the total amount in both envelopes is a constant formula_1, with formula_2 in one envelope and formula_3 in the other.if you select the envelope with formula_2 first you gain the amount formula_2 by swapping. if you select the envelope with formula_3 first you lose the amount formula_2 by swapping. so you gain on average formula_8 by swapping.swapping is not better than keeping. the expected value formula_9 is the same for both the envelopes. thus no contradiction exists.