## The First Bookie

Posted in Football, mathematics, Sport with tags , , , , , , on April 24, 2019 by telescoper

I read an interesting piece in Sunday’s Observer which is mainly about the challenges facing the modern sports betting industry but which also included some interesting historical snippets about the history of gambling.

One thing that I didn’t know before reading this article was that it is generally accepted that the first ever bookmaker was a chap called Harry Ogden who started business in the late 18th century on Newmarket Heath. Organized horse-racing had been going on for over a century by then, and gambling had co-existed with it, not always legally. Before Harry Ogden, however, the types of wager were very different from what we have nowadays. For one thing bets would generally be offered on one particular horse (the Favourite), against the field. There being only two outcomes these were generally even-money bets, and the wagers were made between individuals rather than being administered by a `turf accountant’.

Then up stepped Harry Ogden, who introduced the innovation of laying odds on every horse in a race. He set the odds based on his knowledge of the form of the different horses (i.e. on their results in previous races), using this data to estimate probabilities of success for each one. This kind of `book’, listing odds for all the runners in a race, rapidly became very popular and is still with us today. The way of specifying odds as fractions (e.g. 6/1 against, 7/1 on) derives from this period.

Ogden wasn’t interested in merely facilitating other people’s wagers: he wanted to make a profit out of this process and the system he put in place to achieve this survives to this day. In particular he introduced a version of the overround, which works as follows. I’ll use a simple example from football rather than horse-racing because I was thinking about it the other day while I was looking at the bookies odds on relegation from the Premiership.

Suppose there is a football match, which can result either in a HOME win, an AWAY win or a DRAW. Suppose the bookmaker’s expert analysts – modern bookmakers employ huge teams of these – judge the odds of these three outcomes to be: 1-1 (evens) on a HOME win, 2-1 against the DRAW and 5-1 against the AWAY win. The corresponding probabilities are: 1/2 for the HOME win, 1/3 for the DRAW and 1/6 for the AWAY win. Note that these add up to 100%, as they are meant to be probabilities and these are the only three possible outcomes. These are `true odds’.

Offering these probabilities as odds to punters would not guarantee a return for the bookie, who would instead change the odds so they add up to more than 100%. In the case above the bookie’s odds might be: 4-6 for the HOME win; 6-4 for the DRAW and 4-1 against the AWAY win. The implied probabilities here are 3/5, 2/5 and 1/5 respectively, which adds up to 120%, not 100%. The excess is the overround or `bookmaker’s margin’ – in this case 20%.

This is quite the opposite to the Dutch Book case I discussed here.

Harry Ogden applied his method to horse races with many more possible outcomes, but the principle is the same: work out your best estimate of the true odds then apply your margin to calculate the odds offered to the punter.

One thing this means is that you have to be careful f you want to estimate the probability of an event from a bookie’s odds. If they offer you even money then that does not mean they you have a 50-50 chance!

## From here to Astragalo

Posted in Biographical, History with tags , , , , on September 5, 2015 by telescoper

Now that I’m back to the relatively autumnal setting of Brighton, I can’t help reflecting on last week’s meeting. On Monday evening I attended a cocktail party in a very pleasant bar in Castiglioncello overlooking the sea. Sunset views are something of a speciality from this location:

Anyway, the name of the place we were in was Astragalo. I checked and, as I suspected, this the Italian word for astragalus, which has an approximately tetrahedral shape. Astragalus is also a kind of plant, which is perhaps more likely to be associated with the name of a seaside bar, but that spoils the connection I wish to make with probability theory, a topic that came up regularly during the conference I was attending, so I’ll ignore it.

Nowadays gambling is generally looked down on as something shady and disreputable, not to be discussed in polite company, or even to be banned altogether. However, the formulation of the basic laws of probability was almost exclusively inspired by their potential application to games of chance. Once established, these laws found a much wide range of applications in scientific contexts, including my own field of astronomy. The astragalus provides a very early example.

Gambling in various forms has been around for millennia. Sumerian and Assyrian archaeological sites are littered with examples the astragalus (or talus bone). This is found just above the heel and its roughly tetrahedral shape (in sheep and deer at any rate) is such that when it is tossed in the air it can land in any one of four possible orientations; it’s fairly similar in fact to the four-sided dice used in some role-playing games. The astragalus can be used to generate “random” outcomes and is in many ways the forerunner of modern six-sided dice. The astragalus is known to have been used for gambling games as early as 3600 BC.

Unlike modern dice, which began to appear around 2000BC, the astragalus is not quite symmetrical, giving a different probability of it landing in each orientation. It is not thought that there was a mathematical understanding of how to calculate odds in games involving this object or its more symmetrical successors (right).

## Selling Shorts in the September Sun

Posted in Finance with tags , on September 19, 2008 by telescoper

I’ve been following the wild instabilities in the stock market over the last few weeks with a mixture of amusement and despair. On the one hand it’s not at all unpleasant to see some overpaid city slickers brought back down to earth, but on the other it’s alarming to see how the world economy depends so strongly on a the whims of a bunch of erratic traders.

After what seems like weeks of falls on the stock market, shares suddenly leaped up by about 8% this morning on news that the government had banned “short-selling” on a particular set of shares. As I understand it, short selling basically means you borrow shares in a company and then sell them in the hope that the price will fall. When it does, you buy back the shares at a lower price, return them to wherever you borrowed them from, and pocket the difference. Basically it’s a bet on the future behaviour of the shares. This violates one of my two rules about gambling, namely that you should only gamble with your own money and it is a bit surprising it was ever allowed anyway.

On the other hand, even this is a bit more transparent than the practice of buying and selling derivatives, where you don’t even have to possess (however temporarily) the thing you sell. This kind of activity is what hedge funds do all the time. They operate on the principle that you can make different kinds of bets at the same time in such a way as to guarantee a win. Bookies on a racetrack are smart enough to ensure that a punter can never make a combination of bets that ensures a profit, but this is not the case with shares and other financial dealings.

Anyway, apparently the reason why banking shares have plummetted recently is that there’s been a lot of short selling and the government decided to stop it, at least temporarily. I suppose it’s good that they are actually trying to do something to stop the chaos, but I think the underlying problem is that the UK and other western economies have been living beyond their means for many years and, despite best efforts to paper over the cracks, some kind of retribution is inevitable. It wouldn’t surprise me if next week the FTSE dived again as emerges that hedge funds weren’t really responsible for the problem in the first place.

Maybe the reason why the FTSE has really been falling has been overlooked. Over the last two years since the credit crunch became apparent, the weather in the UK has been very poor. Two summers of heavy rain may have had more influence on the optimism of city traders that interbank lending rates. Perhaps that’s the kind of liquidity that really gets them down (geddit?). This week the weather is nicer, so shares have risen. I’m sure you can correlate the FTSE index with the weather and a result at least as significant as with any other econometric indicator.

I’ve got a little bit of personal interest in this because, although I’m not really a player on the stock market, I do have a 10-year investment plan that matures at the end of October this year. If I’d been able to bale out this time last year I would have made a healthy profit on it, but now it looks like this years losses will wipe most of that out. Even if they don’t, it’s been a white knuckle ride so when I do get the cash I’ll probably put it somewhere much safer, allthough I don’t know what is really safe these days and I’m maxed out on grannie bonds.

In the meantime, I’m just left with the feeling that so much of our modern economy is not only artificial but also impenetrable to ordinary people. In a sense it doesn’t matter very much if a few city tossers get burned, but the fallout from the ongoing Credit Crunch will have a real impact on the lives of ordinary people through redundancies and loan defaults as unsustainable companies go to the wall. We all fool ourselves that we live in a democracy where we can influence the way the country is run, but the fact of the matter is that governments really don’t have the resources to control or even influence global capitalism to any great extent.

Surely there has to be a better way…

## Gambling for Losers

Posted in Biographical, Finance with tags , on September 16, 2008 by telescoper

In order to encourage fresh-faced school students to pick a Physics degree out of all the possible courses they could University, one of the most persuasive arguments admissions tutors have always trotted out is that it would qualify them for highly paid jobs in the financial services sector. This argument is backed up by surveys of graduate destinations, and is explained by the fact that banking and insurance companies are crying out for numerate people with the ability to analyse complex and often chaotic systems with quantitative rigour.

The most recent episode of the so-called “Credit Crunch” is the fall-out from the collapse of the Lehman Brothers bank which caused heavy falls on Wall Street yesterday and corresponding panic overnight on Asian markets. Apparently far-eastern stocks were affected by the sudden realization that many companies had liabilities arising from the Lehman crisis. It’s interesting that this was all hidden until the bank actually folded…

Anyway, with inflation rising, shares falling and the economy stuttering into recession I wonder how many recent physics graduates may be regretting their choice of career. The rewards may be high, but the risks are high too. I’m glad I remained a physicist, even if my own portfolio appears to be flying south for the winter.

Not that I’m sanctimonious about gambling, as long as (a) it’s with your own money and (b) you don’t bet more than you can afford to lose. I like to bet on various things, and I have a fool-proof system. I usually only bet on events where there are only two outcomes (e.g. football matches) and where I actually support one of the two teams. I bet on the opposition to win, on the grounds that if my team wins I lose the bet but am happy anyway. If the opposition wins then I am financially compensated for my loss.

Being a supporter of Newcastle United, this strategy has stood me in good financial stead because a bet on the opposition is more often than not a good one. Last Saturday’s embarrassing home defeat to lowly Hull City resulted in an especially handsome dividend.

On the other hand the strategy doesn’t always work. A few day’s previously I made a substantial investment on Croatia to beat England in their World Cup qualifying match (in Zagreb). The odds weren’t great and I was sure that Croatia would win. Surprisingly, England won 4-1 and I lost £100.

You can criticise my interest in gambling if you like, but I think this form of betting is more more reputable than the murky dealings taking place on today’s stock markets. And if I happen to lose a bet, it’s not going to make a big hole in anybody’s pension.