Please look more closely at the article Submitted by Anonymous on November 24 2012.
The article is not really looking at the odds of a combination of three flips of a coin where there are 8 possible combinations and as you have stated TTH is one of those eight combinations, and as an equal chance of coming up as the other seven combinations.
The article is looking at a number of flips and the first occurance of a combination, they looked at the easiest combination to see HHH and said that if HHH was not the first three flips then if you kept flipping THH must come up before HHH.
This is a random number of flips TTHTHTTHHH as you can see HHH occurs at the end on flips 8,9 and 10 but just before it flips 7,8 and 9 have THH so THH comes up first.
So as long as there is a T in one of the first three flips THH will always come up before HHH, you can write T's and H's all day long and as long as you have a T in the first three flips then THH will always come up before HHH.
Please look more closely at the article Submitted by Anonymous on November 24 2012.
The article is not really looking at the odds of a combination of three flips of a coin where there are 8 possible combinations and as you have stated TTH is one of those eight combinations, and as an equal chance of coming up as the other seven combinations.
The article is looking at a number of flips and the first occurance of a combination, they looked at the easiest combination to see HHH and said that if HHH was not the first three flips then if you kept flipping THH must come up before HHH.
This is a random number of flips TTHTHTTHHH as you can see HHH occurs at the end on flips 8,9 and 10 but just before it flips 7,8 and 9 have THH so THH comes up first.
So as long as there is a T in one of the first three flips THH will always come up before HHH, you can write T's and H's all day long and as long as you have a T in the first three flips then THH will always come up before HHH.