I just returned from a losing Vegas trip. After analyzing my play, I have determined that my losses were due to my low rate of double- down wins. I play double deck exclusively. If I play perfect basic strategy, what is the overall probability that I will win my double down? It must be better than 50%, or the casino would allow me to double after the split. Admittedly, I probably did not get into the long run as I only played about 12 hours. Secondly, a reliable matrix shows an A,9 vs 6 at over 60% probability of a double down win. Basic strategy is to stand. Considering a 200% profit vs 100% if I stand, why is doubling not the better choice?
[Editor's Note: As we usually do with blackjack questions, for this answer we turned to Arnold Snyder, author of Blackbelt in Blackjack, The Big Book of Blackjack, Blackjack Shuffle Tracker's Cookbook, and Blackjack Wisdom, as well as being the brains behind our sister site, ToplessVegasOnline.com.]
You're correct that the probability of winning on any basic strategy double down is better than 50%. That’s why it’s basic strategy to make the play. How much over 50% depends primarily on the rules. Obviously, if you can only double down on hard 10 or 11, as opposed to any two cards, your doubling opportunities are reduced. Also, doubling allowed after splits and even the number of decks in play and less common rules (like doubling allowed on three or more cards) affects the number of opportunities and your overall win percentage from doubling.
But the exact percentage over 50% isn’t all that important when you’re looking at only 12 hours of play. Assuming you play 100 hands per hour (and you’ll play far fewer at full tables), you won’t see more than a relative handful of doubling opportunities in that time frame and the variance on so few hands is extremely high.
But let’s look at the hand you specifically asked about — A,9 v 6. If you take a single hit on this hand, you'll win about 64% of the time and lose 36%. That gives this hand an overall expectation of 64 – 36 = 28% if you take a hit. That means for every time you're dealt this hand with a $100 bet, you would expect to win $28 over the long run.
When you double your bet, you don’t change the actual win rate at all, since doubling is the same thing as taking a single hit. But now, winning 64% of the time will earn you $56, since you’re getting paid on a $200 bet instead of $100. Therefore, doubling is the preferred strategy to hitting. So, if your only choices are to hit or double, doubling makes sense.
But you have a third choice — standing. Standing on A,9 v 6 will actually win about 85% of the time and lose about 15% of the time. And 85 – 15 = 70, so standing will return $70 for every $100 you bet on this hand, significantly more than the $58 you’d get from doubling. (Note: for simplicity, I’m ignoring the effect of pushes in my analyses.)
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JimBeam
Dec-03-2017
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