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I ran some numbers

On the turn...
Against {66+} you have 11% equity on the turn
Against {66+,AK} you have 18% equity
Against {66+,AK,AQ} you have 30% equity

On the river...
Against {66+} you have 0% equity
Against {66+,AK} you have 8% equity
Against {66+,AK,AQ} you have 25% equity

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I did that as well. If there is any chance he does this with less than a pair, you have to call because of pot size. I guess I would call here most times.

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That statement is not quite correct. If there is a 5% chance he plays AK / AQ like this then it is not correct to call.