3 ms·
Your re-framing is actually not quite right either (or at least, not complete). Key point: if the host picks the car, the game essentially re-sets. Imagine the
by empyrrhicist 3y ago
Your re-framing is actually not quite right either (or at least, not complete). Key point: if the host picks the car, the game essentially re-sets.
Imagine the extreme scenario with 999 goats and 1 car. You select the first door, the host opens 998 doors at random, leaving your selected door and one other. Two scenarios are now possible:
1. There was a car in the 998 doors that got opened. Tough luck, you lose the game automatically now (game resets).
2. There was not a car in the 998 doors. In this scenario, you are still advised to switch.
Edit - I guess I misremembered a simulation I once did about it.
- Swizec 3y agoAlso you're picking between Reward and Bigger Reward. Positive EV no matter your choice so eh don't worry about it too much :) A nice goat fetches up to $1000 to according to a quick google.
- klyrs 3y agoA nice goat, you say? How much for a mean goat, jaded from years of being the spoiler prize that nobody wants?
- bemusedthrow75 3y agoWhenever someone talks about mean goats I think of only one thing: Buttermilk the baby goat, being a jerk. https://www.youtube.com/watch?v=AWvefaN8USk https://www.youtube.com/watch?v=AWvefaN8USk Enjoy.
- deleted 3y ago[deleted]
- bemusedthrow75 3y agoI am suddenly reminded of the clever, morally educational joke about the dead horse raffle.
- pxx 3y agoNope. Write the simulation for 2. Or look at this case analysis for the three element case. https://news.ycombinator.com/item?id=24714612 https://news.ycombinator.com/item?id=24714612 You can get intuition by understanding that the cases where the game is ruined are only the cases where you didn't choose the car.
- topaz0 3y agoAs I explained in my reply to your comment on mine, this analysis doesn't work out, even in this very-lopsided case. If the game resets when a car is revealed, then games where you first choice happened to be a car will always complete, and games where your first choice was a goat will almost always reset. On average, of 1000 games, your first pick will be a goat 999 times, and of those, 998 will be reset because MH opens the car and 1 will complete and give you the car if you switch, whereas in 1 in 1000 you will pick the car first, in which case the game is certain to complete but you will lose the car if you switch. Therefore, most games will reset, but of the ones that complete, there is no advantage to switching.