Mason is sexy

[Demiparadigm]

http://www.twoplustwo.com/magazine/c...lmuth1205.html
He is specifically talking about limit, but this has obvious NL applications as well.

Suppose you are in late position and hold

3 3

There is a raise by a player in early position, and three other players call him. Should you call the two bets cold?

First notice that you almost always need to flop a set if you play to win the pot, and that it is 7½-to-1 to flop a set with a standard 52-card deck. Furthermore, just because you do catch that third trey, it doesn't mean that you have a guaranteed winner. We have all flopped sets and have gotten them cracked, and that's not any fun. So what this means is that your implied odds when you flop a set and win need to be higher than 7½-to-1. I think that 10-to-1 is probably about right.

Notice that in this spot you're likely to get immediate odds from the pot of approximately 5-to-1 since there is blind money in there as well as the other four active players, and one or more of the remaining players, including the blinds, may come. So this means you need to make on average an additional five double-sized bets those times you flop a set and have your hand hold up for this call to be correct. In many games that seems like a tough order to me, so the obvious conclusion is that the pair of treys should quickly hit the muck.

But not so fast. Let's think a little about bunching. Since the initial raiser is in early position, he should have a good hand which probably does not include a trey. Furthermore, by the same argument, none of the callers should hold a trey. Of course a trey could be out there in the discarded hands, but in this situation there are fewer of them than normal. So it seems to me that it is a little more likely to flop your set here than it would typically be. My educated guess is that instead of being 7½- to-1 to catch that third trey, a better estimate is more like 5-to-1.

This means that your implied odds don't need to be 10-to-1 to make this hand playable. Indeed 7-to-1 might be acceptable, and that should be easily achievable those times you make a set and it holds up. So I'm definitely playing any small pair here.

Let's switch to another example. This time you have the same pair of treys in the big blind. Everyone has passed to the button who raises — you know that in this spot he will raise with a large range of hands — and the small blind also folds. Do you call?

For your call to be profitable, it means you must win the pot a fair amount of time. This includes those times you flop a set, plus those times you are able to win without improving. But what are your chances of flopping a set here?

It's my conjecture, due to bunching, that it again is no longer 7½-to-1. Instead 10-to-1 is probably a better estimate. That's because given the way this hand has developed with everyone folding, it should be more likely than normal for a trey to have been discarded. This also means that one of the ways in which you rely on winning the pot, namely flopping a set, is a little less likely. Thus, in my opinion, this hand should be folded here, and I doubt if many players do it.

Another point I thought of is flopping a straight draw with 2 broadway cards in a mutiway raised pot. It is very likely that someone holds some of your outs, or you could be up against a set with a strong redraw if you happen to hit on the turn.
There are a lot of applications here that many players don't consider.

[midas06]

I agree, a lot of people don't consider that their outs may not be good.

In games like Stud it's easy to see that your outs are bad. In HE, do you have to assume that some of your outs aren't good?

[harmisajedi]

In games like Stud it's easy to see that your outs are bad. In HE, do you have to assume that some of your outs aren't good?

depends on preflop action. i hate playing unraised pots because everybody could have virtually anything (i've been in a situation where my nut flush went down to a boat made on the river b/c i refused to believe anybody would play q2 from midposition.)

if 2 people call a 3xbb raise utg & i'm in last position w/ 56s, i'll usually put 2 ppl on high card & one on a pp hoping to hit their set. if 3 people call a 2xbb raise in second or third position & i'm the one holding 56s, i have to assume some of the folks in front of me are playing suited connectors too & my open-ended on the flop is not drawing to 8 outs after all.

[BankItDrew]

So in a 4-way tournee game with 2 callers to a 2xbb raise, i should call the extra 1xbb on the bb with 33, because my deposit is 1/8 and the odds of hitting the three are greater than that?

[LeFou]

Of course a trey could be out there in the discarded hands, but in this situation there are fewer of them than normal. So it seems to me that it is a little more likely to flop your set here than it would typically be.

He kinda lost me here. I understood the previous bit about the 8 cards that the callers hold not containing 3s very often. But the discards? "Fewer of them" = "fewer discards"?

[EricE]

Of course a trey could be out there in the discarded hands, but in this situation there are fewer of them than normal. So it seems to me that it is a little more likely to flop your set here than it would typically be.

He kinda lost me here. I understood the previous bit about the 8 cards that the callers hold not containing 3s very often. But the discards? "Fewer of them" = "fewer discards"?

He is saying there are fewer discards than normal...more callers. That being the case it is unlikely any of the callers have a 3. therefore, likely 2 3s still exist in the remainder of the deck to be dealt on the flop/turn/river.

[Telepath]

I'm sorry but I can't agree with the author's idea... I don't mean to be an expert, but anyway.

Pocket threes simply has too much value to be automatically folded to an automatic raise from the button, especially given that you know he can raise with a great many hands in this situation. Headsup there is a 50% chance he won't even hit. There are more outs for you than simply flopping a set.

In this situation I would reraise and lead out betting.

T.

[badandy519]

I'm kinda lost too, how can you assume from the preflop action that someone either called with A3s or chucked T3o?? I understand how you can narrow down someone's range of hands, but how do you discount one particular card value being in play or mucked when it is a 4-5 way flop?

[Demiparadigm]

I'm kinda lost too, how can you assume from the preflop action that someone either called with A3s or chucked T3o?? I understand how you can narrow down someone's range of hands, but how do you discount one particular card value being in play or mucked when it is a 4-5 way flop?

It is much less likely someone is in a raised pot with A3, as compared to an unraised pot.

[badandy519]

Ok, my question was a bad example.... What I meant to ask was how can you figure if either of the two 3's are live or dead? I mean, you could reasonably think that no one is in a raised pot with an unpaired 3 but how can you determine whether one has been mucked or they are both in the deck to come?

[Demiparadigm]

Ok, my question was a bad example.... What I meant to ask was how can you figure if either of the two 3's are live or dead? I mean, you could reasonably think that no one is in a raised pot with an unpaired 3 but how can you determine whether one has been mucked or they are both in the deck to come?

Since you can assume that none of the players in the pot have a 3 you no longer have 2/50 outs, but 2/40 or so...
Your chances of flopping a set have improved from 12% to 15% (a 25% increase)

[badandy519]

ahhhh, i see the light! thanks demi, sorry i'm such a moron.