- 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.