Arbitrage in Gambling

I don’t generally gamble much. My brain just doesn’t seem to be wired right for gambling – I get no real thrill from winning and feel no real pain when losing. I’m aware it’s not even zero-sum for the gamblers – the book-maker takes a large cut – and so unless I have some form of edge, I know that in any large-enough set of bets I will average losing money, so I don’t bet.

However, a few years back I encountered the concept of arbitrage, as applied against gambling. By arbitrage I can make money with (in theory) minimal risk, although not huge amounts of money. For some reason though, the gaming of the gaming systems really tickles me – the money is almost just a way to keep track. Still, in certain situations I can and have made money with a much better rate of return than would occur if I just put my money in the stock funds or similar, so it’s not too bad…

I thought the concept may be of interest to some of my readers, and so will describe it below.

The Principle

The Concise OED defines arbitrage as: “the simultaneous buying and selling of assets in different markets or in derivative forms, taking advantage of the differing prices.”

In longer term, the idea is that you both buy and sell something, or in gambling bet for and against something, in different places such that no matter what the result, you win. For example, say you’re going on holiday to the US, and a dollar costs £0.80 at one currency exchange (A), but £0.90 at another (B), you’ll obviously buy your dollars from A. However, most places tend to quote two different prices – one for you to buy dollars, and the other for you to sell them dollars. The larger the difference between the prices, the more profit the currency exchange will make on every transaction – this ‘spread’ is one of the ways currency exchanges make their money, and in general if somewhere does a trade with ‘0% commision’ then their larger spead will more than make up the difference. But that’s a whinge for another day…

Let’s say in the example above, A sells dollars to you for £0.80, and buys them back for £0.75. B however sells at £0.90 and buys back at £0.85. It wouldn’t make much sense buying a load of dollars from A, and then selling them back again, as you’ll lose £0.05 for every dollar you trade. But what about buying from A, and selling to B? You can buy a dollar for £0.80, but then sell it back for £0.85 – that’s £0.05 profit for every dollar you trade! Free money!!

There are some risks, and some problems though. Firstly, say you’ve only got £800 to spend. That means you can only buy $1000 at A, to take to B, to then sell. Then you can go back to A and buy another $1000, and either pocket the £50 profit, or use that to buy even more dollars. Unfortunately though the spread in most activities is normally more like 0.5%, so you’d only make £5 for every $1000 dollars you trade, and it would tie up your £800 to do so.

Let’s say you’ve done this a couple of times, and you’re now walking to B with your $1000, ready to sell them. Unfortunately, when you get to B, you get a big shock! B now has lots of dollars, more than they need. So they have reduced their buy/sell prices to the same as A. So you now have $1000 dollars which, if you sell them, you’ll lose £50 instead of make £50. Now in this example it’s fine – you need the money to go on holiday with anyway. But what happens if this is stock, or a bet, which you really don’t want? Well, that’s one of the several risks in arb’ing.

Arbitrage in gambling

The previous example used the currency market (albeit in a high-street context) as an example. Unfortunately, the spread between buy and sell prices for currency on the high street is generally far too large for there to be any prospect of arb’ing there, and the international currency markets, and stock markets, are playing by the big boys, with millions of pounds of computers – there’s no real chance of playing there either.

However, there still exists somewhere you can perform arbitrage. And it’s not even illegal (unless you’re in the US) or immoral (unless your religion bans it). And that place is, gambling.

Traditional Book-makers

The traditional bookies allows you to bet on an event happening, for example to bet on a horse winning. Say there’s a 2 horse race, each given odds of 2.0 (or 1/1 in fractional odds – see http://oddsconverter.co.uk/ for an easy way to convert between). If you put £1 on horse 1, you’ll get £2 back if it wins – that is you’ll win £1, and get your original £1 back. If horse 1 loses, you lose it all. And ditto for betting on horse 2, and horse 2 winning – £2 back.

In reality though, the bookies always make money. How do they do that? By fixing the odds. For example, in the 2-horse race above, they may choose to set the odds at 1.8 (4/5), so if you bet £1 and win you get £1.80 back. If 100 people bet on horse 1, and 100 on horse 2, then all the people who bet on horse 1 get £1.80 – the bookie pays out £180, but £100 of that is just the money that the people bet on horse 1, i.e. their stake. So horse 1 cost the bookie £80. However, all the people who bet on horse 2 get nothing, and so the bookie keeps their £100. So his profit on the race was £20 – and that would happen no matter which horse won. What if lots of people had bet on horse 1, and very few on horse 2, you may ask. Well, in that case the bookie would have changed the odds – shortening the odds on horse 1 (so, for example they only get 20p of winnings instead of 80p), and lengthening them on horse 2 (so they may get £1.20 instead of 80p). This way, again, no matter what, the bookie wins.

Now in this traditional world, you could arbitrage between different book-makers, especially when there are only a small number of contenders. Boxing, for example, only has 2 contenders, and if one bookie is offering good odds on boxer A, and another on boxer B, you could spread your bets between them and guarantee a profit. Each bookie sets their own odds, based on how much is being bet with them for each contender, so you could also take advantage of national or regional boundaries. For example, more people will bet for their local team, so in Barcelona vs Man Utd, it may make sense to bet on Man Utd with a bookie in Barcelona, and Barcelona with a bookie in Manchester. Maybe.

Unfortunately, the bookies do monitor each other, and furthermore many are large international chains, so large variations don’t occur. Also, the spread in odds is so large that, similar to the currency exchange problem, arbitrage opportunities are unlikely to occur.

And this brings me to something I encountered properly for the first time only a few years ago – the betting exchange.

Betting Exchanges

The betting exchanges exist to match up people who want to bet both for, and against, something. The exchange takes a small (often 2.5-5%) cut of any profits a gambler makes, rather than setting the odds themselves. What they instead do is provide a forum by which people can make, and accept, bets.

Say there’s a horse race, with several horses. You’re pretty confident that horse X won’t win, but don’t know which of the others will. Due to the large margins traditional bookies use, there would be no real way to make the bet that you want – the closest equivalent would be to bet on everyone except X, but that wouldn’t be profitable even if X did lose.

With a betting exchange what happens is that you offer to accept someone betting on X with odds A, up to value B. This is called a ‘lay’. If someone else thinks X will win, and they find your odds acceptable, then they’ll place a bet with you for up-to B. This is a ‘back’. You pay into escrow the money that that you would have to pay the backer if X wins, and the backer pays into escrow the money they would have to pay you if it loses. Thus in this case, you are sort-of playing the role of the traditional bookie.

As there is no traditional book-maker at play here, there tends to be very small spreads between back and lay positions. Furthermore, the odds being offered can vary very quickly – individual gamblers will often react more quickly than the traditional bookies.

This opens up several possibilities:-

  1. Bet with a traditional bookie, and ‘lay’ with the betting exchange
  2. Take advantage of positive-sum (for you) conditions in odds, where you can bet on (or against) every option but the odds are such that you win money no matter what
  3. Take advantage of variations in odds over time (technically not arbitrage as their not simultaneous, but good enough)
  4. Take advantage of variations across different betting exchanges

The primary betting exchange I use is Betfair. Over time their terms and conditions have become slightly less advantageous, but they’re still the best I’ve encountered. Even cooler they have open APIs which allow you to monitor the odds etc for different bets, and even make bets if you feel that insane.

Most bookies do not like arbitrage, and will cancel your account or limit the amount you can spend if you do it. Betting exchanges in general, and Betfair specifically, take quite the opposite stance. In fact, they do cute things such as if you make a profitable arbitrage on a given condition (i.e. race + winner) such that part of the money held in escrow will be paid out to you irrespective of the winner, then betfair will return that money to you immediately. This allows you to increase your leverage.

Examples

The examples I used below are broadly factual. The odds have been made up, but the events themselves occurred, and I did make a killing off it.

Example 1: Before/after leaders debates for 2010 UK general election (Betfair)
In the lead-up to the 2010 UK general election, I felt the Lib Dems were going to do reasonably well, so I placed a couple of bets. At the time they were on odds like 15 and 16 (i.e. 14/1, 15/1). Then the first leaders debate happened – at which Nick Clegg did very very well.

Suddenly, the Lib Dems were looking like real contenders. Initial feedback was positive, but no-one went straight to their computers. On a hunch, I put a bit more money down on Lib Dem positions in marginal seats where they may have stood a chance, and on the overall result. The next day, the first of the new polls came out, giving the Lib Dems a huge bump. Within a few hours, the odds had massively shortened, from the 15 or so range at which I’d bought in, to phenomenally low levels such as 3 or 4 (2/1, 3/1). It appears that betting exchanges are as liable for over-compensation as stock markets.

So I was facing a bit of a quandry. Option 1, stick to my guns, and make lots of money if the Lib Dems actually did well. However, knowing UK political history, and the vagaries of the First-Past-The-Post system, I was aware that the Lib Dems would need an absolutely immense swing in order to do as well as some people were suggesting. So I used Option 2, arbitrage.

Any position I’d taken where there was a greater than 5% swing, and that had no other fun politics around it (e.g. Bercow’s seat), I cashed in. In many cases the swing was much, much larger. For example, I had backed £10 with odds of 14 (i.e. bet on the Lib Dems winning a seat, at 13/1 odds). I then layed the same seat at odds of ~4, putting £40 down to say that they wouldn’t win. This worked out at around £28 profit. And what’s even better, as I’d done both bets with Betfair, I immediately got all the money I’d bet/lay, plus the profit, back – essentially the bet was transferred so that the person who’d backed my lay was now matched with the person who’d layed my back. I had become a sort of middle-man, just extracting my profit in the interim!

Example 2: After leaders debates for 2010 UK general election (Multiple book-makers
Very quickly I had exhausted my original positions with the Lib Dems, and started looking out for other possibilities. Positions kept popping up over the course of the elections, but gone were the 20-50% profit margins – things settled down to around the 5% mark (I didn’t bother with anything less than that).

Another option opened up, however, that of using the traditional bookies.

Following the successes of Nick Clegg at the leader’s debates, combined with the general levels of dissatisfaction towards both the Tory and Labour parties, the Lib Dems continued to look very popular. The betting exchanges were very much in favour of the Lib Dems, and so the odds were generally quite short for them, for both back and lay positions. What’s more, these odds stabilised within very short time frames of key polls being published, or debates happening.

The traditional book-makers however were a lot slower to change their odds. This led to the situation where the odds at the traditional bookies (essentially a ‘back’ position, as they don’t offer ‘lay’ positions) were much longer than the ‘lay’ positions on the betting exchange. This is a situation which guarantees profit, and the margins were often in the 5-10% range, with some 15%.

The one downside of using the traditional bookie is that you won’t get any winnings until the actual event occurs. Thus you cannot repeatedly leverage the same money in the way that you can in Example 1. By the end of the election period I had some £2000 tied up in arbitrage positions in this way.

All told though, from that £2000 I made a profit of over £200. Not too bad for 30 days of ‘investment’…

Algorithms

So, how to do arbitrage. Well, it’s not just a case of sticking your finger in the air and hoping. The whole process is very methodical and mathematical. What’s more, you need to be very sure of your maths – if you get things wrong you can lose a lot of money very quickly.

The other thing you need to do is get organised. When you have several positions on a given candidate/horse/whatever, made up of several bids and lays, of varying amounts, made over a period of time, life can get very complicated. Personally I’ve a spreadsheet to calculate things, and am in the process of writing some software (the election finished before I completed it, and I lost interest after).

That said, there are some rules of thumb. Firstly you need to Back high, and Lay low. If you do it the other way round, you’re in trouble. Secondly, you’ll generally need to put more money down for the Lay, than for the Back (unless the Lay has gone very short odds indeed).

There are some really useful websites to help you with your calculations. The one at http://www.chromaweb.com/bets/calculator/index.php is excellent, and I have used it extensively. It doesn’t just allow you to calculate the amount you need to Back/Lay to cover a given Lay/Back position, but also allows for an acceptance of liability. For example, rather than take a 50/50 share of the profits irrespective of the result, if you think that the back position is much more likely then you could take a 100/0 share – i.e. only Lay enough to ensure you never lose money, but make lots more money in the event of the Back coming true.

For the algorithms themselves, I leave that as an exercise for the reader. If I find my spreadsheets, I’ll make them available here, but I think they’re lost in the ether. Make sure you test, test, test though when you do come up with your own algorithms. I messed up on my first try (can’t remember why), and ended up barely scraping even on about £1000 of trades!

Risks

There are several risks that arise when arb’ing, and especially when doing arbitrage with gambling/book-makers. I’ve highlighted the big ones below, let me know if there are others. The big thing to remember is that due to the small margins when doing arbitrage, and hence the large amounts you will need to leverage in order to make any real money, all it needs is for a negative event to happen once to wipe out the profits from a hundred successful arbitrage trades. Even worse, you may lose all the money you have ‘invested’, not just the profits.

That last point bears repeating. In the worst case, say you’ve bet heavily against some seemingly sure event, tried to arb in the opposite case, and that arb failed, then you could be left with a position where you have a huge bet riding. If the seemingly sure event actually happened, you will lose all the money you bet. So as ever, never bet more than you can afford to lose!!!! Arbitrage may seem like a sure deal, but as ever if it looks too good to be true, it is!

So, what are these risks….?

  1. Price changes: If you back, and then lay, and the lay odds have changed in the interim, you may end up losing money
  2. Bookies don’t like arbitrage: And they may choose not to accept a bet. Furthermore, they may limit the amount they allow you to bet in any event, which could seriously affect the amount you can leverage. To reduce the risk from this, I prefer to place my bets with the most likely event first (so that if I end up with an umatched arb, at least it’s the likely event I have my money on). Also, only bet whole and sensible numbers with the bookies – £10 will raise much fewer red flags than £10.36.
  3. Race/event/whatever cancelled: If an event is cancelled, normally your money will be returned to you. This is fine as long as both back and lay positions are returned, but if you’ve taken a more complex set of positions, this could cause problems.
  4. Evidence of market manipulation: Bookies all reserve the right to cancel bets at any point, if they think there’s been any manipulation, or any technical problem that has led to incorrect odds. So, if you see a sure thing at 50/1, then don’t take an arb out on it – there’s a chance the bookie will cancel the bet. You’ll get your Back money back, but the lay bet will still stand, leaving you in an unenviable position which may lose you lots of money. Rule of thumb, don’t take arb positions on anything with a margin greater than 20%, unless you’ve a very good reason to do so.
  5. Maths cock-up: Everyone makes mistakes with their maths. If you’ve got your maths wrong, you may end up in a situation where you have a guaranteed loss, rather than a guaranteed profit.
Advertisements

3 thoughts on “Arbitrage in Gambling

  1. ok from above you bet high and lay low.

    if i then lay on liverpool £10 at 5.0

    what would i have to back liverpool for to get a profit, no matter how small. is it just 5.1 and over?

    how does that work?

    • Okay, say you’ve placed a lay bet of £10 at 5.0 (i.e. 4/1)

      In theory, as long as there’s no commision or anything else, yes, anything above 5.0 will result in a profit, _if_ you bet enough. In this case, if we go to http://www.chromaweb.com/bets/calculator/index.php and put in the “If you’ve already Layed and want to Back:” box, the values given, then at 5.1 odds for the back, you’ll need to bet £9.80. You’ll then be guaranteed a profit of £0.19. Not much, given all told you’ve tied up £59.80 of your money – that’s a whole 0.3% profit. However, if the odds for backing were 10.0, meaning you would have to place a Back bet of £5, then you would be guaranteed a £5 profit – much more like it.

      Note that for a Lay bet, what we’re talking about here is the size of bet you will accept, and _not_ your liability. This is a really important point, and one of the many places the maths can go wrong! The stake is basically the amount you will bet, or accept as a bet. The liability is how much you will pay out if you lose. For a Back, they’re one and the same. For a Lay, the liability is the size of the stake _times_ the odds (minus 1 (for the original stake) if you’re using decimal odds).

      A lay stake of £10 at 4/1 odds (5.0 in decimal), places a liability of £40 against you! i.e. if the event happens (Liverpool wins) you won’t be paying out £10, but £40, plus the original stake back. In the calculations on Chromaweb, and in Betfair, everything is based on the stake and not the liability, but you need to factor in your liability when working out whether an arb is affordable, and profit margins.

      I tend not to do Arbs with a lay above 15, as it ties up waaaay too much money. (For example, say I lay a £10 stake at 20.0, and then back with £6.66 at 30.0, that only gets me £3.33 profit. And it has tied up (£10 * (20-1) + £6.66) = £196.66 to get that, making my profit only 1.7%, and yet the odds appear to have changed by 50%!

      Compare this to a change from a lay at 2.5 and a back at 5. As your liability is less, you can use larger stakes. If you lay at £50 stake, that’s only £75 liability. You then back with a stake of £25 and you guarantee £25 profit – so you’ve only tied up £100 to make £25, a much nicer sum :)

      Of course, the odds are more likely to move 19/1 to 29/1 than 3/2 to 5/1, but the point stands. And it also applies for very small odds, but in reverse – lay bets at 1.01 look great – you only have £1 liability for every £100 stake, but if you then back at 1.1 (which is a large change in odds) then you’ll have to pay £91.81 for the Back stake…

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s