How do bookmakers calculate odds

We all like a flutter down at the bookies every now and then. But how do bookies decide on the odds they want to use and how do they make a profit? Seasoned gamblers will probably have a fair idea already, but I spent some time doing research online to work out how the system works and how bookies keep a roof over their heads. Don’t be surprised to learn that the real odds of an event, a race or a match, are not the odds that the bookies will offer you. They have to adapt the odds to make a profit, whilst making them appealing to you the punter. With a little help from the internet I’ve drawn up an example of how the odds work and how bookies set up their book. I’m going to use Football betting as an easy to follow example:

Say we have: Manchester United and Arsenal and their true probabilities are the following:
Man Utd: 55% chance of winning
Arsenal: 25% chance of winning
A draw between the two sides: 20% chance
When you add up these percentages you get obviously get 100%, this of course means that if the bookmaker offered you those odds they wouldn’t either win or loose. So in order for them to turn a profit the bookies will tweak the original chance percentages in a similar fashion to what I’ve outlined below:
Man Utd: 54% chance of winning
Arsenal: 32.4% chance of winning
A draw between the two sides: 21.6% chance
Now the percentages add up to 108%. This tweak will guarantee your bookie a profit of 8% or 8 pence on every pound.

Using the decimal format that is popular with betting sites such as Betfair, these percentages are now more recognisable as the following odds:
54% = 1.85
32.4% = 3.09
21.6% = 4.63
Using these decimal or ‘European’ odds, the bookmaker will pay out the player’s stake (the money they used to bet with) and then multiply this by 1.85 or by 3.09 or by 4.63 depending on the outcome of the match.

So we can try to avoid confusion, I’ll try and keep this as simple as possible:
Using these decimal odds and the newly tweaked percentages, you are able to can calculate back to 8%: the amount of profit the bookie will make:
For each ?100 staked, ?50 would be on Man Utd to win, ?30 on Arsenal to win, and ?20 on a draw.
If Man Utd win, the bookie pays out 50*1.85 = ?92.50
If Arsenal win, the bookie pays out 30*3.09 = ?92.70
If the two sides draw, the bookie pays out 20*4.63 = ?92.60
This would work in a perfect world for the bookie if all his punters bet to the odds. You and I both know that most punters bet on their favourite, rather than THE favourite.This is known as the “public opinion spread”. This means that even though Arsenal only have a 32.4% chance of winning the match, their fans would still be likely to bet on them winning.
As a more realistic look at the ‘public opinion spread’ we’ll assume it’s more like:
70% total money staked on Manchester United to win
25% total money staked on Arsenal to win
5% total money staked on a draw between the two sides
For every ?100 staked, the bookie recieves ?70 on Man Utd, ?25 on Arsenal, and ?5 on a draw.
If bookies only offered odds in accordance with the ‘true’ probabilities – and didn’t work out the real spread of bets, for every ?100 they recieved, they would be forced to pay out (incl. profit margin):
If Man Utd wins: 70*1.85 = ?129.50
If Arsenal wins: 25*3.09 = ?77.25
If the two sides draw: 5*4.63 = ?23.15
Clearly this is not an easy way to make money, as with the money he makes in one hand, he gives away with the other. So instead, the bookies try and generate a more consistent profit by working out the odds based on the spread of bets rather than the likely outcomes.
So a bookie who was expecting the following spread of bets:
70% total money staked on Man Utd to win
25% total money staked on Arsenal to win
5% total money staked on a draw between the two sides
will tweak his or her profit margin to 8%. This means the percentages will now be – 75.6% / 27% / 5.4%
And converting these figures to odds:
1.32 Man Utd to win
3.70 Arsenal to win
18.52 for a draw between the two sides
So on each ?100 staked:
If Man Utd wins bookmaker pays out 1.32*70 = ?92.40
If Arsenal wins bookmaker pays out 3.70*25 = ?92.50
If it’s a draw bookmaker pays out 18.52*5 = ?92.60
Thus the bookmaker’s profit is between ?7 and ?8 = 8%. (Rounding of figures dictates that the profit is not always precisely 8%.)
Bookmakers employ further formulas to calculate adjustments to make to odds depending on the actual money flow on each outcome of an event.

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