Let's say I make you an offer you can't refuse. You'll put up money, bet on the flip of a fair coin, and if you win, I'll pay you two to one. If you lose, you just surrender your bet. What's more, we'll do it once every day, for as many days as you want. And you can pick the stakes before each flip. If you're smart, this is enough to make you rich.
Here's the catch. You have 100 bucks left in your gambling fund, and you've promised your wife that you'll never use another cent for gambling if you lose that.
In this setup, the state of zero wealth is an absorbing state. Once you hit it, you can't ever get out, because you have nothing left to bet. So if by some run of bad luck (or as we'll see, bets that are too big) you do get to zero, then you're finished, and you've wasted this opportunity to never have to work again. You've achieved what is known in math and statistics as gambler's ruin.
Ruined by Odds Bets
Though you're not likely to encounter someone generous or foolish enough to make bets like this, gambler's ruin does come into play in lots of situations. On Spring Break in Key West once, a friend and I went on one of those three-hour gambling cruises. We each brought 200 dollars or so onto the boat, got a few drinks in us, and headed out to sea for three hours.
I'd never played craps before, but my friend had played it lots, so he offered to show me how it's played. He made a few pass line bets and come bets, each time betting the max on the odds bets, explaining to me that at even-money, these are the best bets you'll find in a casino; you have to take odds if you know what you're doing.
You can see where this is going. A seven-out, a few more pass line and come bets, many more odds bets, another seven out. And that was the end of my friend's fun for three hours. His bets weren't stupid, but now he was stuck in the zero state, on a boat for two and half more hours. Gambler's ruin.
This story would be a little better as an example if my friend had been playing a positive-expectation game. Imagine that instead of being even-money, his odds bets paid out slightly higher, so he'd actually have an small edge by making them. But that small edge wouldn't change the end of the story. The point is that with too much on the table, a run of bad luck can wipe you out, even when you're making good bets, if you're not making them in the right amounts.
So how do you know how much to bet, in the rare case that you do find yourself with an edge? Maybe, for example, you know for a fact you can pick games better than your bookie. In my next post, I'll introduce the Kelly Criterion, a mathematical formula for bet sizing that has been proven—in the logical, mathematical sense—to maximize long-term wealth.
Ruined by 5-10
I'll end this post with one more example of gambler's ruin in a real-life situation. When I was way too young to being doing so, I played a lot of limit holdem. This was in the very, very early days of online poker (remember when Planet Poker was the big one?). I played there a little, but mostly at an Indian reservation where they allowed 18 year-olds to play with the bunch of coffee-drinking retirees. I had read a lot of books and I was very interested in the basic mathematics behind limit poker. Since limit holdem is much more science than art, this alone enabled me to consistently beat a 2-4 or 3-6 game for a very small profit.
Looking, of course, to increase this profit, I moved myself up to the 5-10 game. The players were identical to those in the 3-6 game (literally, the same Folgers-guzzlers), so there was no reason I'd have much trouble with it. But I did. I could never beat it. Every single time I played, I'd get cleaned out.
I told myself I was too nervous, that it was more money than I was comfortable betting and it threw off my game. But that wasn't it. I didn't play any differently. I know now what it was; it was a classic example of gambler's ruin. I had a tiny edge, and just enough money to weather the swings of a 2-4 or 3-6 game. But when the stakes nearly doubled (and my starting bankroll didn't), my bets became too big for my edge.
All it would take was being on the short end of a suck-out or two, followed by calling a few raises on the way to missed flush draw, and I'd be wiped out.
Absorbed at zero. In a word, ruined.
Tags: craps, gambler's ruin, limit holdem
As I was brainstorming topics to blog about for my first post since the introduction, I came up with a list of about 20, but none of them seemed quite right. It seemed like there was a certain foundation that had to be established before any of them could be understood in the correct context. And that foundation, I realized, was the idea of an efficient market.
This idea is counterintuitive to those who don't know much about the way markets work (and that's just what a betting exchange is, a market). To those who have spent a lot of time in the stock market or gambling, the idea is blatantly obvious.
Here it is: In a perfectly efficient market, all relevant available information is already incorporated into the price.
I'm not here to argue that the stock market or sports betting markets are perfectly efficient (a good thing if you're trying to beat them). But I want you to understand market efficiency in order to understand what will and what will not help you win more bets.
Let's say two aces are pitching in an MLB game, maybe Johan Santana is facing Roy Halladay in an interleague game. The guy who doesn't understand efficient markets (let's call him "local sports radio host") is the one who, without even looking at the number for the over/under, says "You'd have to be crazy to take the over in that one." But this moron doesn't understand that not only does the guy setting the initial line know that runs against Santana and Halladay are hard to come by, but in the rare case that his line is way off, the money coming in on the under would cause the bookie to lower the number.
Hopefully this is obvious to you, but some people just don't get it.
A lot of people, especially academics, will tell you that the stock market is perfectly efficient. This means any effort you make to pick stocks is wasted, since everything is already at the exact price it should be. If by chance something were priced too high or too low, the big companies with their seemingly infinite resources and technology would instantaneously recognize this, step in and buy or sell, and thereby drive the price toward its true value.
The good news about efficient markets is that it makes it hard to mess up too badly. Let's say you build a sports betting model that sucks (believe me, I've done this a few times). If the betting market is efficient and the line is exactly where it should be, then it doesn't matter what side your crappy system takes. We can't say what side is better, so any random pick you make is going to hit 50% of the time.
The bad news, of course, is that if the market is efficient, then you can't win long term, since you can only win by pricing games better than the bookies do.
I'm not sure if I believe that the stock market is completely efficient, and since I don't work in it I'm in no place to judge. But I do have a strong belief that betting markets are not nearly as efficient as the stock market. The reason: the better you are at handicapping, the harder it becomes to get bets down as you make a name for yourself. While a financial trader can make trades of almost any size, sportsbooks have bet limits. So even if you're not on their radar as a wiseguy yet, you still can't bet more than the limit on an event that you believe is mispriced. These sort of barriers lead to me to believe that while games should move toward their correct prices, it's certainly not an instantaneous process. Which means there's time for you to get down a solid bet while the line is still wrong.
But the guys making the initial lines and the early bets are no dummies. They're in the business for a reason. So your strategy of always betting dogs or always betting lefty starters isn't going to work. If it had ever worked, it would have been noticed, and they'd have learned to account for this when they publish their lines. If you want to win, you need something pretty advanced. That might be a mathematical model that they don't have, or it might just be that you truly are a great handicapper because you've been around the game so long.
But I'll tell you what it's not.
It's not your casual fan knowledge that your home team isn't getting enough respect, or your idea that this QB doesn't play well against that defense. The bookies already know this, and even if they didn't, then other people have already taken advantage of the wrong line. And as a result, that wrong line is no longer around.
Tags: market efficiency
Or maybe you can't; I don't know. That's not my purpose for starting this blog. I'm not here to peddle my picks; in fact, for the time being I don't even have any picks.
What I want to do with this blog is share the knowledge I've picked up over the past 10 years or so of being absolutely fascinated by gambling and the math behind it. I've read dozens of books about risk, randomness, and betting, and it's something that I can honestly call a passion of mine. I have a Master's degree in Applied Math, and I'm working on my Ph.D., so I've learned a lot of stuff in math and statistics classes that can be directly applied to gambling. My thesis research is in a specific area of mathematical finance (microsimulation of markets), and really, what's investing if not a form of gambling?
So I do believe that the information I have to share can be a huge help to anyone trying to beat the casinos. And when I say casinos, I'm not talking about most of the games you'll find there. As you certainly know, most games aren't beatable. My interest is mainly in sports betting, though I'll also post a little bit about poker, horseracing, blackjack, and some others that, under the right circumstances, may be beatable. And I'll also occasionally write a post that has no practical use at all, but that highlights an interesting puzzle or example from gambling to shed light on questions like why we gamble, from the perspective of rational behavior in economics.
I've invested a lot of my time in constructing and programming mathematical models for predicting the outcomes of baseball and football games, and in making a model for no-limit poker all-in strategy. I also have a general model which, with some tweaking, could apply to almost any sport, and it's that model that I'm most proud of. I've had a success rate with this model that's statistically unlikely to be the result of pure luck, so I'm holding onto some hope that it might one day be ready for primetime. But I am by nature a skeptic, and as a mathematician I'm aware of how tempting it can be to view one's own results in an overly-optimistic light.
So that's the gist of why I'm writing this blog. In addition to sharing my own knowledge, I'm excited to read comments from others with the same interest. And who knows, maybe I'll meet someone through this blog whose skills complement mine and with whom I can work on future attempts to beat those "unbeatable" sportsbooks.
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