[chezlaw]

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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.

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Its not a fairness issue. The confusion is whether there's some external book-keeping going on.

chez

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Right, he accepts that the coin is fair, he just thinks its hyper-fair.

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Yes, if we were talking about picking black cards from a deck without replacement then the friend would be correct about hyper-fairness.

Its a very common view, some people can't be persuaded against hyper-fairness even when there's no reason to believe the events are dependent and all the evidence demonstrates independence.

The main point for the op is its not a misunderstanding of statistics so concentrating on statistical principles isn't going to clear up any confusion.

chez