Preferences

Here’s a situation.

I give you $300 with the following options:
a) Give you $100 dollar more
b) toss a coin and give you $200 more if you won and nothing if you lose

It was found that most preferred option a.

Here’s a little change

I give you $500 with the following options:
c) you need to give me back $100
d) toss a coin and pay $200 if you lost but nothing if you win

Now the option d was a more preferred one.
But from the probabilistic theory all these four choices are identical. They all have the expected value of $400. Then why do we have such strong preferences?

Because we are more willing to gamble when it comes to losses but are risk averse when it comes to gains.