四盒子硬币游戏：期望抛掷次数

Consider four boxes in a row numbered 1, 2, 3, and 4. You start with a pebble in Box 1. We toss a fair coin. If it is heads you move the pebble forward one step to Box 2, but if it is tails you move the pebble forward two steps to Box 3. Then we toss the coin again. If it is heads, you move the pebble back to Box 1, but if it is tails you advance it to Box 4. If you reach Box 4 the game is over. If you are back in Box 1, however, then we toss again following the same rules. What is the expected number of coin tosses it will take to reach Box 4?