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Best of Alan Krigman

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Playing It Smart: Passing up Basic Strategy splits at blackjack

26 May 2009

Proficient blackjack players normally split pairs when Basic Strategy says to do so. "Normally," meaning having enough reserve to fund possible resplits and doubles-after-splits, neither sweating the outcome nor risking a bust-out if fate is frowning.

Circumstances that aren't normal may pose a dilemma. That is, whether to sacrifice edge by standing or hitting, as the next best option may be, versus taking a greater immediate monetary risk. This is an example of a situation involving an edge-volatility trade-off. Players low on dough may judiciously opt to forego the split. That is, to accept reduced expectation while avoiding a potentially ruinous single-hand disappointment.

What about circumstances that are adverse but not dire? Cash that's dwindling, but not so far that a split gone awry will spell curtains. Two factors might then inform the decision.

First, Basic Strategy splits may be "defensive" or "offensive." Defensive situations are likely losers either way, but less so when the pair is split. Offensive splits may shift a hand from disadvantage to advantage, or from a lower to a higher expected gain. Solid citizens running close to empty might logically avoid defensive splits; they're more apt to lose than win split or not; and the amount may be more critical at the moment than the average difference in the severity of the two probable losses.

Second, splits offer varying degrees of gains in expectation. If the advantage benefit of the additional money at risk is small, it may be wise to think twice before blindly following a rule predicated on long-term averages rather than short-term outcomes.

Defensive splits, the best candidates for bypassing, are 6-6 vs 2, 3, and 4; 7-7 vs 2, 3, and 7; 8-8 vs 8, 9, 10, and A; 9-9 vs 9.

The most marginal of these are 6-6 vs 2 and 8-8 vs 10, which only save an expected $0.05 per dollar of initial bet; 9-9 vs 9 offers an improvement of just $0.09 per dollar. The strongest are 8-8 vs 8 which enhances prospects by almost $0.37 on the dollar, 7-7 vs 7 where the split is worth nearly $0.25 per dollar, and 7-7 vs 3 which reduces the penalty by close to $0.19 per dollar.

The offensive splits that raise underdogs to favorites may best justify the exposure of limited resources. These are: 2-2 vs 4 and 5; 3-3 vs 4, 5, and 6; 6-6 vs 5 and 6; 7-7 vs 4, 5, and 6; 8-8 vs 2, 3, 4, 5, 6, and 7; A-A vs 9, 10, and A.

The least beneficial of these are 2-2 and 3-3 vs 4 at about $0.10 on the dollar. The most propitious are 8-8 vs 6 and 5 at $0.48 and $0.41 on the dollar, respectively.

Splits on which hitting or standing is already favorable but splitting is more so are: 2-2 vs 6; 9-9 vs 2, 3, 4, 5, 6, and 8; A-A vs 2, 3, 4, 5, 6, 7, and 8.

The weakest are 9-9 vs 2 and 3 at $0.06 and $0.09 per dollar, respectively; skipping these splits represents a comparatively small concession in edge. The best start with A-A; per dollar of initial bet, splitting improves average profit over hitting by $0.49 vs 6, $0.47 vs 5, $0.45 vs 4, $0.43 vs 3, and $0.40 vs 2.

Experienced players don't enter games so underfunded relative to their bet sizes that they could reasonably forego opportunities to split pairs from the outset. But anyone can get into a hole in which switching to a mode that optimizes chance of survival then and there would be superior to playing for long term expectation. The poet, Sumner A Ingmark, put it perceptively when he piped:

In midstream sometimes changing horses,
May save you from pernicious forces.

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.