Ok here's something which I've debated with friends and co-workers in the past. Now it is common knowledge that if you flip a (perfectly balanced) coin the outcome will not be influenced by the outcome of previous flips, there will always be a 50/50 chance that head will come up and equally so for tails, I completely agree with this. However let's say hypothetically we flip a coin 1000 times, then in a perfect enviroment 500 should be heads and 500 should be tails. Ok then let's say on the first 500 flips even with a perfect coin in a perfect enviroment that heads came up every single time (that will probably lead to the conclusion the coin is not balanced, but lets just say it is)... then statiscally shouldn't the next 500 flips be all tails and hence making the chance of tails coming on flip 501 be higher than 50/50? As I mentioned I totally agree with notion of each flips being completely independent of any previous outcomes, but yet everytime I ponder this notion I can't help bringing in the latter scenario which on my reasoning seem to contradict it. Anyone wanna comment or explain to me where my reasoning is faulted?