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thats the problem though isnt it?
Scenario 1: We bet x
Villain has 3 options
Folds, which he only does with hands we are currently beating and something we dont want
Calls: Something hands we beat and hands that beat us may both do. This includes flush draws, slowplayed jacks, slow overpairs, straight draws etc. This gives us no information and if he bets river we have to fold (although we may be committed depending on the bet x)
Raises: he can do this with hands we beat like strflush draws, a jack, a set, or something crazy and unreasonable that is typical of a 2nl villain. We have to fold here too, although that pot commitment thing is there.
Situation 2: We check
villain now has check or bet
check: all hands we beat, and some slowplayed hands...at 2nl this is likely to mean "i got nothing" though considering the turn check.
bet: because many 2nl villains know about the "i got nothing" sign, many will try to steal the pot on the river with grabage hands, including a pair of 6s, Ts, busted draws, and a whole bunch of other random stuff. Of course, he also does this with hands that crush us. THe thing is though, his bluffing % increased when we checked, and thus we can call a reasonable bet profitably.
This thinking is assuming no info on villain and that the 10 cent donk bet on the flop didnt mean "i have a jack i hope its good".
That is pretty much the jist of my thinking, in that betting will only be bad for us as we lose money if we're beat and lose money if we're not (by not winning more from the river bluffs).
One last thing, i agree that QQ is somewhat marginal in this particular spot, but it is also because of this fact that we dont want to be investing a large amount of money. Id rather save the big pots for situations where its a easier situation.
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