Unless your gut tells
you otherwise, you find a fold on the flop. On the flop, you only hold the 5th best option, if we are generous and lump in KK along with "any king". As the coaches have pointed out, the runout makes it unique since you now know he definitely didn't have KK and if had two of the other flops that crushed you 88 and TT you just rivered him.
The only time I'd find myself in an all in river showdown would be 1 of 2 reasons. Like I said, I'm going with gut/instinct over gameplay since he is indicating that he has you beat and only does that when he DOES have you beat or when he is bluffing
like he does. Plenty of other spots to not have to have such a tough decision against such a polarized range. The 2nd reason is a SERIOUS leak in my current game since I've returned to online poker in the last year. I will sometimes call it all the way down for information. I used to do this back in the day all the time and it was very profitable in the long run because even when you're opponent tried to use the information he just provided to alter his tactics it was pretty obvious. Nowadays, though, I'd find myself calling for information. No matter the outcome, whether he did win with AA AK or I won with anything else, I wrongly assume that I have learned something about this player. Next thing I know he's shoving all in with the nuts and getting a call and with air, getting a fold and showing to piss me off. It's as though the information I just paid for ended up working in HIS favor instead of my own.