I am absolutely fascinated by the decision theory. It is of interest to philosophers and economists. It deals with how to behave rationally in various practical situations. A decision situation is one where the subject of an action (let us call it P) has a choice between different actions (say D1 and D2). P may, for example, consider which of the two horses to bet on in the approaching race.
What should be taken into account in a decision situation? The two basic features of any such situation are the value (usefulness), i.e. how much W is desired in a given action D, and the probability that if you do D, you actually get W.
In horse racing the matter is quite simple, because bettors usually have only one goal: to make money. Let's say that bookmakers bet 50:1 on horse 1 and 10:1 on horse 2, and you wonder which one to bet your ten dollars on. Of course, the potential value of betting on horse 1 is much greater than betting on horse 2: you have a chance to win $500, not just 100.
But the probability that the horse you're going to bet on will win is equally important. Let's look at some examples. Let's assume that there are two horses in the race, horse 1 and horse 2. Suppose that you think that horse 1 has a 1% chance of winning, while the chance of winning a horse 2 is 99%. In that case you should bet on horse 2: although this way you can only win $100, the chance of actually winning is huge. On the other hand, if you think that the chances of winning a horse 1 are 50%, then you should bet on that horse. No matter how you bet, the chances of winning are the same: 50%. However, you will win much more by betting on the winning horse 1 than on the winning horse 2.
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Harry Wellington from pozycjonowanie