Doubling for less: Why it's a big mistake

Picture this: I'm playing blackjack with a tall Texan wearing a 10-gallon cowboy hat who is sitting at third base. He's been steadily losing, and then unexpectedly he places four green chips in his betting spot. The cards are dealt and Mr. T. cracks a smile as he stares at his good hand, a 7-4. But his smile turns to a frown when he glances at the dealer's upcard, a 10. When the action gets to him, he picks up four green chips from his chip-stack as if he's going to double down. But instead he hesitates and intensely stares at that dealer's 10. He probably knows that the basic strategy play for an 11 against a 10 is to double down. But against a dealer's 10, well, you can tell he was getting a little queasy about putting out another $100 and possibly losing $200 if the dealer were to beat him. We patiently waited for what seemed like forever (well, maybe 30 seconds or so) until he finally made a decision. It kind of surprised everyone. Instead of doubling down for $100, or possibly just hitting his hand, he instead took a middle-of-the-road approach and shoved out one green chip ($25), nervously announcing to the dealer, "I'm going to double for less."

It turns out Mr. T. pushed on his hand, and he quietly left the table with far fewer chips than he came with. Another player then made this comment to the dealer: "I didn't know that you could double down for less." The young dealer responded, "Yes, and that's a pretty smart play when I've got a strong upcard."

Let me say this as politically correctly as I can: Doubling for less is one of the dumbest plays a blackjack player can make, and any dealer who offers this advice to players ought to be taken out to the wood shed and ... well, you know.

Before I continue with my rant, let me pause for a second to ask you this question: Which of these betting propositions would you take?

1. Winning $100 56 percent of the time, or
2. Winning $200 54 percent of the time?

While you ponder the answer to this question, let's get back to Mr. T., who decided not to double for the full amount, but instead, creatively doubled for less. If you remember, he bet $100 on his 11 against a dealer's 10 and then "doubled" for $25. Let me show you the folly of this, and what it cost him, compared to doubling down for the full amount, or just hitting his hand.

Option #1: Hit

If you hit an 11 when the dealer shows a 10, you will win 56 percent of the time, on average. This means for every 100 times you get this hand, with pushes excluded, you can expect to win 56 hands and lose 44 hands.

Mr. T. bet $100. Therefore, his expectation if he chose to always hit his 11 against a dealer's 10 is to win $1,200 (over 100 hands). This is calculated as follows:

He wins $100 56 times for a total win of +$5,600.
He loses $100 44 times for a total loss of $4,400.

His net expectation is the difference of his expected win minus his expected loss which equals +$1,200. Not bad, and it's obvious that hitting an 11 against a dealer's 10 (aha!) is obviously a profitable play. But, you can do even better when you double down.

Option #2: Doubling for the full amount

Blackjack players have the option to double down on any two first cards. (Although some casinos will restrict players from doubling on some initial hands, the vast majority of casinos allow DOA or double on anything.) When you double down, the casinos will allow you to make a secondary bet up to the amount of your initial wager (meaning you can double your initial bet, which is why this rule is known as doubling down).

In return for the casino's allowing you to double your bet in beneficial situations, you only get one draw card. So if you were to double down on 11 and draw a 3, you are stuck with a 14. Because you can't draw more than one card when you double down, the percentage of the times that you win your hand is often less than hitting.

Take the case of Mr. T.'s 11 against the 10. If you hit 11 against the 10, you win 56 percent of time, but if you double down you win only 54 percent of the time, or 2 percent less.

You're probably saying to yourself, "Wait a minute ... if I win fewer hands when I double down, how can it be a better play than hitting?" Stay with me and I'll explain.

In order to analyze the benefits of doubling down, we have to factor in the amount bet. In the case of Mr. T., he could have doubled for the full amount of $100, which equals a total of $200 wagered on the hand. Therefore, his expectation if he would have doubled for $200, is as follows:

Win $200 54 times = +$10,800
Lose $200 46 times = ­$9,200.

Mr. T. would have had an expectation of winning $1,600 (over 100 hands).

If you compare the expected win of $1,600 by doubling down for the full amount, with the $1,200 if you hit instead, you can clearly see the answer to the question I posed to you earlier in this article, namely:

You are better off winning $200 54 percent of the time than winning $100 56 percent of the time.

Option #3: Doubling for less

Now let's take a look at that doubling-for-less play made by Mr. T., which the dealer praised.

Instead of doubling for $100, Mr. T. "doubled" for $25. His expectation is:

Win $125 54 times = +$6,750
Lose $125 46 times = ­$5,750

Net expectation is $1,000.

The following table summarizes Mr. T.'s expectation for the three possible choices he had on the hand.

(Note: Doubling for less is not always inferior to hitting, as in the above case of an 11 against a dealer's 10. In hands such as an 11 against a 6, where a player would always draw only one card if he were to hit (and then stand), doubling for any amount of money more than the original wager (but not 100 percent) would be superior to hitting, but still inferior to doubling for the full amount.)

It turns out that Mr. T's brilliant double-for-less play was the absolute worst of the possible three plays he could have made. He would be $200 better off hitting his 11 against the 10 or, better yet, $600 better off if he doubled for the full amount. (I'm sure the casino bosses were thrilled when Mr. T. decided to creatively double down for only $25!!) You've got the best of it when basic strategy says to double down, so always double for the full amount and never, ever double-for-less.

I guess now you know why casinos allow their players to double for less. In fact, if I owned a casino, I'd put signs on every table that clearly state in bold type: DOUBLING FOR LESS ALLOWED. Better yet, I'd promote this great rule on my million dollar, state-of-the-art, gigantic electronic display located outside so all the tourists would know what a great deal they'd be getting when they played blackjack in my casino. (Yeah, right!)