Answer: HTT will take fewer flips (average 8, HTH an average 10)
After you throw an HT, the odds of winning either in the next throw are 50%. But if you lose playing the HTT game, then you've just thrown an H and you are 1/3 into the pattern again. See http://ceki.blogspot.com/2008/08/hth-or-htt.html
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