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Are you in a ring or tournament? (Your examples sound like tournaments.)
Who is it that moved in on you? Are the loose, tight, short stacked, drunk, stoned etc...?
When they moved in did they do it from UTG, Button, or somewhere in between?
How many people were already in the pot and were they all limpers or raisers?
What odds are the pot offering on the call?
Add up all of the above factors and make and educated guess. It is foolish to say only call AI with A, B, or C hands.
Here's an extreme example: Let's say you are big stack in tournament with 27o in the BB. Everyone folds to Smallest stack who can't cover the next blind goes AI from the Button. Blinds and antes offer you sleightly less that 1:1 pot odds or your call. What do you do? Hell, call his AI w/ 72o. I've seen it done many times and I've seen 72o knock out the short stack.
Tourny play is much more complicated overall, but calling AI is always a much graver decision that being the first one to push because of the gap concept ie. you need a better hand to call a raise with than you do to put in the first raise yourself.
In a ring game, try to avoid it unless you have the AA, KK or QQ.
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