Friday, 5 February 2010

Betfair Bots and the Opportunity Out There

I am lucky to know some of the people behind the original Betfair bot: uberbot. At one point uberbot was making more than £100,000 each month in profits - and the computers that ran the system filled a small room. (And generated quite a lot of heat, and some significant electricity bills.) One story I heard, and I don't know if this is true, is that uberbot was accounting for 20 to 30% of Betfair's server capacity at one point.

The success of uberbot has led to a raft of competitors. There are now four to five syndicates running large automated botting (betting, geddit?) networks, with various strategies (automated arbitrage, statistical arbitrage, Duckworth Lewis related algorithms, etc.) And while, as far as I know, these are all nicely profitable, the easy days when three or four people could knock together a system that made them more than £1m a year, while the founders headed off to the pub, are probably over.

Having been involved at the cross-section of the gambling and technology industries for over a decade, I am reasonably au fait with how some of these bots worked. Perhaps taking a single example of a - for a time - very profitable algorithm would be instructive. What I am about to share was once a great secret, known to relatively few people, and which may have generated significant sums. But knowledge spreads, and the more people that know about a strategy, and the more people execute it, the less profitable it will be. This strategy is so simple, and so copyable that BETDAQ themselves run it on their markets! (Personally, I don't think the exchange should be engaged in simple arbitrage, but that's another story.) Many (smart) people who decide to write a Betfair bot stumble across this idea, then spend time implementing it, only to discover they make, alas, no money. So, don't think you can just reimplement this and retire rich!

What's the big idea?

Well, let's start by looking at a simple two outcome market; literally a two horse race. Let's choose some random American Football match: the Miami Dolphins versus the New Orleans Saints. Now, Betfair displays the market like this:


BackLay
Miami Dolphins2.12.4
New Orleans Saints1.51.8

(Regular Betfair bettors will notice I've simplified it - taking out all the non-core elements.)

Focussing just on the top, Miami Dolphins line. I have the choice of betting on the Miami Dolphins to win (i.e., I can back them) at 2.1. This means, if I put £1 down, I get £2.1 back if they win - a profit of £1.1, or lose £1 if the Dolphins lose. Likewise, I can bet on the Miami Dolphins to lose (i.e., I can lay them) at 2.4. When I lay something, I am acting as bookmaker. Somebody else is backing the Miami Dolphins to win. In other words: if they bet £1 and I have laid the Miami Dolphins at 2.4, then I owe them £1.4 if they win. And if the Dolphins lose, then I make a profit of £1.

Now, there is one thing here that is very interesting. A bet on the Miami Dolphins to win is *exactly* the same as a bet on the New Orleans Saints to lose. And backing the Saints is the same as laying the Dolphins.

Got that?

So, if I want to bet on the Dolphins to win, should I take the back Dolphins odds, or should I take the lay Saints odds? Well, let's convert these numbers to raw implied probabilities, to see which one offers the better value.

Miami Dolphins - chance of winning, based on back price = 1 / 2.1 = 47.6%
New Orleans - chance of winning, based on lay price = 1/1.8 = 55.6%

Clear yet? Perhaps not. Let's invert the New Orleans number so it is comparable with the Miami Dolphins win number.

New Orleans - chance of losing, based on lay price = 1 - 55.6% = 44.4%

So, if you want to bet on the Miami Dolphins winning, you can either back them at a 47.6% probability, or at a 44.4% probability. Which is better? Well, given you are paid 100% on win (as opposed to 0% on lose), then you want to bet on the option with the lowest probability. To bet on the the Dolphins, you should lay the New Orleans Saints.

But what has this to do with arbitrage? Well, you can put a new bet in the Betfair system, that will be *better* than the best current back price. And if someone takes your bet, you can they 'lay it off', generating a guaranteed profit. So, we could offer to lay the Miami Dolphins at 2.12. (This would mean that the Betfair odds table would look like this.)


BackLay
Miami Dolphins2.122.4
New Orleans Saints1.51.8

If someone took this bet, we would then bet an equivalent amount on the New Orleans Saints to lose (laying at 1.8), and we'd capture a small but very real profit.

Of course, to do this, you need to be constantly monitoring hundreds of different markets. And if the prices offered changed (so, for example, it was no longer possible to lay the Saints at 1.8), then you'd want to pull your bets. Similarly, you'd need to make sure that as soon as someone took your offered 2.12, you lay it off as soon as possible - otherwise you'd run the risk of someone taking the lay Saints price before you got a chance to.

This system works with multiple selection markets too - although the mathematics start becoming a little more complex. The bad news, though, is that you're unlikely to make any money with it. Because lots and lots of people, with expensive and powerful computer systems, are already running these models, scraping pennies up from markets. The ubiquity of these algorithms can easily be seen by looking at the relative over-round (and under-round) on various events. If the over-round is equal to 1/under-round (or vice-versa) then you have exactly the same take laying the whole market as backing it. (There are very often differences, but the gap is usually so small, it is impossible to benefit because you are forced to bet in certain increments, making exact matches harder than they might be.) This is a characteristic of a market where the differences between back and lay prices have been well and truly arbitraged out. Look at the list below:


(Essentially, any situation where the theoretical opportunity is less than 1% is not going to be exploitable. I am slightly surprised to see that there is an opportunity to make a small amount of money in the Birmingham versus Wolves game. Of course, just because you put a riskless bet into the system, doesn't mean someone is going to take you up on it.)

That this system is - broadly - un-exploitable should not be disheartening. This blog is about giving you the tools to create your own bots, and to understand the interaction of technology and gambling. There are perhaps 1,000 hedge funds with profitable quantitative trading strategies. There is no reason why there cannot be the same opportunities in the betting markets (although the sums involved will be, inevitably rather smaller).

Anyway... till next post...

46 comments:

  1. Interesting article! ITYM "we could offer to *back* the Miami Dolphins at 2.12", though.

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  2. 'The bad news, though, is that you're unlikely to make any money with it. Because lots and lots of people, with expensive and powerful computer systems, are already running these models, scraping pennies up from markets.'

    No, the bad news is that you're unlikely to make any money with it as Betfair introduced the current version of their cross-matching engine on 24/07/08.

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