My intended correct answer is that, on this data, you technically can adjust your belief very slightly; but because the prior for a biased coin is so tiny, the update is not worth doing. The calculation cost way exceeds any benefit you can get from gruel this thin. I would say "Null hypothesis [ie unbiased coin] not disconfirmed; move along, nothing to see here". And if you had a political reason for wishing the coin to be biased towards heads, then you should definitely not make any such update; because you certainly wouldn't have done so, if tails had come up six times. In that case it would immediately have been "P-level is in the double digits" and "no statistical significance means exactly that" and "with those errors we're still consistent with a heads bias".