How does fate and free will determine the outcome of the play?
The play also plays around with the idea of the author being the ultimate controller of characters. No character really chooses -- the author writes the choices. When Rosencrantz and Guildenstern ask the play "who decides?" The player's response is "Decides? It is written." I think that is a wink and a nod to authorial control.
On another note, the theme of fate vs. free will also plays into the existential themes of the play. Existentialism is predicated on the idea of man's responsibilty to take positive action in his life. Clearly these characters don't do that, therefore they are dead (exisitentially) from the very start. If one starts reading the play with that in mind, it creates even more irony in their choices and frustations thoughout the play.
I think the play shows fate as the dominant force throughout the play. Rosencrantz and Guildenstern are not in control of what is happening from the very beginning. They don't know why they are travelling, they are transported to new locations, their attempts to escape fail, and they can't even complete the 'mission' for which they were sent. Their death at the end is out of their control - throughout the entire play, it is like there is a wave of fate propeling them forward. They can choose their responses to it, but even those responses don't matter.