Yes it does matter if you change your mind,If your swap yourmorelikely to win!

but you may ask why?

well lets go through the game as the host.

You start playing and you pick your frist box, On your first go the chances of you picking a box without the prize is 2/3

Now lets look at the two left. 2 thrids of the time the host will not have a choice of what boxhe/she may take away! because there are only two to choose from and one is the prize so it may not be taken away.

so you can dedue that the 2 thrids of the time the box taken away is the only box the host could take away. meaning it would be a good idea to swap unless of course you pick the correct box the first time round (but there is only a 1/3 chance of that happening)