## FOOTBALL BETTING

# BOOKMAKERS' MATHEMATICAL ADVANTAGE

### Bookmakers Always Win

In **football betting** this simple statement is a harsh reality for all mug punters. Everyone has the feeling sooner or later that there is nothing to do and in the end they, the bookmakers, always win. In truth, for the mug punters it is just so, maybe they do not really realize bookmaker’s *mathematical advantage* because they alternate winnings with losses and always chase the winning of life that will bring them the much-desired luck, but behind this dream lies the hard truth, so at the end the bookmaker always wins. Yes, that’s fine, but how is that possible? To answer this question about __football betting__ you need to understand how a book works.

### How a Book Works

As explained in the __article on transforming odds into probabilities, each price represents the probability of a given event occurring. If we do this for the price of each selection offered by the bookmaker within a certain market we get what is called the overround. Let’s see a practical example:__

Horse | Odds |
---|---|

Miss Elsa | 1.91 |

Roca Magica | 2.5 |

Ruby Gates | 5.5 |

Crystal Carole | 26 |

Islay Mist | 51 |

Let’s proceed to the transformation of the odds into probabilities:

Horse | Probability |
---|---|

Miss Elsa | 100/1.91=52.35% |

Roca Magica | 100/2.50=40.00% |

Ruby Gates | 100/5.50=18.18% |

Crystal Carole | 100/26=3.84% |

Islay Mist | 100/51=1.96% |

### The Overround

From the calculation above, it immediately emerges the need to explain the concept of overround that has been manifested here.

The sum of all probabilities resulting from the odds is called overround. In our case the overround for this horse race is 116.33%. In a fair market should be 100% (since the probability of all events should not exceed 100%) but evidently that’s not the case.

This is where the bookmaker’s commission (or the bookmaker’s margin) comes in; in the case above it is equal to 16.33%. This is the bookmaker’s profit. As you can see in fact betting on all the horses we would get this result:

Horse | Odds | Stake | Potential win |
---|---|---|---|

Miss Elsa | 1.91 | 45.00 £ | 85.95 £ |

Roca Magica | 2.50 | 34.38 £ | 85.95 £ |

Ruby Gates | 5.50 | 15.63 £ | 85.95 £ |

Crystal Carole | 26 | 3.31 £ | 85.95 £ |

Islay Mist | 51 | 1.69 £ | 85.95 £ |

Amount wagered | 100 £ |

### Unfair Odds

From the calculation just made it becomes clear that the offered odds are certainly unfair, since the return (85.95 £) is less than the amount wagered (100 £).

It’s a bit like in coin toss: with each toss we get a 1.80 price for the exit of the tail. Always punting on that face of the coin in the long term we will definitely get a loss (in fact the fair price for the coin toss should have been 2.00).

That’s the reason why bookmakers always win.

### Where Bookmakers Make the Most Money

The mathematical advantage of unfair odds is added to the cumulative benefit of multiple (when you put in your bet slip more than one selection to multiply the profit), to boost bookmakers’ profit.

The real probability of making a profit is almost nil using high profit multiple if considered along with the concept of unfair odds. Let’s look at this example:

Horse | Odds |
---|---|

Aramon | 7.5 |

Latest Exhibition | 5.5 |

Goshen | 3.5 |

Total odds of the multiple | 144.38 |

In the treble above betting 100 £ on the selections you can win 14,437.50 £. Wow what a profit! In fact, in the face of such a high profit the chances of victory are just

100/144.38= 0.69%, almost 7 out of a thousand. Really nothing…

### The Solution: Betting Exchanges

The only way to minimize the ovverround is to place bets on a betting exchange like Betfair.com

Going back to the example on horse racing the overround on the exchange on Betfair.com is equal (at the time we write this article) to

Horse | Odds | Probability |
---|---|---|

Miss Elsa | 2.26 | 100/2.26=44.25% |

Roca Magica | 2.72 | 100/2.72=36.76% |

Ruby Gates | 4.50 | 100/4.50=22.22% |

Crystal Carole | 18 | 100/18=5.56% |

Islay Mist | 24 | 100/24=1.96% |

Total overround | 112.96% |

At the moment the difference between the bookmaker’s margin and that of the exchange is low (3.37%) because there are many hours left until the start of the race, but as the start approaches the overround will be very close to 100%. This is due to the fact that in the exchange the house does not earn on the basis of the overround but rather a fixed percentage equal to 5% on winning bets. So prices are determined exclusively by players with their bets so the overround will get very close to 100%.

### How Can We do to Reverse The Mathematical Advantage

Is it therefore possible to overcome the initial deficit given by the bookmaker’s mathematical advantage? The answer is Yes.

There are two ways, both apparently profitable, but only a long-term sustainable one.

__The Seemingly Easy Road: Sure Bets__

The first apparently easiest way is the one given by sure bets. What are surebets? They are bets in which the outcome is certain and favorable to the player since the ovveround is always less than one hundred. Think about this tennis match between Nadal priced by Bookmaker X at 2.10 and Federer priced by Bookmaker Y at 2.10. By wagering £ 100 on both players on the two bookmakers we would have the following scenario:

Player | Odds | Stake | Return |
---|---|---|---|

Nadal | 2.10 | £ 100 | £ 210 |

Federer | 2.10 | £ 100 | £ 210 |

Total wagered: £ 200

Net profit: £ 10

In any case, on the one hand we win £ 110 net and on the other we lose 100 for a safe win of 10 £.

Very well: at first glance it looks wonderful, pity that in no time we will be intercepted by bookmakers (who know this technique and fight it) and our accounts will therefore be frozen.

__The Truly Correct Path: The Value Bets__

The correct way to invert the mathematical advantage is to resort to value bets: in this regard, we invite you to read this blog article.

__Value Bets on Steroids__

If the value bets are the way to invert the mathematical advantage in favor of the punter, using them during live events means amplifying the potential of this instrument exponentially; we could define them value bets on steroids, since in certain markets odds rise inexorably over the time (think of the over / under markets in football and the match odds market itself)

__Rely on Bia to Find The Value Bets__

In conclusion, as you understand, reversing the mathematical advantage of the bookmaker in your favor is possible but not easy, unless you rely on cutting-edge tools such as Bia – the artificial intelligence that comes from the future.

You can also read this article on Wikipedia.