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Card Counting: Section III - Simple Math

If Ben and Professor Rosen’s (Kevin Spacey) classroom banter threw you off, that’s probably because your high school teachers weren’t doing their jobs when it came to teaching you probability. Actually, their whole spiel is really just “simple math,” and you can pick up these card-counting principles, as well as counting itself, just as easily as the next guy. First, what you have to understand is that the law of probability is only determining what your odds are based on a limited number of possibilities. Basically, you take the total number of desired outcomes over the total number of potential outcomes.

The tricky part to all this, though, is that you have to be sure of what the proposition actually is. For example, in the case of Ben and Professor Rosen’s chalkboard game, it might seem that Ben is only picking a winner out of three random possibilities. Fair enough, you say, that means he has a 1:3 chance of choosing right.

The problem with thinking this way is that whether or not Ben chooses the winning board the first time is neither here nor there. Either way, Professor Rosen is actually the one doing the choosing, with the stipulation that he can’t slide down the chalkboard Ben picked. Since there is only one prize in this problem and it is only behind one of the doors, there is a 2:3 chance that Rosen will select a losing chalkboard. And because Rosen is only selecting one chalkboard, there is a 2:3 chance that Ben will select a non-losing one. As you can see, then, the chances are really in Ben’s favor the first round; he has a 2:3 chance of not selecting a losing board, and he has a 2:3 chance that Rosen will.

Assuming, then, that Rosen does reveal a non-winner, in the second round Ben’s chances now become dependent on the probability that he would have chosen the winner in the first round. If the game were “pick a board, and we’ll immediately reveal the other unpicked boards,” Ben would have a 1:3 chance of choosing correctly and, like Professor Rosen, a 2:3 chance of choosing incorrectly. Meanwhile, the probability that either of the two boards, which Ben doesn’t pick, conceal the prize is 2:3. To put it to you another way: since one of the other two boards is now eliminated, his original selection has only a 1:3 chance to the remaining unselected board’s 2:3. From here, then, the answer is simple. When Rosen asks him if he’d like to switch, he does—and wins an all-expenses paid trip to Vegas.

This little game is actually called “The Monty Hall Problem”—named for the famous “Let’s Make a Deal” host who asked contestants to pick between three doors—and it’s the kind of situation card counters deal with all the time. Like the possibility of getting certain cards out of an entire deck, the individual choices players made between doors in Monty Hall’s door game were not always “mutually exclusive.” That is, choosing one door in the first round did not mean that all the other options were permanently ruled out.

A good way to think of this is to compare dice and cards. Say, for instance, you roll a die and are shooting for a 6 and a 2. You can’t actually roll both numbers on the six-sided die without re-rolling it and, therefore, resetting the odds. Now say you try the same experiment with a deck of cards. Unless you reshuffle the deck before every draw, you can easily pull both numbers without either of them eliminating the possibility of drawing the other.

Yet, at the same time, both possible draws from an un-shuffled deck are dependent on each other. This is known as joint probability and, because of it, math nerds set the probability of drawing two cards in succession differently than they would for drawing two of them separately. For situations where the individual propositions are NOT mutually exclusive but still dependent, the probability of one event happening, say drawing a King and an Ace in succession, is the probability of drawing a King, times the probability of drawing the Ace after the King is subtracted from the deck. So, the math works out something like this:

The probability of drawing a King, if there are four Kings in a 52-card deck is 4:52, or - simplified by dividing both numbers by four - 1:12 (i.e., for every 12 cards you draw in a well shuffled deck, one of them is bound to be a King).

The probability of drawing an Ace, if there are four Aces in a 52-card deck and one of the cards (the King) has been removed is 4:51.

The probability of drawing the King, then drawing the Ace right after it is 1:12 x 4:52 or:

Taken to an extreme, it is easy to see how this concept plays out in card counting. If, for instance, every 2,3,4,5,6,7,8 and 9 has been removed, the probability of drawing an Ace is 4:20 or 1:5, and the probability of drawing a ten-point card, like a King, after that Ace has been removed is 16:19. What’s more, the probability of doing both and landing yourself a cool, soft natural is 16:95, which when you divide 16 by 95 to determine the percentage, comes out to about a 17 percent likelihood. Now compare that to the 1:153, which is the equivalent of a 0.65 percent likelihood.

That in a nutshell is what card counting literally is: using the laws of probability to get one over on the house. But as for how counting happens, that’s another story altogether.

Essentially, counting works according to count systems. The number of decks isn’t exactly important because the number of trump cards remains proportionate to the whole shoe. Determining the number of decks though is key, and when we’re talking upwards of five or more, even those ritzy MIT kids can’t do all the math in their heads. What generations of them have done, however, is figure out short-hand methods for recognizing when a deck or shoe is and is not loaded, as well as the best ways to insert themselves into a table when the pickins are ripe.

The most basic of these systems, and the one featured in “21,” is known as “Hi-Lo” and was pioneered by the granddaddy of all counters, Ed Thorp. In this system, you assign one positive point to every 2, 3, 4, 5 and 6 you see, no points to 7-9 and one negative point to each 10, J, Q, K and A. Long story short, when the count is high, “winner-winner-chicken-dinner.” When it’s low, “loser-loser….” Eh, whatever rhymes with loser.

Needless to say, over the past 50-odd years, “single-level” counts have become obsolete, and counting gurus have devised other plans to keep one step ahead of casinos’ G-men. The following are the most commonly attempted counts (though chances are, if it’s something you’re able to find on a gambling e-zine like GP, casinos already know how to spot it):

 

Card Strategy

 

2

 

3

 

4

 

5

 

6

 

7

 

8

 

9

 

10

 

J

 

Q

 

K

 

A

 

Wizard Ace/Five

 

0

 

0

 

0

 

1

 

0

 

0

 

0

 

0

 

0

 

0

 

0

 

0

 

−1

 

KO

 

1

 

1

 

1

 

1

 

1

 

1

 

0

 

0

 

−1

 

−1

 

−1

 

−1

 

−1

 

Hi-Lo

 

1

 

1

 

1

 

1

 

1

 

0

 

0

 

0

 

−1

 

−1

 

−1

 

−1

 

−1

 

Hi-Opt I

 

0

 

1

 

1

 

1

 

1

 

0

 

0

 

0

 

−1

 

−1

 

−1

 

−1

 

0

 

Hi-Opt II

 

1

 

1

 

2

 

2

 

1

 

1

 

0

 

0

 

−2

 

−2

 

−2

 

−2

 

0

 

Zen Count

 

1

 

1

 

2

 

2

 

2

 

1

 

0

 

0

 

−2

 

−2

 

−2

 

−2

 

−1

 

Omega II

 

1

 

1

 

2

 

2

 

2

 

1

 

0

 

−1

 

−2

 

−2

 

−2

 

−2

 

0

 

 

As far as known counting systems go, the chart above about covers it. But there are a few other practices we should probably cue you in on before you put your nuts on the proverbial chopping block. First of all, if you remember, we mentioned something called “wonging” back in Section I. This is the method the “21” team was using when one of them would sit down and bet the lower limit, then flag down Ben when the count was in the players’ favor. Originally, it was intended for the days when one man could go it alone and simply watch the table until it was time to insert himself. But casinos, as we mentioned before, have since wisened up, and “21” is pretty realistic insomuch as the best way around their defenses is to use a team spotter so they can invite you in mid-shoe.

Also, you need to remember that the 2.5 percent max advantage over the house is only gotten through using both counting AND Basic Strategy (hence we covered it), and the reason you get better odds counting is because you know when to bet big. For instance, it’s not worth your while to simply sit there and win 5:6 wagers. Eventually the house will still gobble you up simply because they have unlimited funds to press you with. Instead, what you need to do is double down and split when you know the next card is in your favor. That way you’ll actually get so far ahead that the casinos will have a reason to be suspicious.

Finally, as this article’s big bold CAVEAT, do keep in mind that casinos are looking for counters and that while it’s not illegal to do so, in some states (particularly Nevada) violating the private property rights of a casino will not only land you a broken nose—or worse—but also a possible lawsuit for trespassing. The best way around this, of course, is to simply not get caught, and the secret to doing that is to lose. A-L-O-T.

Most modern casinos now sport computer programs jacked in to their eye-in-the-sky systems that can follow the count and match the regularity of your wins to an ideal count over time. This means that what you’ll really want to do is follow the count and seemingly lose most of the time, then bet big enough at the right moment to make up your losses and haul away some extra for mamma. This might not be the fairy-tale scenario you were dreaming of when you watched Ben and the gang weasel the casinos, but it’s the one that will make you rich and keep you out of the hospital.

Card Counting - Blackjack

 

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