When we toss an unbiased coin, the probability of observing both heads and tails is 1/2. I take that to mean that over a really large number of coin tosses the number of times the coin will turn heads will be almost equal* to the number of times the coin will turn tails.
My question is, if we witness a series of coin tosses that happens to have many more number of, say heads, than tails then will we not expect the upcoming coin tosses to be 'mean-reverting' i.e. more inclined to produce tails than heads - only in order to maintain the definition of probability being 1/2 as per the previous paragraph?
I think what I am really asking is whether an unbiased coin-tossing is a Markov process. I would add that if it is, then my understanding of why the probability of heads/tails is 1/2 is wrong.
[*] - If not, then we need more coin tosses such that the ratio of number of heads (or tails) to the total number of coin tosses approaches 1/2 as the number of coin tosses approaches infinity.