So can I start with
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
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