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HIGHER ADVANTAGE SIGNIFICANTLY INCREASES RISK

It’s time for your annual trip to Vegas. But it’ll be different this time. No more being a patsy to the casinos. No sir! This time you’ve got the upper hand. You’ve bought the book. You’re going to learn to count cards. This time you’re going to see fear in the pit boss’s eyes. You’re going to strike and be gone before they know what hit them. You’re going to be an advantage blackjack player.

Is this a good idea? We’ll put aside the fact that learning to count cards takes considerably more time than reading a book. You’re smart; you’re a quick study; you can do it. As a card counter you may find yourself unwelcome at your favorite game. But we’ll assume they remember you from your previous trips and the red carpet will be out. They’ll never suspect that you’ve been boning up and are going to turn the tables. So, just from a dollar-and-cents point of view, what are the pros and cons of counting cards versus playing solid basic strategy?

Let’s say you find a six-deck game, double after split, dealer stands on soft 17. This is about the best game you’ll find in Vegas, and even this is getting difficult, but we’ll assume you find one. Also, assume they only cut off one of the six decks (even harder to find in Vegas now days). You’ll understand the importance of this after you read that book.

You only have the weekend and plan to spend 20 hours of it at the blackjack tables. Shows, booze and sleep can wait. This trip is serious. If you can find uncrowded tables you should be able to play 100 hands per hour, or 2,000 hands for the weekend.

Your usual is to play basic strategy, flat betting $30 a hand. You’re smart enough to know better than to use any of those progressive betting systems. With this approach you would bet a total of $67,000 over the 20 hours. This is a bit more than $30 a hand because 9.6% of the hands will be doubled down, and you’ll split pairs another 2.4%.

This game has a house edge of 0.44%, making your expected basic strategy loss for the weekend $290. But that loss is for the old you, the one who didn’t know how to count cards. The new you, the advantage blackjack player, will play a 1–12 spread with a basic unit of $20. That is, you will vary your bet from $20 at low counts to a top bet of $240.

With this betting unit and range you’ll bet $70,000 over the 20 hours, almost the same as with the basic strategy. But this time the expected return is 1.02% in your favor, or an expected profit of $714.

That’s a $1,004 swing from basic strategy. More than enough to pay for that book and the trip, if not enough to justify the hours you spent studying. But we both know this isn’t about the money; it’s about beating the house.

Unfortunately this isn’t the whole story. There’s something else to consider—the standard deviational. All professional gamblers know (or soon learn) that it’s not just the size of the pot of gold at the end of the road that matters, but how big the bumps along the way. We used the term expected win or loss. This is the term statisticians use to mean the long-run (very long-run) average. “Expected” is somewhat of a misnomer. It implies that’s what you can expect to happen, even in the shorter run. In fact, most anything can happen in the short run. As the pundit said, “In the short run anything can happen, and in the long run we’re all dead.” Sobering, but worth remembering.

We can’t say exactly what you can expect in the short run, but we can place some reasonable limits on it. First, let’s see what range we can put on the basic strategy play. The standard deviation for the situation described above is $1,476. (Calculating the standard deviation for blackjack is no simple task. I’m using the results of an extensive simulation by Don Schlesinger and John Auston published in Blackjack Attack by Schlesinger, 1997/2004 eds.)

A normal distribution gives a 90% confidence interval for the basic strategy play of –$2,725 to +$2,145.

This means that 90% of the time your final win or loss will be in this range. This is quite a range, and the extremes pretty well dwarf that expected loss of $290. Your “expected” loss is $290, but 5% of the time it will exceed $2,725. It also means that 42% of the time you’ll go home a winner just playing basic strategy.

Don’t confuse that lower limit of $2,725 with the bankroll required to give a 95% chance of not going broke. The bankroll requirement is even greater. The lower limit, $2,725, is the 95% point after all of the 2,000 hands have been played. If your bankroll was just $2,725, you would have gone broke and not been able to play the full 2,000 hands.

Let’s do the same calculation for the card-counting strategy. In this case the standard deviation is $2,996; more than twice the basic strategy standard deviation. This means that 5% of the time your loss will exceed $4,200. That’s more than 50% larger than the 5% point with basic strategy. True, card counting gives you an advantage; in fact you’ll come out a winner 59% of the time, but it also significantly increases your risk. The cost of improving your chances of coming out ahead is a considerably bigger bankroll requirement.

Why is this? Why does playing with an advantage increase your potential losses? Remember with the basic strategy you bet $30 on every hand. This gives you 2,000 hands toward the long run. (This does not a “long run” make, but it’s a start.)

When you count cards you vary your bet. Of the 2,000 hands about 83%, or 1,660 hands, will be bet at $20, while around 4%, or 80 hands, will be at $240. (The rest are somewhere in between.) How you come out in the end will be heavily dependent on how you did on those 80 big-bet hands. If 2,000 hands don’t make a long run, 80 isn’t even a dash. That’s the rub. The long run takes a lot longer when you count cards. Remember that in the short run anything can happen. And, well, you know what happens in the long run.

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