What If You Can't Afford to Double or Split at Blackjack?

2 October 2000

By Alan Krigman

Veteran blackjack buffs are often aghast at the thought of defying Basic Strategy. Some go as far as to leave a table where another player is committing this iniquity; it's not out of pity or moral indignation, but belief that such action changes the flow of the cards and ruins the game for everyone else. Others become insulting, deriding solid citizens for "wrongly" taking or not taking cards and therefore being to blame for the bad draws to follow, including the dealer "making" instead of breaking. And a cadre cackle confidently at their own gambling savoir-faire compared to the mindless minions who flaunt meaningful money while the secrets of blackjack remain mired in mystery to them.

Oddly, only a smattering of experienced players actually know what's behind "the book" they hold so holy. It has nothing to do with maintaining an ordained sequence of cards in the deck or shoe. And, contrary to popular opinion, it isn't even the set of decisions that wins the most hands. Rather, it's the decisions that give bettors the greatest expected profit or least expected loss on the wagers they made prior to the deal on each round.

The distinction between winning more hands or more money is subtle. For instance, Basic Strategy says to double on 10 versus a dealer's nine. The profit expected by doing so is just under $0.15 per initial $1 wagered. Expected profit for simply hitting is almost $0.12 per $1 initial bet. So, doubling meets the optimization criterion: it earns more money in the long haul. But hitting will win the initial bet more frequently than doubling will bring in the two units. Is it worth risking $20 instead of $10, shooting for the additional $0.30? Not everyone will think so. Certainly not all of the time.

Pair splitting spawns similar situations. For instance, splitting threes versus a three is expected to lose about $0.06 per initial $1 while hitting should cost nearly $0.11. Splitting saves $0.05 per $1 so it's correct Basic Strategy. But splitting involves twice the exposure, more when the chance arises to double on one or both sides. Would you risk $200, $300, or $400 instead of $100 to save $5 under what begins as an admittedly adverse condition?

I don't advocate flouting Basic Strategy when, or because, it calls for more risk and promises only small benefits. But I don't advise playing underfunded, either. Still, you may find yourself in a game with less bankroll than you really need. Maybe you started that way without realizing the depth of the hole you should have anticipated your bet sizing could dig. Or your budget has been blown away by an cold streak. If so, you may balk at a split or double, despite the upside expectation, because the extra downside loss could knock you out of contention altogether.

For such circumstances, you ought to know the hands on which the penalty is low for hitting, rather than pushing more money into the ring for splitting or doubling. The accompanying charts show when this fallback alternative imposes a theoretical cost of $0.05 or less per $1 of initial wager.

Basic Strategy splits for which expectation penalty for hitting is under $0.05 per $1 of initial wager

2-2 vs 2

3-3 vs 2, 3

4-4 vs 6

6-6 vs 2

8-8 vs 10

Basic Strategy doubles for which expectation penalty for hitting is under $0.05 per $1 of initial wager

A-2 vs 5, 6

A-3 vs 5, 6

A-4 vs 4, 5

A-5 vs 4, 5

A-6 vs 3

9 vs 3

10 vs 9

Oh, yes. Say you violate Basic Strategy, making one of these conservative plays in an attempt to save your skin. And some self-appointed expert faults you fiercely for altering the very laws of nature, bringing the wrath of the gambling gods, and spoiling what was or would soon have been a hot table. If you can't ignore the churlishness, and are too sophisticated to rebut in kind, respond resolutely but respectfully by reciting this rhyme from the repertoire of the revered poet, Sumner A Ingmark:

A shuffle's rarely so exotic,
That cards are ordered, not chaotic.