Brilli The Ant And His Numberline Wall

Brilli the ant starts on a number line at the number 0, and flips a fair coin. If it lands on heads, he goes to the right (+1), but if it lands on tails, Brilli goes to the left (-1). However, there is a wall at the point \(-1000\), and as such if Brilli ever finds himself at the point \(-1000\), he will always go to the right, regardless of what the result of the coin flip is.

Brilli keeps flipping coins and moving until he eventually reaches the point 100. What is the expected number of times Brilli visited the wall at -1000?

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