Dice Game

[ChromePony]

This could probably go in the probability forum, but theres way too much philosophy around here and not enough math so lets give it a shot.

A friend of mine posed this to me after he was asked it on a job interview, heres the game, its pretty simple.

You roll a fair 6 sided die and are given an amount of money equal to the number you roll, 1=$1 2=$2...etc. The caveat is that if you wish to reroll you may, but would then be stuck with whatever you get the second time.

The question is, how much would you be willing to pay to play this game? read: what is the EV
(this is what he was asked to figure out on the spot)

A slightly less trival extension, what if you get up to 6 rolls, meaning you can choose to reroll 5 times before you are stuck with the 6th.
(he was given this as 'homework')

Finally and most interestingly, how about generalizing it for n rolls...just for kicks