# Cup and ball game: what are the odds of that?

#### bonedoctor

##### New Member
OK we are having an intelectual discussion (no, really) about the change in odds during the classic cup and ball game. To explain:

• a dealer has three cups under one of which is a ball
• you pick one
• the probability at this stage of winning is 1 in 3
• the dealer then guarantees they will remove an empty cup

If the "experiment" remains unchanged the probability at this stage, as I understand it, is 2 in 3 as your cup is one of the two remaining cups which must have the ball underneath.

If, however, you change your mind (equivalent to a post-hoc analysis) then you change the game and essentially the probability becomes 1 in 2.

Can someone with a bigger brain than mine confirm or deny this?

Thanks.

#### fed1

##### TS Contributor
http://en.wikipedia.org/wiki/Monty_Hall_problem

You have discovered the monty hall problem (c 1990).

turns out you should switch , gives you chance of 2/3 of winning.

Their is alot of interesting history tied to this problem as well, the person who solved this apparently put alot of phd's in their place!

#### bonedoctor

##### New Member
Thanks!

Mate that's awesome. The link explains things very well.

Guess we can lock this thread off now.

Thanks.