Assume that we toss a coin n times and the result looks like this
HTHTHTHTHTHTHTHT... . Would a (Probability-) Frequentist conclude that that the probability for the coin to land heads is 0.5? It seems to be the long run frequency, but on the other hand it is not really random whether the coin lands heads or tails, which makes me kind of reluctant to talk about probabilities in this case. As P(Heads|uneven) = 1 and P(Heads|even) = 0 the example strengthens my intuition, that probabilities reflect our knowledge and reasoning abilities rather than some objective property (which is how I believe Frequentists interprete probabilities). Even if we assume that the long run frequency exists, it is not this fact, that we attribute a 0.5 probability to the above example but our lack of knowledge whether it is an even or uneven try.
EDIT: While all the answers were helpful I want to add that my focus is more on a philosophical level. Frequentists define probabilities as long run frequencies, the above example is a long run frequency, the randomness/predictability of the experiment however depends on the information state of the observer. Does this imply that probability is subjective?