[Sephus]

the correct answer (if it's possible that the coin is not fair) is switch to tails, because you have slightly more evidence that the coin is biased toward tails than toward heads.

if you somehow know that the coin is unbiased it obviously doesn't matter.

the only way to justify preferring to stick with heads rather than switch to tails is if you came into the day suspecting that your friend is more likely to bring a coin biased in your favor (heads) than his own (tails).