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(1) EP limper, we raise AQo on the BU, limper calls...
We are way ahead here, and am always loving this situation. Your range is assuming villain is limping hands like JJ-AA, AQ-AK, KQs, etc, when in fact those hands usually aren't in his range, due to the fact he usually opens those hands himself. Instead, a weak player's limp/calling range in this situation will consist of alot of small-mid pps, suited connectors, suited gappers, 'weaker' broadway (QTo, KJo, etc), as well as some other retarded trash like A4o, etc. Our equity is going to be ahead of their range preflop, we are going to be in position postflop, and this leads to +EV spots.
(2) AQ on button, one 3x raiser from CO.. Call or 3bet?
This is dependent on a number of villain's tendencies. Depending on villain's opening range, and the range of hands he would continue with facing a 3bet, should be examined to determine our action. If he's opening a wide range, then calling is +EV, as we have sufficient equity as well as a positional advantage. If he's opening a narrow range, then our equity decreases, while things like reverse implied odds increases, and the hand merges closer to a fold (probably never a fold CO v Bu).
If he is opening a wide range, and continuing with a narrow range of only premiums (like JJ+, AK), then calling is still +EV due to us having enough equity against his opening range. However, 3betting is bad because we are a dog to his 3bet calling range (which will obviously differ from his opening range). In situations like this, villain will be folding hands you beat, like AJ/AT/etc and only calling with hands that are a favorite over your AQo. Thus, a 3bet here would builld a large pot that you are an underdog to win.
However, if villain is opening a wide range, and continuing to a 3bet with some dominated hands, then 3betting very well could be correct. If he's calling with hands like AJ/AT/KQ/QJs, then our equity against his 3bet calling range increases. This makes building a large pot profitable because now not only do we have position, we are a favorite to win the hand.
(3) AQ in a blind battle
Once again it's dependent on villain's range. If BB is a competent opponent, then an aware SB should not be opening a very wide range. Because BB has position on the SB, the BB should call and 3bet with a fairly high frequency. However, much SBs aren't competent, and just open religiously because they already have some money 'invested' in the pot. So I would never just fold to a SB open here. Calling is definitely +EV. To determine if 3betting is better, then you need to again look at his 3bet calling range, and see how AQo fairs there.
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