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For the faint of heart, here's another way to look at blackjack splits

1 October 2012

Proper splitting of pairs in blackjack subtracts 0.4 percent from what would otherwise be the house advantage in the game. Overall, this benefit is less than that afforded by following Basic Strategy for standing on low totals, doubling down, and hitting soft 17s and 18s. Taken individually, however, splits are typically worth as much as or more than these options. The small apparent gain results because opportunities for beneficial splits only occur on one out of every 39.6 hands; in contrast, as an example, doubling is the optimum move on one out of 10.4.

Most solid citizens readily double down when “the book” says to do so. Although more money must be placed at risk, the play isn’t considered especially perilous. Reasons include:

1. The additional card drawn can’t lead to a bust.
2. The alternative to is to hit, anyway, in all cases except soft-18 versus three- through six-up.
3. Inability to draw more than one card, if later desired, is an example of an action nobody wants to take until they can’t, so it seems unimportant at the moment the go/no-go decision is made.
4. Players wary about adding to their wagers can “double for less,” erroneously thinking they’re not sacrificing advantage but only reducing possible gain in proportion to possible loss.
5. Doubling starts with hands perceived to be strong when simply hit.

Splitting is a different matter. Splits such as pairs of nines against five take hands perceived to be favorable and make them better. Others, like pairs of eights against seven, move underdogs to the catbird seat. The problems are with the third type, totals that start weak and improve by getting less bad, but still aren’t good, when split. It’s these on which even experienced players hesitate because they perceive that splitting exposes them to losing twice as much.

A pair of eights against a 10 offers a classic object lesson. Neither hitting nor standing on the 16 are especially auspicious. Intuition here is confirmed by analysis indicating an expectation of losing 53.5¢ per dollar of initial bet by hitting and 53.7¢ by standing. But starting with eight against a 10 isn’t exactly promising either – a perception reinforced by the math showing the expectation for the split of losing 47.5¢ per initial dollar. But comparing the results mathematically shows that, on the average, splitting loses 6.0¢ per initial dollar less.

There’s another way to envision the value of Basic Strategy splits. Say you bet $10 and get a pair against a dealer’s upcard for which splitting is the recommended choice. At the start of the round, the house had 0.5 percent edge so you began with an expectation of losing a nickel on the average. The expectation improves or worsens depending on your two cards and what the dealer displays. Say it’s a pair of nines against an eight. Standing on the 18 yields an average profit of $0.99. Splitting the pair, your $20 total wager is projected to win an average of $2.30. The additional sawbuck slid onto the table raises your expectation by $2.30 - $0.99 or $1.31. The fresh moolah was therefore wagered with an edge over the bosses of $1.31/$10 or 13.1 percent.

Bettors have an advantage on the extra money laid out whenever they follow the dictates of Basic Strategy to split a pair. The accompanying table gives the players’ edge for the additional bet on the strongest and weakest 10 sanctioned splits. As an illustration of interpreting the data, splitting a pair of eights against a 10 gives the player 6.06 percent edge on the new wager. The weakest split by this criterion is a pair of threes versus two-up, where the edge on the extra cash is 0.89 percent – less than a penny on the dollar but positive nevertheless. The strongest split is a pair of eights against seven-up; there, the player is favored on that extra wager by 72.83 percent – a whopping 72.83¢ on the dollar.

Advantage for players on the extra money placed at risk to split Basic Strategy pairs for the 10 strongest and 10 weakest cases

strongest    edge on extra    weakest case    edge on extra
 case             bet                              bet
8-8 vs 7       72.83%          2-2 vs 7          9.75%
8-8 vs 6       56.41%          2-2 vs 3          7.62%
A-A vs 6       49.17%          9-9 vs 2          7.38%
A-A vs 5       47.32%          8-8 vs T          6.06%
8-8 vs 5       47.11%          3-3 vs 3          5.91%
A-A vs 4       45.37%          6-6 vs 2          5.66%
8-8 vs 4       43.57%          4-4 vs 6          4.33%
A-A vs 3       42.71%          2-2 vs 2          3.71%
8-8 vs 8       42.49%          4-4 vs 5          2.78%
7-7 vs 6       40.57%          3-3 vs 2          0.89%

In the weakest instance, the pair of threes versus a two, the player’s advantage on the extra dollar is roughly twice as great as the overall edge the casino has on the game as a whole. That house advantage is the source of the casino’s net earnings. Players can profit at twice that rate on the least potentially profitable splits. Are you gonna pass that up? Or, as Sumner A Ingmark noted:

Although a profit may be small,
It beats a loss, or none at all.
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.