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Best of Alan Krigman

Gaming Guru

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Playing It Smart: Doubling down in blackjack: is it the edge or the volatility?

13 July 2009

Edge is what makes casinos win. But, is it what makes players lose? Collectively, yes, gambling being an instance of what the economists call a zero-sum game. For punters individually, no.

People may indeed lose exactly, or close to, the product of edge times their gross wagers during a session. But it would be purely coincidental. Rather, a few solid citizens win moderate to large amounts, while the majority lose most or all of their stakes. This is a result of the volatility of the action, which swamps edge over the statistically small number of coups folks encounter during particular sessions or casino visits. It averages out for the casino but not in a way that any one gambler would notice.

Some games and bets have inherently high volatility. Slots and table games with low-probability jackpot payoffs or longshots often induce wild bankroll swings. You can win big with a few 35-to-1 single-spot roulette payoffs. Or, waiting for such hits, you can lose far more than 5.26 percent of the total you bet.

In other games, where the usual payoffs are 1-to-1, volatility is inherently low. You can raise it yourself for a given average wager by varying your bets. To illustrate, in blackjack, say you slide out a flat $15 for 100 rounds. Chances are roughly two out of three that your bankroll will stay between $163 up and $177 down. Instead, if you bet 20 rounds each at $5, $10, $15, $20, and $25, your average is still $15. But chances are two out of three that your swings will range within $180 up and $194 down.

Doubles and splits are another way to boost blackjack volatility. Technically, these player options were devised to trim the high house edge that arises because the dealer acts after the players and therefore wins when both bust in the same round.

In fact, proper doubling does reduce the overall house advantage. By 1.4 percent in eight-deck games with standard rules, more when fewer decks are shuffled together. But 1.4 percent of the $1,500 risked by a $15 bettor in 100 rounds is only $21. And experienced blackjack buffs know intuitively that doubles have greater impact on their fortunes than this. Unless they get a higher proportion of doubles than the theoretically-expected 10 percent of their hands, the game is apt to grind along boringly with bankrolls gradually rising or falling. Frequent players also know instinctively that receiving a larger fraction of these hands can lead to big profits when they succeed, or to major losses when they fail. They don't know and can't control which will happen.

There's more. You're the favorite when making a proper double. That's the edge. But the edge is weaker than most players think. Of the hands Basic Strategy says to double, average return is over $0.30 per auxiliary dollar bet only on 11 vs 6-up and 11 vs 5-up. Expected return is between $0.20 and $0.30 per extra dollar on 10 vs 6-up, 10 vs 5-up, 11 vs 4-up, 10 vs 4-up, 11 vs 3-up, 10 vs 3-up, and 11 vs 2-up. Theoretical profit is from $0.10 to $0.20 per supplementary dollar for 11 vs 8-up, 11 vs 7-up and 10 vs 7-up, 9 vs 6-up, A-6 vs 6-up, A-7 vs 6-up, and 10 vs 2-up. The rest have expected returns under $0.10 per dollar of extra bet.

The fallout of the second bet being advantageous for the player shouldn't be taken lightly. Either for its average positive projected return or the way it skews the impact of volatility toward the plus side. But the advantage is fragile.

More than twice as many doubles provide expected returns per extra dollar wagered under than over $0.20. At $0.30 on the dollar, ignoring pushes, odds of winning to losing are good at 65-to-35. At $0.20 on the dollar, the odds decline to 60-to-40. Go to $0.10 on the dollar and they're slimmer yet, 55-to-45. These are not slam-dunk propositions. Here's another take. Double on 11, when you're strongest, and five ranks out of 13 (9, 10, J, Q, K) put you in good shape while five (A, 2, 3, 4, 5) leave you nervous. The bard, Sumner A Ingmark, saw such situations soberly:

When sitting in the catbird seat,
You are favored for a win,
But from that height a slip's defeat,
So be sure you're well strapped in.

Alan Krigman

Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.
Alan Krigman
Alan Krigman was a weekly syndicated newspaper gaming columnist and Editor & Publisher of Winning Ways, a monthly newsletter for casino aficionados. His columns focused on gambling probability and statistics. He passed away in October, 2013.