Winning over time the goal in blackjack

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Last week, I mentioned something as a bit of a side note that may have been missed by some of you.

The goal when you gamble is to win the most money, not the most hands.

This may seem obvious when you’re playing roulette but not as much so when you’re playing something like blackjack. In roulette, most of your wagers are at significant odds payouts. You get paid 35 to 1 for hitting a single number. Wager on a column and you get paid 2 to 1. Obviously, you are going to lose the wager more often than you win.

In blackjack, most of the time, all that is at risk is your single initial wager. If you don’t win the majority of the hands, it’s going to be tough to win in that case.

But the game of blackjack is structured to give the player a few advantages.

The first is the 3 to 2 payout on a blackjack. When the dealer has one and you don’t, you only lose your wager. When you have one and he doesn’t you get paid back 150 percent of your wager.

One of the other advantages is the ability to double down. The player can double his wager but draw only one card. While this limitation of drawing only one card reduces the power of doubling, it is clear that this option is to the player’s advantage.

How do we know this? Because it is an optional choice. The player does not have to ever double and he can choose not to at any point. Any choice in a game that is optional – do something or do nothing – is to the player’s advantage. A choice where the player has to do something or fold is generally in the casino’s interest.

So how do we determine when the player should make this optional wager? Frequently, such a decision is made based on whether the player is more or less likely to win from that point.

But blackjack has the one card draw limitation. By its very nature, it should be obvious that this is going to reduce the player’s chances of winning.

If you are doubling down on an 11 vs. a dealer’s 6, then the one card draw is a meaningless limitation. You are never going to take more than one card. Even if you hit a 2, you would still not hit a 13 vs. a dealer’s 6.

But if you are doubling an 11 vs. a dealer’s 9 and you draw a 2, you’re going to wish you could take another card.

So, why do we double on an 11 vs. a dealer’s 9 if that one card draw limitation is going to hurt our chances of winning? Because we get the opportunity to double our wager. And while drawing one card will reduce our chances of winning, when we do win, we will win twice as much as we would if we didn’t double down.

So would you rather win $10 55 percent of the time or win $5 60 percent of the time? In the former you win $550. In the latter only $300. I’d like to hope you’d all say the former.

I just made up those win frequencies. What are the real ones? In reality, the difference is much slimmer than the numbers I presented.

If the player chooses to not double down, he will win the hand 56.6 percent of the time, lose 33.4 percent of the time and push 10 percent of the time. On a $10 initial wager, he can expect to win on average $12.32.

However, if he chooses to double, he will win only 55.1 percent of his wagers, lose 37.5 percent of the time and push only 7.4 percent of the time. So, he’s winning a bit less, losing four percent of the time more often and even pushing a good deal less. 

Yet, his average win on an initial $10 wager will jump to $13.52, or a nearly 50 percent increase in profits.

No one needs to memorize any of these numbers. But why is it important to understand the concept? Because in order to stick to the strategy and realize it is correct, you sometimes need to know what to expect.

Maybe you’re sitting at a table and you’re doubling on these cases and the next guy isn’t. It seems like he’s winning/pushing more hands than you are, so you begin to question your strategy.

The problem is that while your observation is likely correct, your conclusion will be flawed. He’s winning more hands. You’re winning more money. Which matters more?

 

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About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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