Next toss after a streak from an ordinary coin

Someone takes an ordinary-looking coin out of their pocket and tosses it three times, getting heads each time. What would you estimate as the probability that the next toss is a head? How would your estimate change if it had come up heads $100$ times in a row?

About $1/2$ after three heads; close to $1$ after a hundred. Three heads happens one time in eight with a fair coin, which barely shifts a strong prior that pocket coins are fair. A hundred heads has probability $2^{-100}$ under fairness, so even a tiny prior weight on a trick or heavily biased coin dominates the posterior and the next toss is almost surely heads.