HardMarket Making & Games

The Two-Envelope Paradox

Jane Street

Two envelopes hold money, one exactly twice the other. You pick one, open it, and see $100. A voice argues: “The other holds$ 50 or $200 with equal probability, expected value$ 125 — always switch!” The same argument applies before opening ANY envelope, implying you should switch forever. Where exactly does the argument break?

Approach

Ask what prior makes “50/50 whatever you observe” possible.

Seeing the amount is information, not noise.