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I flip a coin three times, and then another three times. If the number of heads is the same the first and second time, I win. If the number of heads is different, then I win. If I win, you pay me one dollar. If you win, I give you 3 dollars. Is this game worth playing?

So I've figured out that for this game the $E[X] = 3p - (1-p)$ but I'm having a hard time coming up with $p$.

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    So you win both times? Certainly worth playing for *you* ;-)2012-10-16
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    You win regardless of whether the number of heads on the first, second and third tosses is the **same or different** as the number of tosses on the fourth, fifth, and sixth tosses. So the game is definitely worth playing for you, and not worth playing at all for me. If it is required for me as a matter of law to play, let's skip the coin tosses and I will give you a dollar.2012-10-16
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    Can you explain that a bit more formally? I'm curious as to the actual expectation of the game.2012-10-16
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    They're commenting on a typo in the text regarding who wins when.2012-10-16

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