Where's the cheese?

Bernoulli places a mouse token at the point 0 on the real line and two cheese tokens at the points \(3\) and \(-3\). Bernoulli then begins flipping a coin repeatedly. Each time the coin is heads, he moves the mouse 1 to the right, and each time the coin is tails, he moves the mouse 1 to the left. Let \(p\) be the probability that the mouse will eventually get a piece of cheese. Determine the value of \(\lfloor 100p \rfloor\).

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