[Check_The_Nuts]

if he has AK and is playing it for a check on the flop he won't bet the river.

I probably shove the turn or the flop, not sure which. 4bet pot I'm never folding, so its better to get the money in to maximize value.

The problem with not shoving at some point is if he had KK or QQ on this river he would shove 100% of the time and I'm pretty sure you would call every time.