[TheWorstPlayer]

Are you firing twice with AK unimproved? If not, can you explain how you know more where you are on the river when the action goes
preflop - limp, raise, call
flop - check, bet pot, call
turn - check, check
river - bet pot

instead of like this
preflop - limp, raise, call
flop - check, check
turn - bet pot, call
river - bet pot

I don't think you really know where you are in either case. That's why heads up play is all about making reads and mixing up your play. If anything, I think that you life is probably a bit tougher in the first case because you have shown weakness on the turn after betting the flop and so your opponent might be betting the river on a bluff induced by your check. In the second line, once you call on the turn, your opponent should fear a slowplay and therefore may be more hesitant to fire again on the river. I think AK unimproved is less likely to be good in the second line than the first, FWIW. Although by no means is it certainly ahead in either case or certainly behind in either case. Of course flop texture and opponent tendencies play the largest role in determining where you are.