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Two weeks ago, I discussed the three key components of Expert Strategy. These are knowing which games to play, knowing the right strategy and knowing what to expect. Most of the effort goes into the middle one. It is where I spend most of my time.

I don’t spend it on learning the right strategy. I spend my time determining it for each game. You’ll note I said “determining” not “creating.” One cannot create the proper strategy for a game. The expert strategy is what it is. The key is to figure out what it is and putting it into a format the average human can use.

I also didn’t use the word discover, as if one would stumble upon it out of sheer luck. The strategy is determined because there are clear methods for determining what it is for each type of scenario. It is all based on math.

Some use formulas alone for determining the strategy. Others use computer programs to determine them. I fall into this latter category. While I still rely on math for guiding me, I prefer computer programs that either run exhaustive analyses of the scenario or simulate the scenarios enough times to get a clear picture of the correct strategy.

In most cases, the strategy is obvious. It is in the relatively small number of cases that two possible choices result in a close call between right and wrong. For example, the decision of what to do with a Hard 15 vs. a Dealer 6 does not take a great deal of effort to determine. You can perform the math calculations to figure out all the possible outcomes or you can run as little as 10,000 hands and figure out Sticking is a much better strategy than any alternative.

But what about hitting a Hard 12 against a Dealer 2? How about a 13 against a Dealer 2? There is a clear answer, but the difference is far smaller than my prior example. The situation is so close the strategy depends on which type of blackjack you are playing. In regular blackjack, you hit the 12 and stick on the 13. But if you’re playing Spanish 21 or a Push 22 variant, you would hit the 13. In Spanish 21, you would even hit a 14!

In fact, in Spanish 21, if you had a 6-Card 15 (not an easy feat) vs. a Dealer 6, you would hit that situation because you are hoping for a 7-card 21 and the bonus payout that comes with it. This just shows the entire process is math based. If Spanish 21 didn’t have these bonus payouts, then you would certainly not hit the 15. But using math to evaluate each of these very discrete possibilities – hit or stick – tells us one is clearly superior to the other.

And here come those very important words – in the long run. One in 13 times, that 15 will draw a 6 (assuming you haven’t been counting and know otherwise). When this happens, you might be tempted to think it is the right decision. Hey, you’ll even take a 4 or a 5. These cards are likely to turn your losing hand into a winning one.

The problem is you are four times more likely to draw a 10 than a 6. Throw in 7 through 9, which also bust your hand, and you are more likely to bust than not bust if you take a hit. But, I think you already realize this with a hand like a 15.

But were you sure about the strategy of hitting the 12 vs. a 2? I’ve seen players groan when other players hit these cases, but it is clearly the right answer, mathematically. However a lot of people use a strategy of don’t risk busting against a dealer “bust” card. Problem is, the 2 isn’t really a bust card for the dealer.

The players who think this way didn’t determine anything. They didn’t learn the right strategy. I’m not sure exactly what they did, but you should be thankful for them. If it wasn’t for all the players who play less than expertly, the casinos wouldn’t be able to offer blackjack with a 99.5% payback. But I’ll save that topic for a future column.

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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