4 ms·
Why are we discarding the games that are ruined? Whether Monty knows for sure or is just picking at random only affects whether games are ruined, not the proba
by tasty_freeze 6y ago
Why are we discarding the games that are ruined?
Whether Monty knows for sure or is just picking at random only affects whether games are ruined, not the probability that the door the contestant picked is a winner.
If there are N doors and the player picks door 1, there is a 1/N chance he will be correct. If he sticks to that door, there is nothing that will ever change that 1/N odds that it was the winner.
Downthread someone enumerated the cases, but again, they discard the 1/3 of the cases where Monty ruined it. What that does is throw out half of the cases where contestant picked the wrong door and had the wrong strategy. Whether Monty ruined the surprise by showing the winning door or Monty got lucky and exposed a goat, that original door always has a 1/3 probability of being the right one.
- kgwgk 6y agoBecause the problem asks what to do after a goat is shown.
- ubercow13 6y ago>Whether Monty ruined the surprise by showing the winning door or Monty got lucky and exposed a goat, that original door always has a 1/3 probability of being the right one. By that logic, so does the remaining door. 1/3 vs 1/3.
- bart_spoon 6y agoBecause that is a fundamental part of the "Monty Hall" problem. You are correct in the case where Monty will randomly pick doors, and sometimes he will pick the winning door and ruin the game, but that is a fundamentally different problem than what is described as the "Monty Hall problem", and therefore irrelevant. Its like saying soccer players could score more if they picked up the ball and ran with it. While true, you are no longer describing the game of soccer.