Will Hillary Clinton run for the next president?
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I think the only way that would happen is if Obama chooses not to run for re-election. It is not impossible for her to run in 2016. She would be 69, and that could be regarded as "too old," though Reagan was about six months older.
Her best shot was 2008, and she has not been a particularly stellar Secretary of State (though a reasonably good one).
She might point out that women live longer, and if her mother is still alive, say "My 97 year old mother thinks I'm pretty young."