If this is being setup as a prop bet and I’m trying to win….and I give you the choice after showing you the door or card.
If doing it one time, I’d have to have better odds on money than 2/3. That way I make money when someone swaps and I make even more money when they don’t.
If multiple times, if you get a choice, I need same better than 2/3 odds on cash, or there’s a stipulation where you can’t swap.
That’s the only way the proposer can make money if he shows a card/door *AND* the person playing has the mental capability of knowing the switch is better decision.