Trope-ic Thunder: Said No More Counting Dollars, We’ll Be Counting Cards

trope-ic-thunder-banner2By Drew Parton

Good luck getting that song out of your head now.

Anyway, now that all of my lab work has quieted down for the summer, I finally had some time to look at my mailbox. First off, I’d like to start by thanking “The Hamfister,” for consistently asking bizarre questions through the feedback form. At least they made my week a little more confusing. But since I have the time, I’d like to hit the few of these that are applicable. So… you’re welcome, Hamfister. One of Mr. Fister’s more applicable questions concerns counting cards:

Sony Pictures

Sony Pictures

What is card-counting? Well, if you’ve ever seen the movie 21, you have a basic handle on it. In 21 a bunch of MIT math students get coached into professional card-counting by Kevin Spacey. As they make a ton of money, they make just as many enemies in casinos. It was loosely based upon the actual story of a similar team of mathematicians from MIT. Instead of a rant, I’ll just barely touch on the blatant white-washing in the film (the actual team was mostly asian with one white dude, the movie reverses that). But the question was about Card-counting and not institutionalized hollywood racism. Despite what people (and the movie) think, card-counting isn’t cheating, nor is it a guaranteed way to win. All it does is give the house slightly less of an edge in Blackjack, and help you keep track of what value cards might be in the deck. Card counting only works for Blackjack, a card game wherein player plays against “the house,” (a casino dealer) and not other players. Players are dealt two cards face-down, and then can add a randomly drawn card’s value (“hit”) or keep what they have (“stay”). The goal is to have a higher total value than the dealer, without going over 21 (Jacks, Queens and Kings are 10; aces are either 11 or 1). There are many different methods of counting cards, but the simplest goes like this:

Sony Pictures

Sony Pictures

Every card has a value (different from the face-value of the card). 2-6 are given a +1. When one comes up onto the table, you add one to your “count.” 7-9 are given a 0, and 10-Ace are given a -1. When cards get played, you begin to develop a rough idea of the possible values left. Basically, if your value is high, there must be a fair amount of high cards still in play (because the 2-6’s are used up); if the count is low, then there are less high cards in play (because they have been used up). That means if your count is very low and you’re sitting with a 12, it’s probably safe to raise since the probability of getting a 10, Jack, Queen, King, or Ace is relatively rare. Now again, it’s not an illegal thing to do- it isn’t really cheating, but it is frowned upon by casinos. That’s why professional players- like our protagonists in 21- use a spotter, who’s job is to count the cards. Once they calculate the odds based on the count, they’ll signal another player to make a big bet when the odds start to approach 50/50 (every single casino game is rigged in the house’s favor). This helps to mask their activities (and make it easier on the player). So no, outside of telepathy, memorizing the deck beforehand, or having an x-ray eyepatch like Austin Powers’ Number 2, there’s no way to know for sure.

The more interesting thing about card games happens during the shuffle. It might not sound cool, but if you actually shuffle a deck of cards- I mean bridging (seven times, to be specific), and not just spreading them out on the table like I do- you are creating a 100% unique deck that will most likely never be played again. We’re talking about mathematics here, specifically permutations and combinations. Permutations are different ways that one can arrange a set of objects. For instance: supposing that we had the letters ORESTOR, how many different “words” can we create? With permutations, the order matters- same thing with a deck of cards. Because there are 52 individual cards, we can have a whole lot of different orders of them. I mean a WHOLE LOT. To calculate the number of different orders we can have, we need to calculate 52! No, that’s not me getting excited about a number. That’s called a “factorial.” What that means is we have to multiply 52 X 51 X 50 X 49… all the way down to 1. Without calculating it, you can tell it’s going to be a huge number. About this huge:

80,658,175,170,943,878,571,660, 636,856,403,766,975,289,505, 440,883,277,824,000,000,000,000

It winds up being close to 8.06 x 10^67 for those that know scientific notations. So what does that mean for your hand? Well, if every 100 Trillion stars had 100 Trillion planets each, and each planet had a population of 100 Trillion people, and each person could shuffle 1 deck of cards every second, it would take about a hundred billion years in order to start running into doubles. You’ll notice that this is longer than the universe has even existed. So take heart, though you may not be unique, the deck of cards you hold in your hand is.

Sony Pictures

Sony Pictures

There you go, Hamfister, one down, a dozen to go. Counting cards is a way that professional blackjack players can tilt the odds a little more to even, but not some sort of konami code of card games like many movies portray it as. Most professional counters don’t amass huge amounts of money as depicted in 21. The MIT blackjack club was really an exception- and that’s why they made a story about it. Anyway, be sure to check out my review column: Mindless Action Mondays and be on the lookout for a special new Parton the Interruption Monday Looking to represent the rooster on your car/notebook/bottle/computer/face? Come check out our stickers and purchase my affection over at Redbubble. As always, like us on Facebook and follow Rooster Illusion and/or MYSELF on twitter Have a science-related question? Be like “The Hamfister” and ask it! Also send me fan/hate mail!

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