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Best of Alan Krigman

Gaming Guru

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Doubling in blackjack when basic strategy says "no"

5 March 2007

Doubling down in blackjack is a powerful tool for players. Solid citizens can make second bets up to the amounts of their first, after seeing their initial two cards. The second bet is an option for use under favorable conditions. A limitation is that players get one and only one card, which isn't always to their liking. And, of course, dealers can finish well even after poor starts.

Basic Strategy is to double when it's projected to yield higher average profits than hitting or standing. This occurs as follows. Soft hands: ace-seven and ace-six versus three through six, ace-five and ace-four versus four through six, and ace-three and ace-two versus five and six. Hard totals: 11 versus two through 10, 10 versus two through nine, and nine versus three through six.

Here's an example of how the Basic Strategy rule is obtained. Consider an 11 versus a dealer's five. Players would normally draw only one card in this situation even if they hit, so chances of results are the same either way. With six decks, they'd be 62.6 percent to win, 6.9 percent to push, and 30.5 percent to lose. Per $100 bet at the start of a round, profit hitting would average $62.60 - $30.50 or $32.60. Doubling applies the same percentages to $200, yielding twice the expected net, or $65.20.

For situations where players might normally take more than a single card were they able — for instance after drawing a four to an 11 against a nine-up — the premium for doubling is less than a factor of two. With 11 versus nine, expected earnings per $100 initial bet are $15.50 hitting and $22.60 doubling.

There may be occasions when players might be justified doubling on hands not sanctioned by Basic Strategy. That is, where they think good prospects of winning $50 by risking $50 outweigh a somewhat better shot at picking up $25 with $25 on the line.

For example, say your total is eight and the dealer shows a five. Hitting is expected to yield an average profit of $2.00 on your $25 while doubling is only worth a theoretical $0.58. But, maybe $50 will put you over the top, while $2.00 and $0.58 are just values on paper. And, while ability to draw again if your first card is a two or three improves your chance of success if you do hit, you're not the underdog when you double. Doubling on eight versus five has chances of 47.8 percent to win and 46.6 percent to lose. On eight versus six, you're stronger yet with 49.6 percent chance of winning as opposed to 45.0 percent of losing.

Soft 20 — ace-nine — versus six offers another illustration. Stand and your expectation is to earn $70.30 per $100 of initial wager. Double and this falls to $57.30. But your chance of triumph is over 60.9 percent, in contrast to 32.3 percent chance of confirming your tablemates' belief that you're an idiot.

Here's the full list of combinations you're favored to win by doubling, despite the laws of probability saying — long term — you'll be further ahead hitting or standing as appropriate. Soft hands: ace-two and ace-three versus four, ace-seven versus two and seven, ace-eight versus two through eight, and ace-nine versus two through nine. Hard totals: eight versus five and six, nine versus two and seven, and 11 versus ace.

Pairs of aces represent a special case. You're favored to win by doubling against four through six. However, splitting the pair gives you significantly greater expectation and you're still up to win or lose twice your initial bet. You also increase the possibility of a push by splitting, not just by equalling the dealer but from one side finishing above and the other below.

None of this is to imply that you should wantonly flout Basic Strategy and double down simply because you have a shot at a bigger score. It does suggest that criteria other than expectation may prevail at certain junctures, and tactics more well founded than going with your gut may then be appropriate. As the Blake of blackjack, Sumner A Ingmark, blithely babbled:

Some actions may seem unconventional, Though well advised and quite intentional.

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.