The Eureka moment for me was similar, but slightly different. Consider a variant game with N doors. You pick a door, then Monty offers you two switch your payou

The Eureka moment for me was similar, but slightly different. Consider a variant game with N doors. You pick a door, then Monty offers you two switch your payout to "the best single result from the remaining N-1 doors". Clearly, you would swap. Now set N to 3, and consider that, by opening a door without the prize, that's exactly what Monty's offering you.