They don't: https://en.wikipedia.org/wiki/Expected_utility
In short, there are three types of people: risk-averse, risk-neutral, and risk-preferring. (In the general case, people can exhibit all three types of behavior at different income levels, but let's keep things simple).
Imagine a graph, with income on the x-axis and utility on the y-axis. A risk-averse person will have a concave utility function (like a square-root function), whereas a risk-netural and risk-preferring person would have a straight-line and a convex utility function, respectively.
You have two income levels: $0 and $1000. Now take the two points (0, U(0)) and (1000, U(1000)) and connect them with a straight line. Since we're dealing with a 90% chance = .9 probability, find the point on that line which is 90% of the way between the two points (closer to the second point). This point represents the utility received from the risky situation, or the expected utility. This is not the same thing as the utility of the expected value! Call this point A, with coordinates (Ax and Ay)
Compare U(Ax) this with the value U($900).
For a risk-neutral person, the two values will be exactly the same, as the utility function is a straight line. For a risk-averse person, the second value will be higher, as the utility function is concave with respect to the origin. For a risk-preferring person, the first value will be higher, as the utility function is convex with respect to the origin.
In practice, the utility function may not have a constant concavity, which explains why people buy insurance (which is only justified under risk-averse behavior) yet also buy lottery tickets or gamble at casinos (which is only justified under risk-preferring behavior).
> Who in their right mind would take the choice that could possibly leave them without a life-changing sum the next day?
As you can see, the answer to your question is, 'A person who is risk-preferring' (or operating under risk-preferring situations which are quite common in practice).