A Math Puzzle

[Timko]

Hello CFC, good to be back.
By now a lot of us has already agreed on the 1/3, 2/3 ratio.
Well consider this:
Let's say instead of having one player we have three players, and they happen to each choose a different door. After a while, the host eliminates one door so one of the players is out. Would both of the remaining players increase their chance of winning if they switch?

No. 567890

 

[superisis]

the reason that these problems can cause controvesy is because they hint at the non-existence of probability. For the person arranging the experiment/problem, there is no question, he must know where the prize is for it to be valid, and such he can choose the correct box/door anytime. For the contestant(s) there exists a subjective probability, that can change with them attaining knowledge from the arranger (who knows the answer). Thus your first choice as a contestent will allways be 1/3 but if the arranger gives you clues that may change. If he tells you straight that the money is behind door number three your probability shoots from 1/3 to 1/1. But thats the subjective probability, the money allways stays in the same place.

That's way rationality may conflict with maths, because it seems as if the moneys is suddenly moving around but as we all know, the arranger will allways pick the right one, i.e probability doesn't exist for him (if you make the arranger God, the player mankind and the game life you'll figure out that objective probability doesn't exist, i.e it isn't real, but merely a figment of our immagination)

 

[Scuffer]

Let's say instead of having one player we have three players, and they happen to each choose a different door. After a while, the host eliminates one door so one of the players is out. Would both of the remaining players increase their chance of winning if they switch?

No, you have 3 equal options, rather than 2 unequal ones.

 

[superisis]

with three players the rules chang in that the host is not confined to eliminating one of the two doors not picked by the one player... With three players, the host can eliminate any one which gives both remaining players an equal chance as to having choosen the correct door. It is similar to one player not choosing a door initially but just waiting until the host has eliminated one door. The chance in both cases are 50-50.