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Viliam comments on Open thread, Nov. 23 - Nov. 29, 2015 - Less Wrong Discussion
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...because heads occurring separately are on average balanced by heads occurring in long sequences; but limiting the length of the series puts a limit on the long sequences.
In other words, in infinite sequences, "heads preceeded by heads" and "heads preceeded by tails" would be in balance, but if you cut out a finite subsequence, if the first one was "head preceeded by head", by cutting out the subsequence you have reclassified it.
Am I correct, or is there more?
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.