Suppose we have a game where we roll one die first. If the number is a one, then we reroll two dice in its place. We continue this until there are no more ones, and the score is all the numbers added together that weren't 1s. Ex. John rolls a dice, gets a 1, then he rerolls two more dice in its place. He gets a 3 and a 1. The 3 remains, but the 1 is replaced by two dice, which are a 5 and a 6. Then his score is 3+5+6 = 14.
If he gets any number besides a 1 on the first roll, game ends.
How would I find the expected number of rounds that will occur. (new round happens when a 1 occurs).