[Izverg04]

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Another post commented: well, what happens when you win, do you do it again? It brings up an interesting point, because of course the expected value of taking this proposition to infinity is that you'll eventually go broke (and most likely in the first 10 such 'double up' scenarios).

So the scenario is a little flawed. But as a one-time shot, i'd put my entire online bankroll on AA all-in preflop in a heartbeat.

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This a good illustration that everyone who said Yes uses an artificial definition of "bankroll". When you win, the wins are added to your bankroll, right? So if you call the amount of money that you put initially on the line "bankroll", it is now doubled, and since you agreed to put your "bankroll" on the line, you'll put it again and again until you lose it.

The reason you are willing to put what you call "bankroll" on AA is because it is a small fraction of your bankroll. When you double it up a couple of times, this amount becomes a much larger fraction of your bankroll, and so you are no longer willing to put it on AA.

Personally, I use Kelly/20 betting, and I'd put at most 8% of my bankroll on the line -- independent of the size of my bankroll.