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Best of Alan Krigman

Gaming Guru

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Here's How to Handle Pairs of Fours at Blackjack. And Why.

27 May 2002

Pairs of fours aren't exactly the answers to blackjack players' prayers. These hands are underdogs against dealer upcards on the average of eight out of every 13 times. Further, the handicap is moderate to reasonably high when the fours are poor prospects, while the advantage is low to middling when they're favored.

More, four-four is one of those combinations on which even seasoned solid citizens are sometimes uncertain about the optimum play. The problem is that the hand can be hit, split, or doubled, and intuition doesn't help in deciding what to do. Worse, Basic Strategy for this hand varies with the rules on the game being spread, so the crib sheet you diligently memorized may not be correct for the conditions at your friendly neighborhood casino.

The accompanying list shows the expected profit or loss on this hand with a $10 initial bet, for each of the three options. The figures are for an eight-deck game where doubling is allowed on any total and is permitted after splitting. Such "expectations," calculated by analyzing the probabilities of all possible results, are the factors that determine Basic Strategy. The selection offering the most gain or the least damage, as luck would have it, is what "the book" ordains in each case.

Statistically expected gain or loss on a $10
initial bet, for a pair of fours against each
dealer upcard. Values for alternate ways to
play the hand assume eight-deck games with
doubling allowed after splitting.

upcard
hit
double
split
A
-$1.98
-$8.09
-$5.63
10
-$2.48
-$7.45
-$6.21
9
-$2.10
-$7.16
-$5.09
8
-$0.59
-$4.51
-$3.26
7
$0.86
-$1.78
-$1.69
6
$1.22
$0.99
$1.64
5
$0.80
$0.22
$1.04
4
$0.46
-$0.54
-$0.02
3
$0.11
-$1.29
-$0.98
2
-$0.20
-$2.01
-$1.88

The values of expectation clearly reveal that doubling is always the worst choice. It's projected to lose more when dealers are strong and win less when they're weak than either alternative.

The data also show that hitting the eight beats splitting the pair against all upcards except five and six. By enough, so none of these decisions can be considered a close call. The narrowest margins involve dealers' fours and sevens. Against four, hitting shows an expected profit of $0.46 on a $10 wager, while splitting is anticipated to lose $0.02. Against seven, the shift is from a theoretical gain of $0.86 for a $10 bet to a loss of $1.69.

Conversely, instances in which splitting is preferred yield relatively minor statistical improvements over hitting. From $0.80 to $1.04 on a $10 wager against five-up; from $1.22 to $1.64 when the dealer shows a six.

Basic Strategy for eight decks, with doubling after splitting, is accordingly to split pairs of fours against dealers' fives and sixes; hit otherwise. Ditto for two or more decks, same rules.

The Basic Strategy exceptions are found in unusually liberal or tight casinos. Here they are. 1) At single-deck tables with no doubling after splitting: double on the eight rather than split the pair against a dealer's five or six. 2) At single-deck tables with doubling after splitting: split the pair rather than hit the eight against four- as well as five- and six-up. 3) At tables using two or more decks, with no doubling after splitting: hit the eight rather than double or split, regardless of upcard.

What about "personal" deviations? Use the expectation list for guidance. For instance, say you bet $10 and get two fours against a five. It's an eight-deck table with doubling after splitting. Ordinarily, you'd split and hope for a five, six, or seven on each of the fours so you could jump on the robust doubles. But, you have only $40 left in your kitty and would hesitate to risk it all at once if the chance arose, despite its being a good shot. How much edge are you throwing away by hitting? Expectation drops by only $1.04 - $0.80 or $0.24, which you may judge a fair price to avoid the danger of busting out in one stroke. Such situations are why the prudent poet, Sumner A Ingmark, professed:

The flock that follows guidelines blindly,
May not find luck responding kindly.

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.