# How efficient is the market? Is it best to gamble on exchanges or with bookies? It is a well-known fact that betting at the track isn’t necessarily the best strategy. Odds are usually higher when betting on exchanges. In this article we set out our theory to explain this. As also noted below, short odds with bookies tend to be more profitable than larger odds. This is because casual punters often find short odds less attractive and jump on larger ones…which are where the bookies make their money.

First, let’s define “Implied Probability”:

This is the probability estimated by all punters at the start of the race and is defined as:

Implied probability = 1 / Starting Price

“Starting Price” is expressed in decimal odds.

We call it implied probability as it reflects what the market thinks is the “true” winning probability of a runner. If this was true, and as we explain further below, a punter’s profit should be nil over an infinite number of such bets (if we ignore transaction costs incurred on exchange).

Let’s call “P” the “true probability” of a runner. Someone betting a £1 stake a very large number of times on such runner would win P percent of the time and earn Starting Price – 1 in such case. He would lose his £1 stake the rest of the time, (1-P) percent of the time. His expected profit is therefore:

Expected Profit = P x (Starting Price – 1) – (1 – P)

When P = 1/Starting Price then the expected profit is nil.

The graph below compares “Implied Probability” and “Realised Probability” for various starting prices at the track. We looked at how often a runner with a starting price of X was wining historically: that is the realised probability. Good punters will prefer betting when the “true probability” (or more exactly, what he thinks is the true probability – and we have used historical winning rate as the best proxy available) is higher than the implied probability (as taken from the odds offered). In such a case the bookie has understated the winning chances of the dog.

The below graph is based on the official starting price at the track. It is on average not the best possible price. It should also be noted that implied probability is on average less than historical probability. As such, punters without inside knowledge or advanced analytical skills to spot mispricing are therefore sure to lose over the long term. It is also interesting to note that the gap between implied and true (or historical) probability reduces on shorter odds: There are usually better bets on shorter odds!