[mathogre]

Take 10 minutes to model it and you'll find there is no benefit in changing. As a couple others have pointed out, it isn't the Monte Hall problem.

Below I did two runs with a million cases. One envelope has 1 unit; the other has 2 units. I shuffle the envelopes, and the "player" chooses an envelope. "noChange" means this is the payoff if the player doesn't switch envelopes. "yaChange" means this is the payoff if the player switches envelopes.

$ python3 ./twoEnvelopes_00.py 1000000 noChange = 1500023 yaChange = 1499977

$ python3 ./twoEnvelopes_00.py 1000000 noChange = 1499984 yaChange = 1500016

When modeling Monte Hall, the payoff for changing is obvious.