[Wyman]

Does your friend believe the same phenomenon occurs if 10 _different_ coins are flipped and each comes heads? Does he believe that an eleventh coin is more likely to come up tails?

You might try to convince him that the "in the long run, flips should be 50/50" concept should hold across all fair coins, not just for any given coin (this is true). Given this, his logic dictates that flipping one coin influences the flip of another. He may agree that this is silly, or you may now have convinced him that coins influence each other.

This is a very interesting question.