Oops, good catch. So a few of my answers were off by a factor of 2.
<font color="white">So if you include the end, the expected number of times the deck is even is 4^n/(2nCn). Your expected value is 4^n/(2nCn) - 1.
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It was a good observation that this was connected to the previous problem.
The value is also very similar to the value of the
multiplicative version.