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There are three aspects to expected value. First, probabilities. Rather than thinking that a three-of-a-kind poker hand is ā€œvery unlikely,ā€ Liv knows that the chance of getting one, before any cards are dealt, is about 5 percent; if the first two cards she’s dealt are a pair, this probability rises to about 12 percent. Though both probabilities are small, the difference between them can easily be enough to affect your decisions at the poker table…

The second aspect of expected value is assigning values to outcomes. For professional poker players, this is comparatively easy: they can just look at their financial returns. But financial returns are not in general the right measure of value. If you need Ā£1000 to pay for a life-saving operation, then the difference in value for you between getting nothing and getting Ā£1000 is much greater than the difference in value between getting Ā£1000 and getting Ā£2000. The value that we assign to outcomes should be based on whatever it is we ultimately care about, such as people’s wellbeing…

This brings us to the third aspect of expected value theory, which is measuring how good or bad a decision is by its expected value. This can be intuitive: in the two-drugs example I just gave, the first drug is the better choice; death is more than ten times as bad as a mild headache, so a 10 percent risk of death is sufficient to outweigh a guarantee of a headache. We can calculate the expected value of a decision as follows. First, we list each possible outcome of the decision. Next, we assign a probability and a value to each outcome, which we then multiply together. Finally, we add up all the probability-times-value products.