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# When and Why to Split Fours at Blackjack

7 July 1997

Of paired starting hands at blackjack, four-four probably causes the greatest confusion. When and why is it best to stand, hit, double down, or split the pair? And, how costly is second-best?

The standard for answering these questions is basic strategy - the decisions yielding the greatest expected return on each blackjack hand. Violate basic strategy and you still may win. You may even do better than by playing the strict percentages. But you're fighting the laws of probability harder than necessary. And you're sacrificing a theoretical edge on your bet.

Nobody stands on totals of eight because hitting, at least, can't hurt and may help. Players seldom double on eight, either, and happily since it's the best option only under rare circumstances.

This leaves the choice between hitting and splitting. Simple enough. So simple, in fact, that three conditions cover it:
1) If your game doesn't let you double down after you split a pair, always hit four-four.
2) If you're allowed to double after splitting and the game is dealt from a single rather than multiple decks, split when the dealer shows a four, five, or six. Otherwise, hit.

3) If you may double after splitting in a game dealt from multiple decks, split when the dealer shows a five or six. Otherwise, hit.

Some solid citizens misplay four-four because they don't know blackjack is more than just luck. Others, who "go by the book," may be going by the wrong book. The ambiguity arises from the "if" clauses in the three-part rule. Basic strategy is sometimes given without clearly specifying the conditions under which it applies. So, you may be hitting four-four against a five, following a rule that assumes no doubling after splits, when this option is allowed and splitting would be preferred.

What penalties do incorrect decisions impose? Here are the figures for a six-deck game in which players can split pairs once and double after splitting.

Say you have a \$10 initial bet and receive a four-four versus a dealer's six. Your expected profit is \$1.61 splitting and \$1.24 hitting. Expectation is positive either way, but you theoretically give the casino \$0.37 by hitting rather than splitting.

Suppose, instead, you had four-four and the dealer showed a five. Expected profit would be \$1.07 splitting and \$0.34 hitting. Violating basic strategy is equivalent to handing the dealer \$0.73 for every \$10 initial bet.

Conversely, assume you bet \$10 and receive a pair of fours against a dealer's four. If you split the pair, your expected gain is \$0.09, compared with \$0.48 by hitting. Your theoretical penalty is \$0.39.

These are the most common and also the least potentially expensive errors. Improperly playing other hands for the assumed rules all involve splitting when basic strategy dictates hitting. Doing so trims your expectation for a \$10 initial bet as follows on the indicated dealer upcards: \$1.40 on two, \$0.92 on three, \$2.20 on seven, \$2.29 on eight, \$2.57 on nine, \$3.19 on 10, \$3.13 on ace.

Are these differences worth bothering to learn a special rule for a hand that doesn't occur very often? Is it worth splitting fours against a five or six to gain a theoretical \$0.73 or \$0.37, putting an additional \$10 at risk in the process? Should you forget about that Ferrari Testarosa and buy a GEO Metro because it gets better gas mileage and has lower total carbon emissions?

I can present the facts. Only you can decide how to act on them. Still, as Sumner A Ingmark, the percentage players' poet, opined:

Though gambling experts propound verity,
A player, acting with temerity,
May flout fate, balancing prosperity,
Against debt passed down to posterity.

Recent Articles
Best of Alan Krigman
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.