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I don't think this is correct. See my reply to AstraSequi.
(But I'm not certain I've understood what you're proposing, and if I haven't then of course your analysis and mine could both be right.)
Oops, you're right.
Using the words from my previous comment, now the trick seems to be that 'heads occurring separately are on average balanced by heads occurring in long sequences' -- but according to the rules of the game, you get only one point of reward for a long sequence, while you could get multiple punishments for the separately occuring heads, if they appear in different series. Well, approximately.