Archive for True Odds

Betting on the Supreme Court

Posted in mathematics with tags , , , , , , , on December 6, 2016 by telescoper

This week the UK Supreme Court is hearing an appeal by HM Government against the judgment recently delivered by the High Court which was that the UK Government must seek the approval of Parliament before it can invoke Article 50 of the Lisbon Treaty and thus begin the process of leaving the European Union. You can watch the proceedings live here. I had a brief look myself this morning but as I’m not a legal expert I found it rather hard to follow as it’s rather technical stuff. That wasn’t helped by the rather dull delivery of James Eade QC who was presenting the government’s case. Nevertheless, it is a very good thing that we can see how the law work in practice. I was surprised at the lack of gowns and wigs!

Although Eade seemed (to me) be on a very sticky wicket for some of the time, it’s impossible for me to come to any informed inference about who’s likely to win. Out of interest, to see what other people think, I therefore had a quick look at the betting markets. Traditional bookmakers (such as William Hill) are offering 1-3 (i.e. 3-1 ON) for the original decision being upheld so they’re clearly expecting the appeal to fail.

These days, however, I’ve started to get interested in other kinds of betting markets, especially the BetFair Exchange. This allows customers to act as bookmakers as well as punters by offering the option to “lay” and/or  “back” various possible bets. “Laying” betting means effectively acting as a bookie, proposing odds on a particular outcome. i.e. selling a bet.  “Backing” a bet means buying a bet. The exchange then advertises this to prospective bettors who sign up of they are prepared to stake money on that particular outcome at those particular odds. It’s very similar in concept to other trading services, e.g. share dealing. Matches aren’t always made of course, so not every bet that’s offered gets accepted. If that happens you can try again with more generous odds.

The advantage of this type of betting is that it represents an “efficient market”. Such a market occurs when all the money going into the market equals all the money being paid out in the market – there is no leakage or profits being taken. Efficient betting markets rarely exist outside of betting exchanges – bookmakers need to reap a profit in order to run a business. For example, though William Hill is offering 1-3 on the Supreme Court ruling being upheld, the odds they offer against this outcome are 12-5. These are not “true odds” in the sense that they can’t represent a consistent pair of probabilities of the two outcomes (as they don’t add up to one). In the case of an exchange market a bet laid at 1-3 is automatically backed at 3-1. These can then be regarded as “true odds”.

This is what the BetFair Exchange on the Supreme Court hearing looks like at the moment (you might want to click on the image to make it clearer):

 

supreme-court

The odds are given in a slightly funny way, giving the gross return for a unit stake (including the stake). In more normal language “4.3” would be 100-30, i.e. a £1 bet gets you £3.33 plus your £1 back. A bet on “overrule” at “4” (3-1) corresponds to a bet against “uphold” at 1.33 (1-3), reflecting what I was saying about “true odds”.

The first thing that struck me is the figure at the top right: £38,427. This is the value of all bets matched in this market. By BetFair standards this is very low. A typical Premiership football match will involve bets at least ten times as big as this. As in the court case itself there just isn’t very much action!

Apart from that you can see that the odds here are broadly similar with William Hill etc with implied odds around 3-1 to 4-1 against overruling.

Before you ask, I’m not going to bet on this myself. My betting strategy usually involves betting on the outcome I don’t want to happen. Although I think Parliament should be involved in Article 50 I am just happy that this matter should be left to our independent judiciary to decide.

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