Teaching an intelligent guy about a basic statistics concept

[Wyman]

If you picked up a coin I had never seen before and flipped 10 heads in a row, I'd be inclined to predict that your next flip will be heads, questioning the fairness of the coin.

If your friend agrees that this is a fair coin, ask him what "fair" means (on each flip, the probability of heads = 0.5). This should end the discussion. If there is a question of whether the coin is fair, the obvious guess is that the coin is biased towards heads. Tails is the least logical thing for him to predict.