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I wrote out a hopefully helpful intution down below [0]. Here's a terse part of it: > Or just imagine monty hall with infinite doors. I'm thinking of a number
by 6gvONxR4sf7o 5y ago
I wrote out a hopefully helpful intution down below [0]. Here's a terse part of it:
> Or just imagine monty hall with infinite doors. I'm thinking of a number between 1 and infinity (secretly, it's 19083412039102388171230123). You pick a number, and then I'll narrow down your choice to two options. Do you think you just happened to pick my number, or do you switch?
You're right that it's absolutely the narrowing down of the choice that's the key. If you happen to have not picked the prize door on your first try (more likely than not), the narrowing down will be your door and the prize door.
[0] https://news.ycombinator.com/item?id=27092614 https://news.ycombinator.com/item?id=27092614
- saeranv 5y agoThis is the best explanation I've read thus far.
- megablast 5y agoOk. But you picked a very very very very small number between 1 and infinity. That can’t be random.
- 6gvONxR4sf7o 5y agoTons of common distributions have infinite support, but the details don't matter for this bit of intuition. If you want to formalize it in a simpler way, just consider it as an arbitrarily large finite number of doors with a uniform distribution.
- CRConrad 5y agoThat it isn't random is precisely the point, isn't it? The only difference that the "very very very very small number" makes is that the odds aren't infinity to one but two to one. Still winning odds.