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):