Suppose we have the numbers 0-7 arranged in a circle. A game is played such that the token starts at position 0 and advances to a larger number depending on a dice roll for each turn. For example, if...

Suppose we have the numbers 0-7 arranged in a circle. A game is played such that the token starts at position 0 and advances to a larger number depending on a dice roll for each turn. For example, if the first turn they roll a 2 and the second turn they roll a 5, then the token advances to position 2 after the first turn, then to position 7 after the second turn. Position 0 comes after position 7 after a complete cycle is made. If the player lands on square 3, then they get a bonus roll for that turn.
Let X denote the number of turns needed to reach orpass 0. Note that bonus roll should not be counted as a separate turn. Find the expected value and variance of X.