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Best of Alan Krigman

Gaming Guru

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Playing It Smart: Doubling down strategies explained

22 January 2008

Blackjack buffs earn much of their money when they get their fair share of hands on which to double-down and win a decent fraction of them. The converse also holds. Too few doubles or too many that fizzle can quickly send the unlucky to the lockers.

Theoretical frequencies of hands suitable for doubling with six and eight decks differ, but not so much that you'd notice. The average is two less doubles per 100,000 hands in six- than eight-deck games. The accompanying table shows expected frequencies. Note that two decimal places corresponds to 10,000 hands.

Chances of receiving two-card hands
appropriate for doubling down

Double	Frequency
on 11	4.38%
on 10	2.54%
on 9	1.08%
TOTAL HARD		8.00%
on A-7	0.37%
on A-6	0.36%
on A-5	0.27%
on A-4	0.27%
on A-3	0.18%
on A-2	0.18%
TOTAL SOFT		1.64%
GRAND TOTAL			9.64%

Over an extended period, you can accordingly expect 96.4 doubles per 1,000 hands. Of these, 80 would be "hard" (you hold nine, 10, or 11) and 16.4 would be "soft" (start with A-2 through A-7). At a table with four total spots in action, you'd get about 85 hands per hour. Consequently, in a three-hour session, you'd anticipate 24 or so legitimate occasions to double-down.

Edge is one reason doubling has a big impact on your fanny-pack. With occurrences and outcomes of doubles close to the frequencies predicted by the laws of the known universe (including casinos), taking this action "by the book" trims house advantage by 1.6 percent. Always hitting or standing whichever is next best on the designated hands, the house edge for otherwise perfect Basic Strategy would increase from under 0.5 to over 2 percent.

The reduction in edge of proper doubling is surpassed only by that of standing correctly against dealer stiffs (3.2 percent) and of receiving 3-to-2 for winning blackjacks (2.5 percent). During a statistically short session, however, reality don't necessarily match augury. It therefore wouldn't be unusual to get discernibly fewer or more chances to double than the theoretical 9.64 percent. Or, to double triumphantly far more or less often than the prophets prognosticate. In such cases, respectively, a solid citizen could temporarily revel in a substantial advantage or suffer Shakespearean slings and arrows of outrageous fortune.

There's also the gambler's best friend or worst enemy, volatility. Neglecting edge, with the bankroll swings of an average game, 95 percent of all $10 bettors would be between $350 down or up after 250 hands. A player could easily get twice the normal number of doubles during a session, and win or lose them in essentially the usual proportions. The swing would then widen from $400 down to $400 up. Success on more or fewer doubles than implied by the averages would shift these $700 and $800 ranges for instance from $250 down to $450 up or $300 down to $500 up.

Some doubles offer punters opportunities to forego a bit of edge in exchange for an increase or decrease in volatility that better suits their personal preferences. An illustration is A-2 versus 5-up. Expectation is to earn an average of $136.36 per $1,000 bet doubling and $136.33 hitting. The gospel is to double because the theoretical return is higher. Hitting lowers the volatility because $1,000 and not $2,000 is at risk, while raising the edge by the equivalent of $0.03. Alternately, on A-7 versus 2-up, standing is projected to earn an average of $123.42 per $1,000 and doubling $120.67. Standing is better by $2.75 per $1,000 so this is the received wisdom. But an individual may be willing to sacrifice this small amount to raise the volatility by doubling.

Of course, such trade-offs ignore the rebuke a reprobate may get from the petulant (losing) player across the felt for "changing the flow of the cards and ruining the game for everyone else." A scolding the celebrated songster, Sumner A Ingmark, put thusly:


The folks who adherence to rules most demand,
Are folks who the rules least of all understand.
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.