that they increase volatility – and do it in a way that pits the potential of a few large profits against multiple minor losses. The high edge on small bets adds up over time. But, the gross it represents is still easily overlooked compared to the bankroll fluctuations induced by the volatility of the base bet. Moreover, admittedly, rare wins of big bucks on side bets can boost players over the top, while frequent losses of chump change only marginally contribute to their scraping the bottoms of their fanny packs.
For many folks who won’t settle for less than a substantial payday, an affordable wager with a high house advantage is the gamble of choice. It’s certainly preferable to an alternative, such as over betting a bankroll to make $50 wagers at 0.5 percent edge, for the same $0.25 equivalent, and busting out on volatility during a short cold spell. This is one of the reasons for the popularity of slot machines, on which a dime, quarter, or dollar gives solid citizens a shot at a jackpot fantasy that can change their lives. And it’s why bettors, who like the élan of the tables, relish the side action. As the venerated versifier, Sumner A Ingmark, sagaciously scribbled:
Though higher bets raise what you earn,
A gambler may in sorrow learn,
That this approach may spell disaster,
Since losses eat up bankrolls faster.
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