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TheOtherDave 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).
That said, it's far from the most easily accessible formulation of that meaning imaginable.
I mean, sure, the future state in which half of my measure has ~1 confidence in "heads" and half my measure has ~0 confidence in "heads" is in some sense not a change from my current state where I have .5 confidence in "heads", but that's not the interpretation most people will adopt of "leave your beliefs unchanged."
It seems more accessible to say that if I expect a test to update my beliefs in a particular direction, I should go ahead and update my beliefs in that direction now (and perform the test as confirmation).
Of course, this advice presumes that I won't anchor on my new belief. Which, given that I'm human, is not a safe assumption.