Envelopes!

[lorinda]

Please note a couple of things about my solution.

1. These numbers are ratios that you would use a random number generator to provide if you could

2. In a medium term game you could "cheat" your opponent by not putting enough $2 envelopes in, however, when his envelope tracker/envelope stat program found this out, he would stop switching when he opened $4 envelopes and you would lose out in the long term, it is to be considered as a pure solution for millions of trials.