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I've been studying NL holdem for a while and feel like I can grasp the basic concepts pretty well, but looking at GTO solver play post flop really makes me wonder. When I'm in a spot where I completely missed the flop, I have no idea if I should be betting as a bluff or not. I understand late position is helpful, but what are the other factors to consider in such a situation? Stack sizes?

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what are the other factors to consider

Short answer: everything.

This play is common, so common it has a phrase to describe it; Follow up bet. For many players, it is almost common to do a follow up bet every time they raise, and often players will make a bet when it is checked to them rather or not they raised before the flop.

This is just bluffing and bluffing is often good to do. I personally watch closely when I am in a hand. If it looks good to take the pot with a bet, don't care what my hand is I take a shot. And then I watch more, to figure out if I need to shoot again or cease fire or give him a river to miss his draw. The simplest way I can describe that thought process is that you put the player on the range of hands they have and make a judgement about how likely they are to lay down the hand.

When your doing a bluff, you also need to be watching your own tells. I was once called on a stone bluff by a guy with jack high and lost. I thought the guy was a moron to call the mighty me with jack high, but I am sure there were tells there that gave me away.

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