The laws of probability

The reader will have noted that, in the previous chapter, we moved uneasily between ‘the true probability p that a certain horse will win a race’, ‘the number p that you believe is the probability that a certain horse will win a race’ and ‘the number p which the odds given imply is the probability that a certain horse will win a race’. The reader will also have observed that, even if there is such a thing as ‘the true probability p that a certain horse will win a race’, we have no means of measuring it. When the race is run, either the horse will win or it will not. Anyone tempted to mutter ‘the probability p is the long run proportion of identical races that the horse will win’ should reflect on the impossibility of arranging even two nearly identical races. (If we could arrange two identical races the same horse would win both of them.)

Does this mean that we should dismiss the whole discussion as rubbish? That would be a pity. Even if the fundamental concepts used in the first chapter appear hazy on close inspection, they do seem to tell us something about how to bet. Experience seems to show that those who have some knowledge of probability, like bookmakers and casino owners, tend to do better than those, like some of their clients, who do not.