You have AA every hand . . . when do you quit?

[Borodog]

My apologies if something like this has already been posted. I don't frequent the Theory forum much.

Here's an interesting thought experiment that came up because of a recent post on another board about Daniel Negreanu buying into a $5-$10 no limit hold'em game at the Wynne with $125,000.

Let's say that you are sitting at the $5-$10 NLHE table one morning. You've just bought in for $500, and are waiting for other players to come along. Up walks Daniel Negreanu. He sits down across from you, introduces himself, he's a nice guy, you chat. No one else is showing up to play though. So to cure his boredom, he offers you a proposition.

Daniel buys in for $125,000. He offers to let you keep the Ace of clubs and the Ace of spades, while he is dealt two random cards from the well-shuffled remainder of the deck. Daniel will then go all-in preflop every single hand. Just to make this clear, every hand you will have pocket aces against Daniel's two (new) random cards (i.e. he gets new random cards each hand), and he is going all-in every hand. If you call, the flop, turn, and river will be dealt and the best hand wins.

Edit to add: If you go broke, the game is over. You cannot rebuy.

How many hands do you play?