The fact that no new information was gained does <i>not</i> mean that your answer to &quot;what do you think the coin flip was?&quot; will neccessarily be equal to &quot;what do you think the result of the coin flip will be?&quot;<p>All it means is that you can already, before going to sleep, make an unconditonal strategy &quot;when woken up, I&#x27;ll say this&quot;. And your knowledge can easily lead you to a statement &quot;right now, I believe the coin flip will be 50&#x2F;50, but when I wake up I&#x27;ll bet on tails&quot;.<p>The coin flip <i>does</i> change the probabilities significantly after you get awakened - e.g. in the 0:1 chance you know that being awakened implies that it <i>must</i> be that particular result, and the 1:100000000 scenario implies that if you&#x27;re awakened then it either was tails or something extremely unlikely happened. The &quot;no new information&quot; clause simply means that you get already informed about this probability before going to sleep, not after the coin flip.