The answer I'm editing says the odds are 1 in 8. This is true only if you actually mean the probability of getting 3 tails in a row, rather than just 3 of either heads or tails in a row.
In mentioned case, the first flip doesn't matter which side it lands on, just the proceeding two flips do.
So, the odds of flipping a coin three times with the same outcome are 1 in 2^2 or 1 in 4.
The odds of flipping three tails in a row are 1 in 2^3 or 1 in 8.
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