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# Why You Split 9s but not 10s in Blackjack

10 August 1998

One of the strictest strictures of basic strategy for blackjack is "never split pairs of 10s." But another edict says split nines against dealer upcards of two through six, eight, or nine. Many bettors see this as a contradiction. As one blackjack buff asked, "when the dealer has a low upcard, 18 is almost as good as 20 and starting with 10 is better than starting with nine. So why split one and not the other?"

I hate to be the bearer of sad tidings. Especially because it's a double whammy.

The first piece of the bad news is that 18 pales before 20, even with a weak dealer upcard. As an example, consider standing on either total against five. An 18 should win 53.9 percent of the time, lose 33.9 percent, and push the other 12.2 percent. This puts expected profit at \$53.90 - \$33.90 or \$20 for every \$100 bet prior to the deal. Conversely, 20 should win 77.9 percent of all hands, lose 10.8 percent, and push 11.3 percent. Here, expected profit is \$77.90 - \$10.80 or \$67.10 per \$100 initial bet.

Why the big difference when the dealer's upcard is a stiff? It's because winning on a dealer's going over 21 is only part of the story, regardless of the upcard. In this instance, the chance a five will ultimately bust is 41.6 percent - in which case 18 and 20 both win. They'll both also beat a dealer starting with five on the 12.2 percent of all hands ending at 17. But 18 pushes while 20 wins when the dealer finishes with 18, the expected result 12.2 percent of the time. Further, 18 loses while 20 wins or pushes when the dealer finishes with 19 or 20, which can be expected 23.1 percent of the time.

Here's the rest of the bad news. When two-card totals are involved, 10 is a better starting point than nine. But this isn't true for the single card resulting from a split in multideck games where players can double down after splitting.

Intuitively, the reason for this is simple. Except under rare circumstances, well outside the criteria governed by basic strategy, no draw to a 10 after a split will yield a total correct for doubling. However, after splitting nines, pulling a deuce will add up to 11; this is suitable for doubling with any dealer upcard on which the original split was proper.

I'll pin down the splits by quantifying expected earnings, with the chances of doubling included in the results. Again, pretend the dealer is showing a five.

A solid citizen splitting nines would expect to earn \$36.75 for every \$100 bet before the deal. This is greater than the \$20 expected by standing on 18, so doubling is in order.

Splitting 10s, expected net is \$51.00 per \$100 initial bet. This is below the \$67.10 expected by standing on 20, so it's not the preferred option.

Of course, when I explained this to the person who asked, I didn't have the numbers handy. Instead, I used qualitative phrases like "busts less than half the time" and "make more by standing." He answered, "that's your opinion, and maybe that's what the guy who wrote the book says. But I don't have to agree."

"You're wrong and you're right," I replied. "Wrong because basic strategy in blackjack isn't a matter of opinion. It's the set of decisions that maximizes player expectation in a shoe not biased by cards previously drawn. Right because maximum expectation isn't always the same as the greatest chance of winning a hand or even a session. Right because you can lose playing by the book and win bucking the percentages. And right because we live in a free country and you're gambling with your money, your self-esteem, and your entertainment experience." Still, as Sumner A Ingmark, who some have the opinion is a poet, once wrote:

Casino patrons having fun,
Know half a chance far outweighs none.

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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.