Okay, i've thought about it some more. Initially, you have a 2 in 3 chance of choosing a situation that will lead to switching winning, whereas you only have a 1 in 3 chance of choosing a situation where staying will win.
I'M CONVERTED!
So what punkworld said about the two staying choices being a subset is correct. They each become a 1 in 6 chance.
In my defence, it was 6 am when we were discussing this earlier.
haha.