I completely understand that the probability of the next toss is unaffected by the outcome of the previous ten, however, the probability that the same outcome of those tosses will appear 10 times in a row is not 1/2 it is 0.5 to the power of 10 and this is the situation we are discussing. I would refute your suggestion that I am confusing myself good sir, (regardless of whether you believe me or not I am currently in an engineering lecture at the university of Cambridge which is a very maths heavy course) Google how to work out the probability of a coin producing heads 10 times in a row and you will get the same answer I have given you