Don't Price Yourself out of Doubles in Blackjack

Aggressive blackjack players sometimes press their bets to a level where they're scared to double down on promising hands. So they "double for less," hit, or -- on soft 18 -- stand, just when the casino is most vulnerable. They exceed their base bet before the deal, but are psychologically or financially unprepared to pounce when the cards tell them the moment has arrived.

Chance, of course, can always rear its awesome head. Standing on soft 18 versus six may win $25 when the dealer flips an ace and stops at 17, while doubling would lose $50 because the next card is an eight and would form 16. Or, maybe doubling nine against a four yields a weak 11, when drawing twice would have gone to 21. Still, competent gamblers don't just assume they can do anything because luck is all that matters. So the critical issues for those seeking to maximize profit don't involve how hands turn out. Rather, they are (a) how much "expectation" is sacrificed with a non-optimal decision, and (b) how much the chance -- as opposed to the amount -- of a win increases by not doubling. The answers depend on the cards in question and the actions taken.

Basic strategy only calls for doubling when it raises expected return. So failing to double when ordained sacrifices theoretical profit, ultimately increasing the house advantage in the game.

The statistical cost of avoiding doubles is least with soft hands against "stiff" dealer upcards. For instance, standing on soft 18 against a dealer's three cuts expectation by under $0.03 per dollar of initial wager. Hitting soft 17 against three forgoes a like amount. The bite worsens for higher stiffs because the dealer is likelier to break and the player more apt to win with a double. Against a six, for example, standing on soft 18 is worth $0.10 per dollar less than doubling and hitting soft 17 has an expectation nearly $0.13 less.

Penalties for not doubling are greatest with starting totals of 11, decreasing somewhat for hands of 10 and nine. Hitting 11 against six-up has an expected profit almost $0.34 per dollar of initial bet. Doubling offers theoretical earnings of $0.68. So hitting is like giving the casino $0.68 - $0.34 = $0.34 per dollar. The effect is a bit less for lower dealer upcards. For instance, against a four, hitting 11 "costs" players $0.29 per dollar relative to doubling. Against higher upcards, the forfeit declines faster but is still of concern. As an illustration, hitting 11 versus a nine is worth $0.07 less than doubling.

When the alternative to doubling is to hit, and only one card will be drawn regardless of its value, the chances of winning are equal either way. This happens with player totals of 10, eleven, or soft 17 against a dealer's four through six. Regardless of what card is drawn, the total then calls for the player to stand.

In all other cases, chances of winning a round are decreased by doubling. To see why, say you have a 10 versus a nine. You double and are dealt anything from two through six. You'd take another hit if you could. Or consider starting with soft 18 against six. Of the 13 possible cards you could receive by doubling, four leave you at 18, three raise you to 19 through 21, and six drop you to 12 through 17. You're twice as likely to fall as rise. Doubling is preferred in these situations because of the extra money bet when eight out of 13 results will be favorable. But the sacrifice incurred by taking the next best alternative has been moderated by the improved chance of winning the initial bet.

Doubling for less -- making an second bet lower than your initial wager but being limited to drawing a single card -- is the worst of both worlds. You're not getting the full benefit of the favorable situation. And, except on hands where you'd only draw one card anyway, you won't win as often as the next best option.

Betting progressions -- based on systems, whims, hunches, omens, or prayers -- can add to gambling excitement and alter the characteristics of a session. They can't reduce house advantage. That's left to proper play. And in blackjack, proper play means doubling and splitting when dictated by basic strategy. Elevated bets make little sense if players balk at the opportunities they present. As the beloved bard, Sumner A Ingmark, observed: