Re: guaranteed aa?
QuattroFour4 has it covered, but any question of this type involving infinity is silly, anyway. Whenever you have an infinite number of trials, all possible outcomes will happen an infinite number of times. If you sit at a table and get dealt an infinite number of hands, not only will you get AA an infinite number of times, but an infinite number of cards will also fly off the table and hit you in the eye and an infinite number of dealers dealing the cards to you will have an infinite number of heart attacks and an infinite number of cocktail waitresses will spill an infinite number of drinks on your head. Obviously, those events are outside the scope of your question, but I am illustrating a point. Infinity is usually useless in this type of question.
A better question might be, "If I get dealt a million two card hands..." in which case you have to choose your own threshold for "guarantee" because the chance of you NOT getting AA in a million hands is very, very tiny but not quite zero.
SpaceAce
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