# Betting Odds

When a bet, or wager, is placed between two parties on a specified event, the total amount risked by both is usually agreed before the outcome of the event. The most basic of bets might involve two friends, Daniel and Joseph, having a wager on the outcome of an England football game. Daniel might offer Joseph £10 if England wins, whilst Joseph will pay Daniel £10 if England fails to win. Provided that England has roughly a 50-50 chance of winning, then this would be a fair wager. If, however, England were playing San Marino, a realistic chance of an England win might be 95%. In this case, Joseph would have a distinct advantage over Daniel, since the chances of him losing £10 are much less than those of him winning £10. Consequently, Daniel and Joseph might agree to change the terms of the bet, with Daniel paying Joseph £10 if England wins, but Joseph paying Daniel £200 if they do not. Since the chances of San Marino drawing or beating England are very small, Joseph must risk a much larger sum in order to gain his potential reward from Daniel, if Daniel is to accept the bet. To ensure that any bet between Daniel and Joseph is fair and acceptable to both, the relative proportions of the amount risked by the two parties will be dependent upon the expected probability of England winning their game. The amount risked or wagered by each party is known as the stake.

**The ratio of Daniel’s stake to Joseph’s stake is known as the odds**. Suppose England play Brazil in a quarter final of the World Cup, and for every £1 that Joseph stakes on an England win, Daniel has agreed to pay him £2 (profit) should England win (extra time and penalties included). Daniel is happy with this figure since he has estimated Brazil is twice as likely as England to win the game. If England and Brazil could play lots of games like this, Daniel has estimated that for every game England wins, Brazil will win two. In other words Daniel believes that England will win 1 in every 3 – or 33.33% – of the games played against Brazil, whilst Brazil will win the other 2, or 66.67%. **It is the estimated probabilities of each possible result which determines the nature of the odds.**

Traditionally in the UK the odds have been quoted by directly referring to the stakes and potential payouts. In this case, England would be quoted at odds of 2/1 since for every £1 bet by Joseph, Daniel will pay him £2 should England win. Brazil, by contrast, would be quoted as 1/2. **More recently and across Europe a decimal notation has been used to quote odds**. Since the odds merely reflect the expected probability of a result, **decimal notation simply represents the inverse of those percentage values**. So a 33.33% probability of a win for England – or 0.3333 – will be represented by decimal odds of 3.00 (calculated by dividing 1 by 0.3333). Brazil, on the other hand, with a 66.67% chance of victory will have odds of 1.50 (or 1 divided by 0.6667).

**European decimal odds also tell us how much money we can expect to get back if our bet wins, including both our profit and original stake**. In this example, if England wins, our return will be a total of £3 from a £1 stake (the £2 profit plus the £1 stake), hence the decimal odds of 3.00. Similarly, for a Brazil victory, our total return would be £1.50. Unlike fractional odds, where we might see all sorts of different stake pairs quoted – for example 8/11, 6/4, 15/8, 10/3 and so on – European decimal odds notation keeps things much simpler by always assuming the stake is 1. Of course, we don’t have to bet 1 unit of currency, but the decimal odds always tell us how much we’ll get back from a 1 unit stake. **To calculate our total return from a winning bet then, we just need to multiply the odds by our stake**. And because the decimal odds are the inverse of the (estimated) probability of the result, they are much more useful than fractional odds for punters who like to analyse them quantitatively by computer.

In summary, then, “Odds” is really just a betting term for probability, in other words the chances of something happening. Sometimes you may see the term “betting price” used. “Betting odds” and “betting price” are essentially one and the same.