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Suppose we play a game where we each pick a pattern of three coin flips, and then continue flipping a fair coin until one of

Suppose we play a game where we each pick a pattern of three coin flips, and then continue flipping a fair coin until one of us wins by seeing the pattern they chose. I choose "HHT" and you choose "HTH". What is the probability that I win, rounded to the nearest tenths place (e.g. 0.6 for 60%)? Feel free to reason this out, calculate it by hand, or simulate it in R

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