[CraigJ]

Exactly the larger the sample size the the closer it is going to come to 50/50. But you are still going to have deviations on both sides. One person flips 20% heads another person flips 80% heads, they average out to 50%. Again a large deviation like 80% or 20% is RARE, but if you have a large enough sample you WILL find it. But it doesn't really affect the over all results of the final average because 1) it is rare and 2) as I mentioned above you will find a deviation on the other end which in a sense balances it out.