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H. G. Muller wrote on Sun, May 25, 2008 03:07 PM UTC:

I would have thought that 'twice the same flip in a row' was pretty
unambiguous, especially in combination with the remark about two-sided
testing. But let's not quibble about the wording.

The point was that for two-sided testing, if you suspect a coin to be
loaded, but have no idea if it is loaded to produce tail or heads, thw two
flips tell you exactly nothing. They are either the same or different, and
on an unbiased coin that would occur with equal probability. So the
'confidence' of any conclusion as to the fairness of the coin drawn from
the two flips would be only 50%. I.e. not better than totally random, you
might as well have guessed if it was fair or not without flipping it at
all. That would also have given you a 50% chance of guessing correct.