My longtime casino pal Blackjack Bob has a nephew, Eric, who has taken up his uncle’s hobby.
“Blackjack Eric doesn’t roll off the tongue, does it?” Bob said on a Zoom coffee morning. “But he likes the game and he’s learning. Eric was surprised when he sat down to play and they wouldn’t let him double down on soft hands. The dealer pointed him to the placard that said, ‘Double on hard 10 or 11 only.’”
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I said it was always disappointing to find rules like that. It tacks nearly two-tenths of a percent onto the house edge in an era when blackjack has been getting tougher to beat.
“Exactly how I feel,” Blackjack Bob said. “ I know you like to run numbers. Want to do it for the doubles he couldn’t make and see what he was missing?”
Sure, I said, and I pulled up the blackjack calculator at wizardofodds.com. I set for the game Eric played — six decks, dealer hit soft 17.
Basic strategy tells us to double down when we can maximize a player edge. Here are the average expected results for each banned double down opportunity. Average profits when doubling are per $1 of your original wager.
Player has hard 9: Numbers vary slightly depending on whether the 9 consists of 7-2, 6-3 or 5-4, but on any, the basic strategy play is to double if the dealer’s up card is a 3, 4, 5 or 6. To illustrate, let’s detail numbers for 6-3.
Average profits when you double are 13 cents vs. 3;19.7 vs. 4; 26.5 vs. 5; and 31.5 vs. 6. If you can’t double, the default play is to hit. Average profits are lower at 10 cents vs. 3; 13.7 vs. 4; 16.9 vs. 5; and 19.3 vs. 6.
Player has Ace-8: Double vs. 6 and the average profit is 46.2 cents. Stand, and it’s 45.2. Close call, and it involves risking an extra bet, but the average profit is higher when you double.
Player has Ace-7: Basic strategy is to double vs. .2 through 6. Working up from dealer 2, average profits when doubling are 11.6, 17.5, 24.5, 30.2 and 35.7 cents. The next best play is to stand, with average profits of 11.3, 14.2, 17.1, 19.9 and 22.3 cents.
Player has Ace-6: Double vs. 3, 4, 5 or 6, and starting from dealer 3, average profits when 5.7, 12.3, 19.7 and 25.2 cents. The next best play is to hit, with average profits of 2.9, 6.2, 9.9 and 12.6 cents.
Player has Ace-5: Double vs. 4, 5 or 6, and starting from dealer 4, average profits are 6.1, 13.0 and 20.2 cents. Average profits when hitting are 4.1, 7.5 and 11.1 cents.
Player has Ace-4: Double vs. 4, 5 or 6, and starting from 4, average profits are 6.5, 13.5 and 20.0 cents. Hit instead, and average profits are 6.1, 9.5 and 12.6 cents.
Player has Ace-3: Double vs. 5 or 6, and starting from 5 average profits are 14.0 and 20.3 cents. Hit, and average profits are 11.6 and 14.6 cents.
Player has Ace-2: Double vs. 5 or 6, and starting from 5 average profits are 14.1 and 20.4 cents. Hit, and average profits are 13.8 and 16.6 cents.
Bob was keeping track as I read off the numbers. At the end, he had a message for nephew Eric.