Maybe I expressed myself somewhat misleadingly. I am not saying that she is surprised because the coincidence is more unlikely than the sequence. You are absolutely right in correcting me that the latter isn‘t even the case (also since P(HHTHTHHT/„HHTHTHHT“)=P(HHTHTHHT)=1/2^8). What I was trying to say is that her suprise about the coincidence arises from the circumtance that the coincidence is both unlikely and looks like a pattern. That fact that an event is unlikely is a necessary condition to be surprised about its occurence but not a sufficient condition.
I agree with you when you are saying that how we structure our perception of the world is biased in some way towards what we are „tracking“ in our minds. And I also agree that this bias could be mathematically modelled by the event spaces you are proposing. But I would not go too far to say that we do only observe such events we are currently tracking (please let me know if I misread you or you feel strawmanned here, since it is absolutely not my intention to annoy you!). If this was true, then we could not observe the event „any other coin sequence“ as well since this event is by definition not being tracked. In fact, in order to detect a correspondence between a coin sequence that we have in mind and the actual sequence, our brain has to compare them to decide if there is a match. I can hardly imagine how this comparison could work without observing the specific actual sequence in the first place. That we classify and perceive a specific sequence as „any other sequence“ can be the result of the comparison, but is not its starting point.
In conclusion, I do not see a contradiction in not being surprised to observe an extremely unlikely event.
Yes. Our human mind is obviously biased to detect patterns. And people tend to react surprised if they observe patterns where they did not expect them to find. If someone has a specific sequence of coin toss results in her mind (eg. „HHTHTHHT“) and she is able to reproduce it with an actual coin on her first try, then she will likely be surprised. What she is really surprised about however, is not that she has observed an unlikely event ({HHTHTHHT}), but that she has observed an unexpected pattern. In this case, the coincidence of the sequence she had in mind and the sequence produced by the coin tosses constitutes a symmetry which our mind readily detects and classifies as such a pattern. One could also say that she has not just observed the event {HHTHTHHT} alone, but also the coincidence which can be regarded as an event, too. Both events, the actual coin toss sequence and the coincidence, are unlikely events and both become extremely unlikely with longer sequences. My reasoning is, that the coincidence is not more surprising than the actual sequence because it is an even more unlikely event than the sequence. Though both events are unlikely and therefore unexpected, the coincidence is more surprising to us simply because it looks like a pattern.