There are several ways for a bookmaker to make money. Chief amongst these is running what they call a “balanced book”. A bookmaker’s book on a sporting event is balanced when he makes money no matter what the outcome.

Consider a soccer match. There are three outcomes a home win, a draw or an away win. Let’s assume the true probabilities are as follows:

Outcome | True Probability | True Odds |
---|---|---|

Home Win | 1/3 | 2-1 |

Away Win | 1/3 | 2-1 |

Draw | 1/3 | 2-1 |

Only one outcome is possible, so if the bookie offers those odds, he will not make any money. For example, say a bookie accepts $100 from several punters and is therefore holding $300. If the Home team wins, he will payout $200 and return the original $100 stake, leaving him with nothing for his time and effort. Bookies, obviously won’t be happy with this. The way they deal with it is to adjust the odds away from the true probabilities:

Outcome | True Probability | True Odds | Offered Odds |
---|---|---|---|

Home Win | 1/3 | 2-1 | 9-5 |

Away Win | 1/3 | 2-1 | 9-5 |

Draw | 1/3 | 2-1 | 9-5 |

So, athoughl the chance of each outcome is 33.3%, the bookie is offering odds of 9-5 equivalent to 35.71%. If you add up the ‘true probabilities’, we get 100%. However, if we add up the probabilities corresponding to the offered odds, we end up with 107.14%. This 7.14% above 100% is known as the overround or sometimes ‘juice’ or ‘vig’ and is where the bookie makes his guaranteed profit.

So if, as in the previous example, the bookie accepts $100 on each of the outcomes and is holding $100, if, say there is a home win, he must pay out $180 in winnings and return the $100 stake, for a total of $280. However, there is a clear, guaranteed $20 profit for the bookie.

Let’s now look at a slightly more real world example.

Consider a football game Barcelona is playing against Poli Ejido. Barcelona is the favourite to win and decimal odds are offered at 1.25. For a draw the odds are 6.67 and the odds offered for a Poli Ejido win are 20.0. The punters have staked a total of €500,000, with most money being staked on Barcelona to win, as follows:

Outcome | Odds | Amount Staked | Potential Payout | Bookie’s Profit or Loss |
---|---|---|---|---|

Barcelona wins | 1.25 | 425,000 | 531,250 | -31,250 |

Draw | 6.67 | 62,500 | 416,817 | 83,333 |

Poli Ejido wins | 20 | 12,500 | 250,000 | 250,00 |

Barcelona is the clear favourite and the odds have been set accordingly. However, from the bookie’s point of view the odds are not correct. The reason for this, is that if Barcelona wins (and there is a high probability that this will be the outcome) then the bookmaker will suffer a loss of €31,250. This is an example of an improperly balanced book. But what if the bookie juggles the odds ever so slightly:

Outcome | Odds | Amount Staked | Potential Payout | Bookie’s Profit or Loss |
---|---|---|---|---|

Barcelona wins | 1.15 | 425,000 | 488,750 | 11,250 |

Draw | 5.0 | 62,500 | 312,500 | 187,500 |

Poli Ejido wins | 17 | 12,500 | 212,500 | 287,500 |

Here, we see that regardless of the outcome the bookmaker has a guaranteed profit of at least €11.250.

Although this article has been about how bookies make money, the above example,where the odds for a Barcelona win are mispriced, shows where a discerning punter can potentially make money.