[nut case ace]

You can't bet this because he's calling with any piece of that board. If he had a big ace too i think he would have 3-bet before the flop and that's the only hand that you can beat that might call. Also, even if you do have him beat, a bet gives him the chance to check-raise you with the worst hand forcing you to fold. There are just way too many ways he calls with the best hand and not enough that he calls with the worst hand to make a value bet correct here.