this is a though experiment,

please lets not get off track

or upset .

We have some absolute truths with tossing a fair coin where 100 % of all tosses are either H or Tail.

1) The odds at every toss are 50:50 that it will be a tail

2) Each toss is independent of the last, the coin has no memory

3) Over a long enough set, there will be the same number of H as T tossed

4) At any given time, there can be more H than T ( or vice versa )

Which leads to the points in other posts, that there is a calculatable probability that for say 1000 tosses there will be 500 H, or 499 H or 498 H etc.

Given 999 tosses,

say we have 490 H and 509 Tails. We can find the probability of that.

say we have 491 H and 508 Tails. We can find the probability of that.

I now have a conundrum,

Given the 490 H case above,

the next toss is 50:50 a H.

But we also know that over time there should be the same number of H as T

So over the next "n" samples there must be more H than T to move towards the 50:50,

if there were not more H, then T would dominate, and the coin is not fair

But we have said the coin is fair, and it has no memory

How do we square that circle