Backward Induction in the Centipede Game

Two players alternate moves for $n$ rounds. At each turn, the active player can "take" (ending the game with payoff $(k+1, k)$ where $k$ is the round) or "pass" (doubling the total pot). If both always pass, the final payoff is $(n+1, n)$. What does backward induction predict? Why does this differ from observed behavior?