Monty Hall

[andrewducker]

[Poll #1770413]

Explanation

I have known what the answer was for ages, but for some reason it only "clicked" in my head today. You can blame sarahs_muse for triggering it.

Comments

[andrewducker]

I wrote some code this afternoon to prove it to myself.

What I discovered was that either I had chosen the prize with my initial guess, or I had not. Opening doors that I hadn't chosen did not change the correctness of my initial guess. And therefore, there was always a one in three chance that my original guess was correct.

Therefore, as there was only one other door to choose, that door must have a two in three chance of being correct.