The mathematics of gambling:

No one can predict the future, but the powers of probability can help. Armed with this knowledge, a high-school mathematics education and £50, I headed off to find out how Thorp, and others like him, have used mathematics to beat the system. Just how much money could probability make me?

The author tries her hand at everything from roulette, counting cards, playing the lottery and beating the bookies through arbitrage. A rather thorough look at the power of probability.


As an admission of guilt, I taught myself how to count cards a few months ago before a trip to Vegas. I’ve always been fascinated by the practice.

There’s a lovely bit in How We Decide about a theoretical physicist named Michael Binger. Now a poker player, Binger got his start counting cards. Thomas describes the method in her article:

The simplest way is to start at zero and add or subtract according to the dealt cards. Add 1 when low cards (two to six) appear, subtract 1 when high cards (10 or above) appear, and stay put on seven, eight and nine. Then place your bets accordingly - bet small when your running total is low, and when your total is high, bet big. This method can earn you a positive return of up to 5 per cent on your investment.

It’s deceptively simple.

The main problem with counting cards isn’t the actual act of counting. Put any person in a quiet room and start turning over cards, and they’ll be more than capable of keeping an accurate count.

Now add some music. Girls in low-cut dresses. Alcohol. A tourist from San Diego who wants nothing more than to talk to you about the great time he had at the craps table moments ago. A dealer calling out numbers every few minutes. Decisions.

Even simple things become incredibly hard in the environment of a casino.

Being the complete nerd I am, I decided to train myself using another bit of insight from Lehrer’s book: trained intuition. The idea that what we call “instinct” is little more than repetition mixed with difference. That as we watch events unfold, our mind is making constant guesses and corrections about what will happen next, getting ever better at guessing the outcome. And when something unexpected happens, or something falls outside our perception of what the pattern should be, our “gut” fires up. Warns us that “here be dragons”.

I built a quick simulator in Cocoa that dealt cards from a shuffled six-deck shoe. As each card was flipped over, slowly at first, the background of the application flashed either red, for -1, or green for +1. At random intervals, the application would stop and ask me whether I should bet low or high. If I was wrong, it flashed and beeped like a expensive car in a hail storm. If I was right, it kept going. Over time it randomized its speed, so I’d never fall into an easy rhythm.

The idea was to not just learn to count cards, but to simultaneously train my intuition. To embed a pattern into my subconcious. In theory, even when intoxicated, I would have an instinctual need to bet high when the count is high, and to play it safe when the count is low.

Some days I wonder how it is I have a girlfriend.

I’ve been to Vegas twice since I wrote the app, and both times, walked away up. But just ever so slightly. Certainly not be the hundreds of thousands I envisioned.

So, did my training work? Most nights, I think “yes”. The vast majority of the time I had what I thought to be an accurate count in my head, and bet according to it. But I wasn’t winning every hand, or even spending every hour up. My pot of chips swung with the rest of the table’s. On my first sit, the deck stayed at between +1 and -1 nearly the entire shoe, giving me no real advantage. I lost more than I’d imagined I could. But I kept seated, went back in, with the knowledge, or more realistically, the hope that I knew what I was doing. That the odds would turn in my favor and that I could recover what I’d lost.

And I came back. I doubled, halved, broke even, went up a bit. Got out when the sun was coming up and my bed finally seemed like a better place to be. Over time, it worked out.

Being the skeptic I am, I know two trips isn’t a good enough sample to proclaim “I’ve mastered counting cards.” I’m also a newly-minted small business owner, so more than a few trips a year is probably a terrible idea. And hell, after this post, I’m sure there are quite a few casinos adding me to their lists of personas non grata.

Still, the idea of it, that basic math mixed with a trained gut can turn probability in your favor, is one I’ll have a hard time getting over. It’s a siren’s call, echoing over the treacherous rocks, beckoning me over to sit down; To play.