ARE MARGINAL HANDS WORTH
THE EXTRA RISK?
The Curious Case of A-2 vs. 5, and
Similar Iffy Situations
by Basil Nestor
Basil Nestor is author of "The Smarter Bet Guide to Craps," "The Smarter Bet Guide to Blackjack," and other comprehensive gambling guides. Got a question? VisitSmarterBet.com and drop him a line.
Blackjack basic strategy is a valuable tool to help you win. However, basic strategy is not a one-size-fits-all monolithic sledgehammer. Itís actually a collection of intricate parts that work like a set of scalpels. Some moves cut deeper than others. Some actions are wildly profitable, while others simply reduce your expected loss, and a curious few are nearly inconsequential. In those latter situations, it doesnít much matter what you do, and volatility becomes an issue. Should you risk gobs of extra money if those bets will barely increase your overall return?
Consider a hand such as A-2 against a dealerís 5. If you get this hand, be very pleased. Chances are good that youíll win. If you receive the hand in an eight-deck game, your average profit will be $13.66 for every $100 you bet initially. When you double down, your net profit increases to $13.76. In other words, the second black chip earns you a dime more in profit (itís actually 9.46 cents without rounding).
Brother, Can You Spare a Dime?
Is that a worthwhile bet? Technically, yes. If you make the bet, the dimes add up over time. But really, it will take a loooooooooong time! Youíll see that situation and earn that 9.46 cents about 1 in 1,091 hands on average, or after about 18 hours of blackjack. Thatís 180 hours to earn $1, or 18,000 hours to cover the extra $100 you risked on the first bet.
In the meantime, volatility may nuke your bankroll. Or it may reward you. Volatility dominates in this situation because the bet is essentially a coin flip.
The situation improves somewhat in a six-deck game where doubling A-2 against 5 is worth an extra $0.34 cents. Moreover, it really goes up in a two-deck game where a hit earns $14.59 and a double down is worth $16.92, or $2.33 more for the double down.
There are more iffy hands like this. Letís look at a few, and youíll see a pattern develop.
Consider A-4 against a 4 in an eight-deck game. A double down is worth $6.42. Thatís only $0.35 more per $100 compared to a hit. In a two-deck game, the extra value of a double increases to $1.27.
Then there are hands that completely switch depending on the number of decks. For example, in an eight-deck game, if you have a 9 that consists of a 7-2, against a 2, a hit earns you $7.35 and a double down only returns $6.56. Therefore, a hit is worth $0.79 more. In a six-deck game, the hit advantage over a double is $0.60, and in a two-deck game, the double down becomes more profitable, returning $8.64, which is about $0.93 more than a hit.
Notice that reducing the number of decks from eight to two has a bigger effect in these situations than the difference between a hit or double down.
Selection, Selection, Selection
Or to put it another way, your best basic strategy decision may be to pick up your chips and find a game dealt with fewer decks, a contest that pays 3:2 for naturals, and rules that allow doubling after splits. Game selection is crucial. Find a good game, and then apply an optimal strategy to those circumstances. Avoid the drag of starting with a mediocre game.
Since this isnít always possible, hereís a short list of borderline optimal moves that increase your profit by less than 1% of the base bet when you double down. Blackjack purists will tell you to always make the optimal moves in these situations, and theyíre mathematically correct. Nevertheless, if you want to reduce volatility, thereís no shame in hitting rather than doubling if the extra black chip will only buy you a few cents of profit.
On the other hand, Iím an aggressive bastard, so my personal cutoff is usually 0%.
By the way, donít equate these razor-thin amounts (less than 1% extra profit for doubling) with the importance of reducing the overall house edge by fractions of 1%. The latter is achieved by pressing huge advantages and winning giant chunks when you have an opportunity. This offsets the casinoís huge frequency advantage.
As a point of comparison, hereís a typical no-gray-area optimal move in an eight-deck game:
7-3 vs. 5 - a double down pays $52.39 which is $26.20 more than hitting.
See? Those are big chunks that knock down the house edge.
The iffy list includes eight-deck and two-deck games when the dealer hits on soft 17. An asterisk indicates that the extra value is also less than 1% in a six-deck game. Notice that some hands drop off the list as the number of decks change because the extra profit exceeds 1%. Another thing to remember is that borderline-optimal choices become even more variable when youíre counting cards. Thatís a whole other subject weíll tackle another time.
Ace-8 vs. 6 - a double down pays $46.18, which is $0.94 more than standing.*
8-3 vs. ace - a double down pays $11.49, which is $0.87 more than hitting.
9-2 vs. ace - a double down pays $11.25, which is $0.66 more than hitting.*
Ace-7 vs. 2 - a double down pays $11.59, which is $0.35 more than standing.*
Ace-4 vs. 4 - a double down pays $6.42, which is $0.35 more than hitting.*
Ace-2 vs. 5 - a double down pays $13.76, which is $0.09 more than hitting.*
7-2 vs. 2 - a double down pays $8.64, which is $0.93 more than hitting.
5-4 vs. 2 - a double down pays $8.62, which is $0.36 more than hitting.
6-3 vs. 2 - a double down pays $8.45, which is $0.31 more than hitting.
Ace-7 vs. 2 - a double down pays $11.95, which is $0.06 more than standing.*
Ace-3 vs. 4 - a double down pays $8.71, which is $0.05 more than hitting.
Ace-6 vs. 2 - a double down pays $0.24 which is $0.02 less than hitting. Note that in this case, a hit is preferred but the hand is so mediocre and so marginally profitable that it hardly matters either way as long as you receive a card. In an eight-deck game, the hand is a net loser and the hit is a clear favorite by losing $0.51 less than a double down.
Pick your best game, and then learn the intricacies of the strategy. And donít be afraid to make adjustments based on your preferences. Remember that a mathematically-optimal move may not be optimal for your temperament or your bankroll. Always play the best game that suits you.
(c) copyright 2011 Basil Nestor
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