[damaniac]

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1) Hero is in BB with A [img]/images/graemlins/diamond.gif[/img]J [img]/images/graemlins/club.gif[/img], 5 limp in front, Hero???????

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Check, you probably have an edge, but it's fairly small, especially OOP, and you can make up for it by keeping the pot smaller postflop (SSHE has an example where the NPA specifically mentions that you might want to check AJo here).
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2) Hero is in SB with K [img]/images/graemlins/spade.gif[/img]T [img]/images/graemlins/spade.gif[/img], 4 limp in front, Hero??????

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I raise quite a bit here, the looser the opposition is the better. I'd be less inclined to raise if there were a tight passive limper or two as there's at least a decent chance of domination, but I don't think it matters much. If you do raise here, make sure you have the discipline not to autobet some missed flops into 5 opponents just b/c you raised preflop. Some people can't help that.

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3) Hero is in BB with 8 [img]/images/graemlins/club.gif[/img]8 [img]/images/graemlins/heart.gif[/img] and 5 limp in front. Hero?????

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This one is interesting. We have an edge in equity, but raising bloats the pot and permits overcards to call profitably, which really reduces our chances of winning. OTOH, we're also getting reasonably close value in terms of flopping a set. If the table is passive I raise here, sometime the flop gets checked around when we miss (not often), if aggressive I raise b/c I can hopefully induce other players to play more aggressively to win a bigger pot, so that when I do flop a set I'll make more, but I don't know that that is correct.

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4) Hero is in SB with A [img]/images/graemlins/diamond.gif[/img]9 [img]/images/graemlins/diamond.gif[/img] and 4 limp in front. Hero?????

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Again, few tight/passive limpers, or passive in general, easier raise, as you are dominated less often. I raise this most of the time.