I am closed in a room and decide to flip a fair coin 5 times (1/2 probability of H and T) and get 5 heads HHHHH so I call a friend to join me inside and he does not know I had flipped the coin 5 times.
If I flip the coin now the 6th time, for my friend (for him it is the first flip) the chance of having head H would be 1/2, for me is it the same 1/2? But actually the probability of having 6 heads in a row on 6 flips is not 1/2.
If we play and I bet that the next flip is tail T, I will win more times then him.
I actually simulated this on 4,459 series of 6 flips 431 times I win the game (6th flip has tail T) and 75 times my friend wins (6th flip has H).
The interesting thing is that for my friend, that does not know about the past results, the probability is the same as it is on one coin flip game so 1/2.
Which is the real probability to have H heads at the 6th flip of 6 coins after 5 heads HHHHH?