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Why is a bet called a flutter?

medium.com - Having a flutter: the real cost of betting explained | by My pensieve - Medium

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Having a flutter: the real cost of betting explained

Having a flutter is a decidedly English pastime. Defined by the Oxford English Dictionary as “a small bet,” it typically means placing a wager in the field of horse racing, the Sport of Kings. For those of us who grew up in the UK, no race captures the collective imagination better than the Grand National. Today it’s big business. It is estimated that £250m was wagered on the 2017 edition by thousands of punters hoping for a big win. And yet, entry into the world of betting prices, known as odds, can be a confusing affair which makes it hard to see how ‘fair’ the wagers really are — just how much are the bookmakers taking off the top? It turns out that the real cost of betting can be much larger than you might think, and also varies dramatically depending which sport, and even which race you choose. The best place to start is with these things known as odds. Most frequently expressed “to-1” as in “the odds on that horse are 15-to-1” the first digit expresses how much you win if you wager the second amount. In other words, a bet of £1 would win £15 if it won. The stake is also returned if (and only if) the bet is a winner resulting in a total payoff of £16. Sometimes the odds are expressed slightly differently, such as “United are now the 5-to-2 favourite” but this is just to avoid having odds expressed as fractions. If you divide the first number by the second you can convert the odds back to the more familiar “to-1” format. Thus, “5-to-2” becomes “2.5-to-1”. Here you need to bet £2 to win £5 for a total payoff of £7 (£5 win + £2 stake returned). The higher the first number relative to the second number, the more you win for a given wager. This is obviously welcome, but it comes at a price: it’s the bookmaker’s way of telling you that the likelihood that event will occur is lower. So far all very intuitive — everyone knows that a 100-to-1 shot is viewed as being far less likely to win than one at 9-to-1. But how to use these prices to estimate the bookmaker’s cut, the margin they are earning on your bet? The key is to convert the odds into probabilities. This step is actually quite simple: you just need to add up the two digits and divide the second number by that sum. For example the probability of a horse winning at 15-to-1 is given as follows:

15 + 1 = 16

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1 / 16 = 0.0625 or 6.25%.

If the odds were 5-to-2 then it would be:

5 + 2=7

2 / 7 = 0.286 or 28.6%.

Things might be a lot simpler if, when making a wager one were simply told that the current probability of the horse winning is 6.25%. In the table below I have done this exercise for all 40 starters of the 2017 Grand National as reported by The Daily Telegraph. The ultimate winner is highlighted (full disclosure: I backed the winner). With so many events that can happen in this particular race, it’s not surprising that the probability of even the favourite winning is less than 10%.

What next? For any event or race the number of outcomes is strictly limited — only one horse can win. Herein lies the key. Since one of these events must occur we can say that, if there is no bookmaker fee, the probabilities should add up to exactly 1.0 or 100%. If the probabilities implied by the odds add up to more than 1.0 then the bookmaker is taking something off the top. The more the probability exceeds 1.0, the higher the skim. Fortunately there’s a simple way to illustrate this. We must ask the following two-part question: is there a way to guarantee winning money on a race? And if so, how much do we need to wager?

For simplicity let’s focus on football, where only three outcomes are possible: Home win, Away win, Draw. The table below shows the prices for a recent English Premier League match between Manchester United and Chelsea (as taken from betfair.com). The odds have been converted to their “to-1” format on the right. To calculate how much to bet to guarantee a win of, say £1, whichever outcome occurs, we need to sum the figures in the “to-1” format and bet 1 divided by that number. For example, with Manchester United at 9-to-5, or 1.8-to-1 the bet needs to be 1 / (1.8 + 1.0) = £0.357. What happens if Manchester United do win? The win would be £0.357 x 1.8 = £0.643 plus the stake which is returned (£0.357) to make a total of £1.00. The table below shows the appropriate bets for each of the three outcomes and confirms that the win in each case is £1.00. So this system guarantees a win of £1.00 whatever happens. If this sounds too good to be true it’s because it is. Do not forget part two of the question above: how much does it cost to set up this set of wagers? This can be seen in the table above — it’s £1.033. We can now see the bookmaker’s edge — in order to set up a guaranteed £1.00 the punter must be £1.033 and therefore guarantee losing £0.033 or a loss of 3.2%.

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This is actually a very small skim. If it were repeated for the Grand National it would mean that on average bookmakers are expecting to make only £8.0m of profits — called gross win in the business — from the £250m staked on the race (of course the actual amount won will vary depending on which horse actually wins). If we return to the probabilities in the table of Grand National runners what do they add up to? It’s 143.4%. Yes, you read correctly. This means that to set up a set of wagers guaranteed to win £1.00 it would cost £1.434. Spending £1.434 to earn a payoff of £1.00 implies a loss of 30.3%, in other words around 10 x as large a margin as on the football match above. Perhaps it’s a little unfair to pick on the Grand National. Let’s take a random Easter Weekend race, the 16:20 from Plumpton on Sunday 16 April 2017. The total probability of 111.1% means that to guarantee a win of £1.00 one must wager £1.111, to guarantee a loss of 10.0%. A 10% fee is clearly a lot less than 30%, but is still 3x the margin earned on the football. I do not mean to imply that there is anything inherently wrong with the bookmaker taking fees off the top; they are in business to make profits after all. But it’s worth bearing in mind next time you think about having a flutter on the Sport of Kings.

medium.com - Having a flutter: the real cost of betting explained | by My pensieve - Medium

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