Tourney Ending I

Alice and Bob play in a tennis tournament such that the winner of each round receives $1$ point, while the loser loses $1$ point. The tournament ends as soon as one of the players reaches $2$ points or $2n$ games have been played, whichever comes first. Alice has probability $0 < p < 1$ of winning each round. Find the expected number of games played in the tournament when $n = 4$ and $p = 1/3$ .

Answer format: round to 2 decimal places.