[eigenvalue]

Let's do some math:

You have a function f with a variable x that represents your initial chip count and f(x) is your expected value. In your example you have f(10,000) = 40,000.

We know that every additional chip that you earn in a tournament has a little less value than the average value of your original chips, so the given function has the property: f(x1 + x2) < f(x1) + f(x2)

Now it's easy:
f(20,000) = f(10,000 + 10,000) < f(10,000) + f(10,000) < 40,000 + 40,000 = 80,000.