"What is Laying overround, Backing underround or Dutching?"

Bookmakers make money by offering odds that are different to the real probabilities in the underlying event. Traditionally all bookmakers offer prices that are overround. By overround we mean that they offer prices for punters to back which exceed the total probability in an event.

For example:-

If we were offering prices for the toss of a coin we know the probability of a head or tail is 50%. Excluding complex variations we know the probability of a head or tail being tossed is 100%. There are no other outcomes to this event.

If we are a bookmaker and want to make money on this event we simply offer up 100% probability at a price higher than 100%. If we offered up a book of 105% we would simply lay heads or tails at 52.5%. This is the equivilant of laying heads and tails at 1.90 (Digital odds). Therefore the punter would back either event at 1.90 and we would guarantee a profit as long as both side of out bet was matched. If both sides of the bet was not matched we would end up paying out a liability on one side and not cover the bet on the other. However as long as our overround is big enough the good and bad days will average each other out over time and in the long term we would make money.

Example:-

Our bookmaker decides to accept betting on an event where there are only two outcomes. He decides to choose the the Oxford and Cambridge boat race.

The bookmaker might open his book by offering odds of 2-1 on Cambridge and 6-4 against Oxford. By a simple calculation (Two divided by three, the sum of the odds (2+1=3)) we can see that 2-1 on represents a probability of 66.67% and 6-4 against represents 40% (Four over ten).

The probabilities add up to 106.67% The excess of 6.67 over 100 percent is known as the over-round. In short he has sold odds of 106.67% but the outcome can only ever be 100%. There is a 100% chance that one horse or the other will win. (We are talking simplistically here). The bookmaker, if he can take bets in the proportion of the probabilities, say £66.67 on Cambridge and £40 on Oxford, will pay out £100 whichever wins on £106.67 taken, a percentage profit to him of 6.25%.

In practice, of course, the bookmaker will need to adjust his odds in accordance with supply and demand. More money for Oxford than the estimated probability indicates will cause him to shorten the odds against Oxford and lengthen those for Cambridge. The same principle works on the stock market when market makers buy and sell shares on their books at different bid and offer prices.

His final book might look like this :-

In this example, he began by seriously under-estimating the fancy for Oxford, and has been forced to reduce his odds from 6-4 to evens, at the same time offering better odds for Cambridge. Before adjusting his odds he stood to pay out £100 on Oxford, having taken only £90 in stakes. The odds offered on a horse race with many runners are calculated and adjusted in the same way. The over-round usually increases with the size of the field.