Thanks, plasmid. It's clear now.
It doesn't really matter if you switch or not.
Let's consider 2 players - Alex and Bob. Alex always switches after picking the first envelope and Bob always keeps the envelope he picked originally. The amounts in the envelopes are always the same and they play this game many times in succession. If switching strategy was beneficial then Alex should end up with more money than Bob, but in reality they will have the same amount of money. Since both pick randomly, both strategies have 50% chance of picking the envelope with the larger amount, so both players will get the large amount 50% of the time and small amount 50% of the time.