Reflecting Plug Walk

A walker moves on ${0, 1, \dots, 20}$. From any position $1 \le i \le 19$ it steps up with probability $p = 0.45$ and down with probability 0.55. Position 0 reflects: from 0 the next step goes to 1 with probability 1. Every step, including a step out of 0, takes one unit of time.

The walker starts at position 4. What is the expected number of steps until it first reaches 20?

Answer format: enter an integer.