Here is the problem with your analysis, first you dont present stack size but if you a decent stack your the donkey, you pushed he called. He may qualify as an idiot, but what the hell do you care if you push all in with AQ and have best hand from the shortstacked position you would hope for and maybe even expect a call, you got unlucky, but if he puts you on pushing with any ace as long as he has two live ones he figures to be close to foury percent to win. So not necessarily a bad call especially with a large stack.