Suppose you have to choose between:
- a. getting 1$
- b. getting a ticket of the lottery L(p) which gives you 1'000'000'000$ with probability p and 0 with probability (1-p), with p such that the expected gain is less than 1$
could it be rational to play?
One could think that the 1$ you get by choosing a doesn't actually change your life in any relevant way, while the choice of b could actually change your life completely, althought with a very small probability, so b seems rational. But this would amount to ignore the size of the probability p (provided it is positive), and this means also we are ignoring the expected value of the utility. So do p and expected utility actually matter for a rational decision?