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The problem I have with this is that the original Monty Hall problem has him opening one door out of 2. With the 100 doors analogy, wouldn’t Monty be opening ju

The problem I have with this is that the original Monty Hall problem has him opening one door out of 2. With the 100 doors analogy, wouldn’t Monty be opening just one of the remaining doors? Or half? Why all 98?

injb 4y ago
Then the question of "switching" wouldn't make sense. Which of the remaining 98 would you be asked to switch to? The whole point is that you end up with a choice of sticking with the door you picked, or switching to the one remaining door.
- colmanhumphrey 4y ago
  Seems fine to me. Do you want to stick with your original or switch to one of the remaining 98? It’s still worth switching too, just a smaller increase in probability.
waynesonfire 4y ago
i think the idea is to demonstrate more easily the information leak by exaggerating the amount of information being leaked. with 3 doors, there are only so many the host can chose to open. with a 100, there is up to 98. sure, it can be 1 or 2... or 98.
jasonswett 4y ago
The rule is "after the player has guessed a door, open ALL the other doors except the door that was guessed plus one other door". I think your confusion is because if there are 100 doors then the rule is self-evident. But when there are only 3 doors, the rule of "open all doors except the door that was guessed plus one other" is indistinguishable from "open just one door". The key is knowing that the rule is the "open all..." rule.
- colmanhumphrey 4y ago
  That’s not the rule from the question in the link nor in the original game (the game’s rule isn’t quite the same as the classic problem, it’s even messier). Your proposed rule doesn’t uniquely extend the original, it’s just one of the possible generalizations.
- thehappypm 4y ago
  Sure, but why is the rule “open all”? In Monty Hall, the rule could also be “open half” or “open one” and it would be the same game!
scambier 4y ago
The point of opening the 98 doors is to make the math - and the fact that switching doors is safer - more obvious.
colmanhumphrey 4y ago
I agree, I had the same thought last year: https://twitter.com/colmanhumphrey/status/1393385716500123651?s=21&t=eZKyx5Yrxgxn7QgR7YfmDw https://twitter.com/colmanhumphrey/status/139338571650012365.... It still helps but now only a small amount: (99/100)*(1/98) ≈ 0.0101, vs 1/100 without switching
petesergeant 4y ago
> is that the original Monty Hall problem has him opening one door out of 2 The better way of thinking about it is that he is leaving one door closed
- arecurrence 4y ago
  I’ve found pointing this out is an “aha” moment for people with even little understanding of statistics. Regardless of the number of doors, the space collapses to two options when the host reveals the rest. That new option is the set of all doors the player never picked. The player’s initial option, 1/3 (33%) for 3 doors or 1% for 100 doors… versus the other option that is the rest of the set. 2 doors or 66% for 3 doors up to 99% of the doors for the 100 case. That other option being the rest of the set must have better probability for any door count greater than two.

injb 4y ago

Then the question of "switching" wouldn't make sense. Which of the remaining 98 would you be asked to switch to? The whole point is that you end up with a choice of sticking with the door you picked, or switching to the one remaining door.

colmanhumphrey 4y ago
Seems fine to me. Do you want to stick with your original or switch to one of the remaining 98? It’s still worth switching too, just a smaller increase in probability.

waynesonfire 4y ago

i think the idea is to demonstrate more easily the information leak by exaggerating the amount of information being leaked. with 3 doors, there are only so many the host can chose to open. with a 100, there is up to 98. sure, it can be 1 or 2... or 98.

jasonswett 4y ago

The rule is "after the player has guessed a door, open ALL the other doors except the door that was guessed plus one other door". I think your confusion is because if there are 100 doors then the rule is self-evident. But when there are only 3 doors, the rule of "open all doors except the door that was guessed plus one other" is indistinguishable from "open just one door". The key is knowing that the rule is the "open all..." rule.

colmanhumphrey 4y ago
That’s not the rule from the question in the link nor in the original game (the game’s rule isn’t quite the same as the classic problem, it’s even messier). Your proposed rule doesn’t uniquely extend the original, it’s just one of the possible generalizations.
thehappypm 4y ago
Sure, but why is the rule “open all”? In Monty Hall, the rule could also be “open half” or “open one” and it would be the same game!

scambier 4y ago

The point of opening the 98 doors is to make the math - and the fact that switching doors is safer - more obvious.

colmanhumphrey 4y ago

I agree, I had the same thought last year: https://twitter.com/colmanhumphrey/status/1393385716500123651?s=21&t=eZKyx5Yrxgxn7QgR7YfmDw https://twitter.com/colmanhumphrey/status/139338571650012365.... It still helps but now only a small amount: (99/100)*(1/98) ≈ 0.0101, vs 1/100 without switching

petesergeant 4y ago

> is that the original Monty Hall problem has him opening one door out of 2 The better way of thinking about it is that he is leaving one door closed

arecurrence 4y ago
I’ve found pointing this out is an “aha” moment for people with even little understanding of statistics. Regardless of the number of doors, the space collapses to two options when the host reveals the rest. That new option is the set of all doors the player never picked. The player’s initial option, 1/3 (33%) for 3 doors or 1% for 100 doors… versus the other option that is the rest of the set. 2 doors or 66% for 3 doors up to 99% of the doors for the 100 case. That other option being the rest of the set must have better probability for any door count greater than two.