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Jiro comments on Bayesianism for Humans - Less Wrong
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The statement, "You should expect that, on average, a test will leave your beliefs unchanged," means that you cannot expect an unbiased test to change you beliefs in a particular direction, as is clear from the original post.
Of course you expect to hold different beliefs after the test. If you didn't, the test would not be worth doing. But you are not more likely to end up at (100% heads, 0% tails) than (0% heads, 100% tails).
On the other hand, if you think it is more likely that you will end up at, say, (0% heads, 100% tails), then you cannot rightly claim that you currently believe the coin to be fair (your 50%, 50% estimate does not reflect your true expectations).
I would suggest that you expect your beliefs to be changed in 100% of cases. Currently, you believe in a 50% probability. After doing the tests, we have a set of universes, some of in which you believe a 100% probability and some of in which you believe a 0% probability. Your belief changed in every single one.
X and Y can be averaged out, but belief in number X and belief in number Y don't average out to be "belief in the average of X and Y".