When a bookmaker produces odds for a race or an event, they are based upon many past and present factors and represent the relative chance of each selection, in comparison to all the other selections in the same event. The implied probability of each selection can be calculated as a percentage and, in theory, all selections of said event add up to 100% when totaled.

 

 Rarely will you see book that does actually add up to exactly 100% though (also called a ‘round’ book). For a book to be profitable, the sum of the selections will equal over 100%. Each book created must carry a weighting of greater than 100% for it to be a viable business venture for the bookmaker. The amount over 100% the book is, is commonly referred to as the over-round.

 

 For example, if a book is running at 105%, the bookie will expect to pay out £100 per every £105 staked, if the stakes have been bet in equal proportions relative to their respective odds. This will provide the bookie with an expected profit of £5 of every £105 staked, or 4.75%;

 

Selection Odds Implied Probability % Stake (£'s) Returns (£'s)   
Horse 1 6/4 40 40 100   
Horse 2 2/1 33.33 33.33 100   
Horse 3 9/2 18.18 18.18 100   
Horse 4 9/1 10 10 100   
Horse 5 25/1 3.85 3.85 100   
 Totals: 105.36% 105.36 Max 100 
 
So, in the example race above, there are 5 horses (selections) to choose from. The odds, when converted to implied probability, add up to 105.36%, creating an over-round of 5.36%. The bookie must try and ensure that stakes received for this race balance in the proportions stated in the ‘stake’ column by a combination of hedging his bets and lengthening or shortening the odds as required to alter the pay out.

 

 If a book should be written that adds up to less than 100%, this is called an under-round. This is uncommon in bookmakers and usually attracts a raft of interest and large stake bets. Basically and under-round book offers a profit as well, but this time to the punter. When the stakes are placed in the correct proportions to every selection in an under-round book, the punter is guaranteed a profit whichever of the selections wins.  Imagine the example race above, and Horse 4 pulled out but the bookie persisted with exactly the same prices for Horses 1,2,3 and 5. The book would now only add up to 95.36% and punters would guarantee themselves £4.64 profit for every £100 staked, providing that they staked in the correct proportions.

 

 Bookies must avoid this scenario or risk large losses (although it is likely the bookmaker would claim palpable error if they present a reasonable case that it was a genuine mistake whilst writing the book). Under-round books do occur occasionally, more frequently so on the online exchanges when the market is young.  Also, punters can create their own under-round books by using selections from differing bookmakers (known as Arbitrage betting).