Escamillo,

Your table analyses all the possible events and shows a 50/50 chance of success.

However not all these events occur in the problem as stated.

sequence:
Player chooses a cup
House displays an empty cup
Player may choose again

Ammended Table:
PRIZE IS IN CUP 1
-----------------
Choose 1, lift 2 OR 3, change to other : loose *
Choose 2, lift 3, change to 1 : win
Choose 3, lift 2, change to 1 : win

PRIZE IS IN CUP 2
Choose 1, lift 3, change to 2 : win
Choose 2, lift 1 OR 3, change to other : loose *
Choose 3, lift 1, change to 2 : win

PRIZE IS IN CUP 3
Choose 1, lift 2, change to 3 : win
Choose 2, lift 1, change to 3 : win
Choose 3, lift 1 OR 2, change to other : loose *

PRIZE IS IN CUP 1
Choose 1, lift 2 OR 3, stay on 1 : win +
Choose 2, lift 3, stay on 2 : loose
Choose 3, lift 2, stay on 3 : loose

PRIZE IS IN CUP 2
Choose 1, lift 3, stay on 1 : loose
Choose 2, lift 1 OR 3, stay on 2 : win +
Choose 3, lift 1, stay on 3 : loose

PRIZE IS IN CUP 3
Choose 1, lift 2, stay on 1 : loose
Choose 2, lift 1, stay on 2 : loose
Choose 3, lift 1 OR 2, stay on 3 : win +

Overall 1/2, but if you always change the probability is 2/3.

* It doesn't matter which cup the house lifts, if you change your choice you lose.
+ Again it doesn't matter which cup the house lifts.

That's my reading of it anyway :)

AndyG