The art of the bookmaker is to achieve profit with a successful guess – no matter how the game has started. A bookie earns primarily by the money that the stakes offer, which do not express the actual probability outcome of the game.
Example: In the article “How to Calculate Odds” we started out on the following situation. Bayern Munich plays at home against Wolfsburg and one bookmaker offers the following odds:
Home win: 1.60 = 62.5% probability; Draw: 3.00 = 33.3% probability; Away Win: 5.00 = 20.0% probability.
If you add up all the probabilities, then the result is a value of 115.8%, although no sporting event in the world can happen with a certainty of more than 100%. If we now calculate 1: 1, 158, then there is a rounded value of 0.864. Again, if we subtract one we get the expected results from 1 to 0.864 = 0.137. Expressed as a percentage, this makes 13.7% of this value, representing the profit margin of the bookmaker.
Now if 62.5% of the total bets is placed on a home win, and 33.3% , respectively – 20% – on the draw or the away win, then the bookmaker wins as in our example, 13.7% of the total bet, no matter how the game ends! In short, the bookmaker, in this case with an event whose probability is 100%, has sold odds for 115.8%, and thus has generated a gain of 13.7%.
The formula to calculate the bookmaker margin (in our example) is: Margin = 1 – [1: (1/1, 60 + 1/3, 00 + 1/5, 00)] = 13.7%
In reality, it will only very rarely happen so that the stakes are distributed just as bookmakers wish them to be; betting odds, therefore, are being continuously adapted to the demand and supply. Usually the bulk of the players is likely to bet on their favorites, which means that the offered rate falls onto the favorites, and finally, the bookmaker balances his “book” by the odds for a draw, and an underdog victory raises it so as to get more people to get these successful results as set.
Moreover, in practice we can say that the bookmakers rarely will distribute the profit margin evenly among all outputs.