I have heard of something like this before. The story went like Deal or no deal, choose 1 of 30 cases. You buzz thru all the cases until the last case. And they offer you to switch your case for the last other case.
The logic stated to take the case you do not own, because the odds that you chose the right case in the very beginning was only like 3%. I chose to stick with the original case, but the debator said it is right to change cases. So I don't know, whichever works and wins you the dough is the right answer to me, not the averages. I'll go with option 3.