To many the world of bookmaking is a mystery. The maths involved and the jargon used can seem intimidating, however, betting with a bookmaker is simple as indeed are the principles behind making a book. In order for your betting to be effective you need to know how the betting markets work and that means understanding the mathematical principles that go into making a book.

It is the bookmaker who sets the odds and they do so in such a way that in the long term they will make a profit. Using a five horse race as an example, although the principles are the same for any event, the probabilities of all the horses' winning chance must total exactly 100%. Assuming each horse has an equal chance of winning the book should look like this,

**Book 1**

Horse | Odds | %age Chance |
---|---|---|

A |
4/1 (5) |
20% |

B |
4/1 (5) |
20% |

C |
4/1 (5) |
20% |

D |
4/1 (5) |
20% |

E |
4/1 (5) |
20% |

If you add all the percentages together the total is 100%.

However,it is unlikely that each horse will have an equal chance of winning, so what the bookmakers do is to employ form and betting experts to make an estimation of each horse's chance of winning. The book would therefore look more like this,

**Book 2**

Horse | Odds | %age Chance |
---|---|---|

A |
6/4 (2.5) |
40% |

B |
3/1 (4) |
25% |

C |
4/1 (5) |
20% |

D |
9/1 (10) |
10% |

E |
19/1 (20) |
5% |

If you add all the percentages together the total is 100%.

The common factor about both these books is that the percentages for each add up to 100%. What this means is that if you back every horse in the race you will receive your money back, neither winning nor losing. In the case of book 1 if you bet £20 on each horse this would cost you £100 (5 bets each at £20) but whichever horse won you would receive £100 (5 X £20) back so breaking even. In the case of book 2, your £100 stake would have to be split differently depending on the odds available in order to achieve the same return. This would be £40 on horse A, £25 on horse B, £20 on horse C, £10 on horse D and £5 on horse E. (This is known as dutching).

For betting purposes this is no use to either punter or bookmaker as nobody would make any money. Therefore, what the bookmaker does to guarantee his profitability is to ensure that the total of the percentage probabilities (the odds) they offer is greater than 100%. The book could therefore look like this.

**Book 3**

Horse | Odds | %age Chance |
---|---|---|

A |
6/4 (2.5) |
40% |

B |
2/1 (3) |
33.33% |

C |
3/1 (4) |
25% |

D |
6/1 (7) |
14.29% |

E |
10/1 (11) |
9% |

If you add all the percentages together the total is 121.62%.

The total of the percentages should be 100% but in book 3 they add up to over 121%. This is known as an "over-round" book and in this case the over-round is 21%. The 21% difference represents the bookmaker's theoretical profit. This means in theory for every £121 in bets the bookmaker takes he will have to pay out £100 leaving him a profit of £21 whichever horse wins. When a book is over-round you cannot back every outcome and make a profit.

Money placed at a bookmaker on a race is not spread evenly across the whole field nor do they win on every race but by ensuring that every book they open is over-round in the long term they will pay out less in winnings that they take in as bets.

**Note:** A book in which the aggregate percentages total under 100% is known as "under-round" or "over-broke" and this means that if you back every runner in the race you would be guaranteed a profit.

The odds originally offered by the bookmaker usually reflect their judgment of the probable winner of the race. A bookmaker may offer artificially low prices on a horse they feel will win in order to discourage punters from backing that horse. Additionally, they may offer artificially high prices on a horse they feel has no chance of winning thereby encouraging punters to back that horse with them rather than another bookmaker.

Once the book has opened and the bookmaker starts accepting bets the prices will change depending on the money received for each runner. If a lot of money is received for one particular horse then that horse's price will shorten, therefore acting as a discouragement for punters, while lengthening the price of all other runners. All the time the bookmaker is monitoring his liabilities and changing the odds to ensure a profit is made.

**Note:** A horse whose price shortens dramatically is known as a "steamer" and a horse whose price lengthens dramatically is known as a "drifter".