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.
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.