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The analogy should have been "if you roll two dice once, each is equally likely to be one through six. But if you roll two dice together, the more times you roll them the more likely they are to average around seven."
Rolling 1 die a bajillion times will not result in a peak around 3 or 4. (plowing through The Drunkard's Walk; statistical errors are a pet peeve at the moment)
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Mathematical averages are NOT the same thing as statistical modes.
Statistics is NOT algebra. Here there be math:
thenewgreen · 4601 days ago · link ·
Just read the description of The Drunkards Walk, it sounds intriguing. Enjoy and thanks for the correction.