It's because it makes the initial choice so increasingly unlikely (increasing with the number of doors) to be correct that when the doors are taken away and you're left with only two, one of which must be right, it means that the other door is incredibly likely to be the right one.

> It's because it makes the initial choice so increasingly unlikely

But you still need to conivnce people that the one remaining unopened door is more likely than the door you originally selected. They were both unlikely to begin with, ramping up the number of doors doesn't explaing why one of them should be preferred.

There are 1000 doors. You choose 1. Anyone knows it's incredibly unlikely that the correct one is chosen first time.

Now 998 doors are removed. There is 1 door from the others and the door you choose. Given that your choice is almost certainly wrong, and that your opponent couldn't remove the correct door from amongst the 998, that means the other door is the correct one.

Is that convincing enough?

Because a 99/100 chance is much better than 2/3 to drive the point home...

Imagine there are 999 boxes with nothing in them and one box with the keys. After picking a box, the hosts opens 998 empty boxes. Would you still stick with your initial choice?

I would change my choice because I understand the problem. But I would also change my choice in the scenario with 3 boxes. I'm not arguing with the conclusion, what I don't understand is the people who have their mind changed by the argument.

> the remaining unopened box is different from the box your picked originally.

Because you now know that every other box is empty. So by process of elimination you know that your box and the remaining one are different.

I've often found it easier to understand things intuitively by putting an idea to the slippery slope test. If such & such were true, imagine changing some parameters to an extreme, how absurd does it become? For monotonic functions it's useful