Three Heads Or Bust
You flip a fair coin repeatedly and stop as soon as one of two patterns has appeared in consecutive flips: HHH or THH.
The race, written as a chain whose state is the useful suffix of what you have seen so far:
| state | on H | on T |
|---|---|---|
| start | H | T |
| H | HH | T |
| HH | HHH wins | T |
| T | TH | T |
| TH | THH wins | T |
What is the probability that THH appears first?
Answer format: round to 3 decimal places.
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