Re: burning-half-the-deck problem
Instead of taking this convoluted problem, why not break it into a series of easy problems, and see where you guys first differ?
For instance, just ask about 4 aces in a shuffled deck. Then 4 aces in a half-deck. Then 2 aces in a half-deck. (I expect she'll disagree when you cut it in half.)
-Sam
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