[DoctorZeus]

Taking out the specific dollar amount doesn't change the math at all. If X designates the amount in the envelope I've selected, than 50% chance the other envelope contains .5 * X and a 50% chance it contains 2 * X, so the expected value of the other envelope is .5 * .5 * X + .5 * 2 * X = 1.25 * X which is greater than X.

[dnautics]

but you are implicitly turning the scenario into one with three values, 1/2X, X, and 2X, so something went wrong with what you're doing. There was only ever a universe of two values.

[DoctorZeus]

Sure, these are variables, so they correspond to different possibilities. X can be anything, and given X, the amount in the other envelope is one of two different possible values - 1/2X OR 2X.

So there are far more than three possible values, but only two actual values.

[dnautics]

Exactly, that's why your model is broken.