At Blackjack, Splitting Pairs Is Rarely Splitting Hairs

24 May 2004

By Alan Krigman

Splitting pairs is a powerful tool for blackjack buffs. However, as is often true in the casino, there's a price to pay. Splits require second wagers, equal to the first. And some solid citizens hesitate to go out on the limb. Either because they're scared by the sum that will be up for grabs, or due to qualms about the advisability of certain splits.

The dilemma posed by the extra money typically results from faulty judgement at the beginning of a round. Anyone willing to bet some amount, who is then uncomfortable following through if the most advantageous tactic is to augment the wager with more, overstepped the bounds of prudent punting at the outset.

Misgivings about Basic Strategy point to people who think the laws of probability that govern the rest of the known universe are suspended in the casino. Much of this perplexment with splitting arises because the play is sometimes a defensive choice between the least of the evils. That is, certain pairs are hobbled no matter how executed, but not as badly when the halves are handled separately. The most common example is 8-8 versus a 10-up; here, the total of 16 is projected to lose almost $0.54 per dollar bet going into a round by standing, a bit less by hitting, and $0.48 by splitting. Twos against two-up is another case; hitting the total of four is expected to cost $0.11 on the dollar, while the anticipated penalty for the split is $0.08.

When a dealer is most vulnerable, with six-up, all Basic Strategy splits are offensive. They either bring home more statistical bacon than the next best alternative, or convert an underdog into a favorite. The expectations for each split against six-up and its nearest fallback option are given in the accompanying table.

Theoretical profit or loss for split pairs and for the totals handled with the next best alternative, per dollar initial bet,
against six-up; doubling is assumed allowed after splitting.

 

hand	split	alternative
A-A	$0.68	$0.19 (double)
2-2	$0.21	$0.01 (hit)
3-3	$0.18	-$0.09 (hit)
4-4	$0.16	$0.12 (hit)
6-6	$0.12	-$0.15 (hit)
7-7	$0.19	-$0.16 (stand)
8-8	$0.33	-$0.16 (stand)
9-9	$0.44	$0.28 (stand)

Data for the six-up show only one moderately close call. The 4-4 is worth just $0.04 more per dollar split than hit. Conversely, splitting 4-4 versus four-up has a $0.04 per dollar penalty over hitting. However, many players deviate from the dogma and split in this case. How bad is the error? Only as bad as you regard paying $0.04 in expectation for a shot at twice the earnings.

Splitting is always foolhardy with 5-5. The total of 10 calls for hitting against 10 or ace and doubling otherwise. Intuitively, splitting is unwise since a starting hand of 10 is sitting pretty while a five is an ugly thought. Against the six, it's a matter of the double coming in at $0.30 on the dollar while the split has a projected worth of $0.14. For a dealer's five, splitting and doubling are also both profitable but the latter more so. In every other situation, splitting turns a profit into a loss.

Splitting 10s is also ill-advised. The ensuing 10-values may seem strong out of the gate. The fly in the ointment is the absence of a rational opportunity to double after the split. Hands formed on each half of the pair will total from 12 to 21 before you act and will be suitable only for hitting, standing, or resplitting if allowed. The expectation splitting 10s against six is a profit of $0.57 per dollar. This exceeds that of any sanctioned split when the dealer has six up other than of A-A, but it falls short of the $0.70 per dollar expected by standing on 20. Penalties for splitting 10s against upcards other than six are greater yet.

Considering all possibilities, proper splits when doubling is allowed on the resulting new hands knock over 0.5 percent off the house advantage in the game. A significant discount, roughly equal to the edge a competent player faces in the game overall. A benefit of this relative magnitude recalls the regularly recited remonstrance of the revered rhymer, Sumner A Ingmark:

Opportunity knocks but rarely,
Be prepared to confront it squarely.