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Best of Alan Krigman

Gaming Guru

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Why Blackjack Players Who Know What They Know Split Their 10s

17 October 2001

Every so often, and I'm not sure but it may be correlated with the full moon, blackjack buffs who know what they know grab me to explain why they split 10s versus low dealer upcards. The "logic" generally boils down to three arguments: 1) Dealers will probably bust with low upcards, so they'll win twice as much. 2) Although initial 20s are strong, starting 10s are, too. 3) "The book" says to split 18s against two through six as well as eight and nine, and you don't sacrifice much more on an 18 than a 20 while you gain a lot by starting the new hands with 10s rather than nines.

You're favored either standing with 20 or splitting the 10s for any upcard. Still, Basic Strategy always ordains standing. The rule comes from weighing the chances and payoffs for every possible outcome, and finding what has the highest "expectation."

Here are the bottom lines for 20 and 18 against six, the weakest dealer upcard. Picture 1,000 rounds, betting $10 each time. With a pair of 10s, the theoretical profit is $7,030 standing and $5,670 splitting; standing has the greater expectation. With a pair of nines, you expect to earn $2,810 standing and $4,390 splitting; splitting has the greater expectation. Basic Strategy is therefore to stand on 20 and split 18.

Now look at the three points advanced for splitting 10s.

First: the dealer will probably bust with a low upcard. No! The dealer is more apt to break with a six-up than anything else. But the chance this will happen is only about 42 percent - less than 50-50. As the upcard decreases to two, the chance of busting gets progressively lower, so high player totals become increasingly important to beat dealer finishing totals.

Second: a 10 is almost as strong a starting point as a 20. No! A player's 20 can only lose to a dealer's 21; it will push a dealer's 20 and beat anything else. What about starting with a 10 after a split? Players get second cards automatically. Avoiding the gory details of the math, figure that of the 13 possible second cards, five (two through six) yield totals under 17 which can't push and only win if the dealer busts, four (the 10s) put the total back at 20 where it began, one (the ace) yields 21 and is an improvement, and the other three (seven through nine) leave the player weakened at 17 through 19. Prospects are not what you'd call propitious when four alternatives are neutral, one is better, and eight are worse - with five of the latter yielding underdogs against even the weakest dealer upcard.

Third: an 18 is almost as good as a 20 while a 10 is better than a nine. No and no! There's a push-pull effect here, two points, which can be viewed separately.

A 20 is actually much better than an 18. A player's 20 only loses to one dealer total - 21; it pushes one - 20, and beats 17, 18, 19, or a bust. A player's 18 loses to three dealer totals - 19, 20, or 21; it pushes one - 18, and only beats a 17 or a bust. Dealer totals of 19 and 20, that defeat players' 18s but lose or push to 20s, make a big difference.

Starting after a split with a nine rather than a 10 is another matter. A two-card nine, in fact, is weaker than a two-card 10. But players don't have two-card nines or 10s after splitting because the initial nines and 10s get automatic hits.

Again, consider the six-up, when the dealer is most vulnerable. Split 10s offer no subsequent decisions (other than resplit) since the two-card totals will be between 12 and 21. Split nines result in two-card totals between 11 and 20. Not as good at the high end. But an 11 is a strong opportunity to double, or hit again. And this situation with nines compensates, in part, for downward shift in two-card totals relative to 10s.

Can you win money splitting 10s? Certainly. And not by luck alone because the expectation is positive when you do so against any upcard. But expectation and potential profitability are greater when you stand. The poet, Sumner A Ingmark, put it like this:

Right and wrong, not absolute but matters of degree,
Choices made, with certainty if we could just foresee.

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.