Poker Mathematics - What To Do When You Flop A Set

You get a pair of four in pre-flop. then the flop comes 9s, Ah, 4c

How would you play this?

Generally I like to come right out firing when I am out of position to the raiser, especially on a flop like this, it's a set miners wet dream. You bet and bet BIG, at least the full pot. You really hope your opponent has AK, AQ, AJ, etc here. Betting into him is often best because if he's got big slick, what's he going to do? He's going to raise you, and by that time it is too late, all the money goes in. You are giving him the best opportunity to hang himself. Check raising is not the best play because it allows your opponent to get off cheap if he bets the flop and you raise him. Ex pot is $10 on flop and you both have $100 behind, you check , he bets $10, you raise to say $40, he folds. All you win is $20. If you lead into him for $10, he's going to raise you to $40, and you push. Even if he folds to your push, you win an additional $30 you would not have if you played it the other way.

On a ragged flop I might check it to the raiser since it is very likely he is holding two high cards that missed. In this case you may only get a continuation bet, and a big flop lead will probably scare him away. I will also do this against loose-aggressive types who raise a lot preflop and usually fire off a pot sized CB. I don't lead because these types of frequent raisers usually have nothing on the flop and are counting on their sheer aggression to take down pots. I like a check raise here because often all you are getting is their continuation bet, and since they are aggressive, if they do happen to have a good second best hand, you are going to get their money anyway.

And sometimes rather than checkraising right off, I will check call and either lead out on the turn, or checkraise the turn.

What it all comes down to is this: When you flop a set your goal is to get all the money in by the river. How you do that depends on the board, your opponent, and your own image.

As far as playing 44 from MP preflop. Look, open limping in NL games is NOT a sin, and don't let anyone tell you otherwise, that is just silly. At this point in the torunament it plays like a cash game, and essentially the blinds are not worth stealing. If you still have 4 or 5 players yet to act, your chances of taking it down with a 4-6 BB raise are pretty low. If you get called (especially in more than one spot) you are going to really need a set to win and might end up costing you more money.

The idea of raising for info here is meaningless. If you get reraised, then you find out you are behind, big deal. You wasted an implied odds hand. If I were to open raise, I would make it two or three times the big blind to go. Sure no one is going to fold that planned on calling anyway, but who cares? 44 is only marginally better than any likely non-pair hand that is calling, and a dog to all other pairs. But the only thing that matters is that you are playing your hand for set value. Making a small raise here is a value bet for the times you do hit your set. You are building a bit of a pot, plus multi-way you are increasing the chances of someone making a second best hand and paying you off.

I am beginning to think that when you make a "proper" sized raise (4XBB +1BB/limper) with an implied odds hand, you are actually cutting down your implied odds in situations where your raise is not very likely to win the blinds uncontested.

You will often not flop much, and even when you do flop a monster, it's not likely your lone opponent caught much.