NL QQ hits Q on turn -- how to get more value?

Since most Ax hands (+) would most likely get the money in by the river we should concentrate on maximizing our value versus the range that can't call a shove on the turn.

What range do you think that is and how can we do the above?

What range do you think that is and how can we do the above?

I think that I can keep KK+ out of his range.
These two would almost certainly have 4Bet pre.

A4,A9,44,99 are still possibilities though.
These hands could have been hoping for a std CBet to c/r

So I would put his range on the turn as:
A9+,44,99-JJ KT+ might also fit his betting pattern, but would be unlikely to call a river shove unimproved.

River cards I don't want to see:
Spades & broadways (Aces & queens are OK though)

If I made my turn raise about $1.30, then a river shove is just about pot sized.
Most of the range above would call that, except for busted straight/flush draws, which would only happen if he actually held those.

Flop Play:

Betting here disguises the strength of your hand and also makes it more straight forward to play. It is also good against players who think your range is wide and will float flop with a wide range of hands since you are bluffing so often on this flop.

To give an example from my own experience at higher limits, when I bet here, people will float me with stuff like JhTh (backdoor draws) and then bluff the River if I check the Flop. The reason is that I am really aggressive preflop and my range is air heavy even on Ace high Flops.

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But checking here is a better play, especially at lower limits where people just misplay so hard vs a Flop Check. You can't really bet for value vs worse, because lower PPs like TT will be scared of the Ace. You also can't bluff out better hands like AX. I don't think the situation described above will apply to you.

So from this perspective, you shouldn't bet the Flop. This is more or less of a Way Ahead Way Behind situation, where he either has 2 outs vs you (with his underpair) or he has you crushed (you have 2 outs vs his set or Top pair). Not too much need to bet for protection either.

You would have to call a Turn bet and perhaps even a River bet. Base your decisions on his timing (snap bet or tank forever and bet), sizing (big or small), and tendencies (is he aggro or passive?)