A coin toss isn't exactly 50% for both sides in a real life scenario, hence the difficulty to reproduce the experiment exactly like its theoretical description. A sequence of 10 coin tosses resulting in heads/tails is not impossible even if it is hard to reproduce, it simply has an absurdly low probability of ocurring.

This focus on the theoretical side of things, the 'comfy confines of calculation', isn't a bad thing, the paradox is still an interesting thought experiment.