The latter problem is more interesting, although as written they're meeting to compare wallets with this game, so both wallets should logically be empty. But a

The latter problem is more interesting, although as written they're meeting to compare wallets with this game, so both wallets should logically be empty. But assuming a more surprise situation in which the game is suggested* the reasoning is pretty good for both if they're happy with a 50% chance at doubling their money + X. But I think maybe its the hidden prize that makes the logic work (or not work)? For one of them the prize is less then double their money (a prize they'd never win but still) so the deal isnt a good deal. Not sure how the math works for that, but a contest where you might win 2a or less then 2a is presumably a different reasoning. *Where similar to the first point we should assume the suggesters wallet is empty.