Mastering the Maths: Part 2

We've shown you how the maths allows successful punters to make profit. So how does it work for bookmakers?

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In part 1 we looked at how the maths of how a betting market works, showing that odds are merely an expression of a horse’s chances of winning:

Whilst this is strictly true, what it doesn’t take into account is that the bookmaker is of course running a business, and needs to make a profit!

In simple terms, a bookmaker does this by increasing his overall market percentage (the sum of all horse’s chances), to ensure there’s a margin on any (or all) runners for him in the long term.

Logically, if you add up all runners’ chances of winning a race, it comes to 100%.  Yet add up the chances of winning in the market shown above: you’ll see it doesn’t come to 100%, but 128%.

How can the chances of any horse winning a race be greater than 100%?

It’s can’t be, of course.  Any amount over and above is simply the bookmaker’s cut.

We’ve already looked at how in the long run, the market is correct. Keep backing $2.50 shots, and over time – once variance has smoothed out – you’ll see that you’re winning about 40% of the time. A $10 bet in each of one hundred races will cost you $1,000. Your forty collects of $25 will also total $1,000.

It’s the same for a bookmaker: if their markets are accurate over time, then in the long-run they’ll break even.  They’re just on the opposite side of the ledger: taking the one hundred $10 bets, and paying out $25 forty times.

So where a profitable punter looks for overlays, the bookmaker needs to do the opposite: lower the amount he’s paying out so that it’s less than the amount he’s taking.  That’s his margin, and where he derives his profit.

For example, in the market above where Phar Lap is marked $2.50 (or a 40% chance of winning), the bookmaker may assess his true odds as 33% (or $3.00).  He puts the price of $2.50 up, and the difference is his margin.

He can do this on any and all runners, ensuring he makes a profit over time.  Of course, he’ll change his prices as money comes in on each runner, to ensure a (hopefully) positive result no matter who wins.

Of course, decreasing the prices (increasing the percentage) means it’s harder for the punter to find the value we spoke about last week.  All the more reason to ensure your markets are accurate.  If they’re not, you better find an accurate analyst!

Stay tuned for next week when we sum up the series with a look at what a profitable punter needs.

Next >>> The dangers of variance

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1: What kind of punter are you? 

2: Mastering the Maths