Perhaps a clearer variation goes as follows: Bill arranges so that if the coin is tails then (a) he will temporarily receive your winnings, if you get any, and (b) he will do a flawless imitation of Omega asking for money.

If you pay Bill then he returns both what you paid and your winnings (which you're guaranteed to have, by hypothesis). If you don't pay him then he has no winnings to give you.