Frequency of blackjack hands

31 December 2017

By John Grochowski

Blackjack hands don't occur with equal frequency. You'll see 20 a lot more often than a staring hand of 5 or 6, and blackjacks more often than other two-card hands that include an ace.

The frequency of 10-value cards makes a major impact. Because we treat 10, jack, queen and king as interchangeable 10s, there are four times as many 10s as any other denomination. Hands that include 10s will occur more often than hands with any other specific denomination.

That's a point I tried to make with Ellis, an East Coast reader who wondered just how important it was to avoid splitting 10s.

"I've been trying to get my dad to stop splitting 10s for at least 20 years, ever since I was old enough to play with him," Ellis wrote. "I've been completely unsuccessful. If the dealer has anything less than his own 20, my dad is splitting.

"I've finally given up. I hate to see him wreck a good hand, but it's not like it happens on every hand."

I told Ellis the frequency of 20s was indeed a problem that magnified the effect of splitting 10s, and that some of his dad's plays ranked high on the awful scale.

Let's take the second point first. When I see 10-splitters in a casino, mostly they confine themselves to splitting when the dealer's up card is 5 or 6, or in extreme cases anything from 2 through 6.

Ellis' dad goes beyond extreme in that he also splits when the dealer shows a 7, 8 or 9. Let's look at how that affects average results.

A pair of 10s isn't guaranteed to win, but it's a very profitable hand. If you stand in a common six-deck, hit soft 17 game, you'll average 63 cents in profit for every $1 you wager if the dealer's face up card is 2. That profit rises slightly to 64 cents vs. 3, 65 vs. 4, 67 vs. 5, 68 vs. 6, 77 vs. 7 and 79 vs. 8, before dropping a bit to 76 vs. 9.

Profits are reduced if you split the 10s. If the dealer shows a 2, your average profit for splitting is 17 cents per $1 of your original wager — a steep drop from the 63 cents for standing.

With dealer up cards through 6, your average profit for splitting increases to 25 cents vs. 3, 33 vs. 4, 42 vs. 5 and 50 vs. 6. Again, the profit is reduced compared to standing instead.

On the really odd plays Ellis' dad makes, average results get worse as the dealer up card increases. If the dealer shows 7, a splitter's profit drops to 35 cents per $1 in the original wager. The profit takes a steep fall to 13 cents against a dealer 8, and if the dealer has a 9, you turn a profitable 20 when you stand into an average loss of 13 cents per dollar when you split.

The effect is magnified because 20 is the most frequent starting hand in blackjack. In a six-deck game, you'll start with 20 a little more than 9% of the time, with pairs at just over 8% and ace-9 hands making up the rest.

The only other starting hands to occur more than 8% of the time are hard 12 and 13.

When a hand occurs as often as a pair of 10-values, it's especially important to get the strategy right. There are just too many opportunities for a mistake to cost you money.

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