Should I call all-in here with bottom set?

Question

Game is $1/$3 NL Hold'em

Hero is in a middle position with $410. Villain is in an earlier position with approx $540.

Pre-Flop:

A few callers, including villain. Hero sees 22 and calls $3. In total, 7 people to the flop.

Flop:

Qd-9c-2d Hero has bottom set.

One or two players check to the villain, who bets $12. Villain seems to be a very solid player who's made a couple very good reads.

Next player folds and hero raises $48.

Folds around to villain who thinks about 10 seconds and pushes all-in.

Question:

Do you call here?

Epilogue:

The hero chose to fold here so unfortunately, I can't report back on what the villain held. The hero's reasons for folding are: 1) based on watching the villain's hands, the villain was playing very wisely and not making foolish bets/raises. Thus, the hero decided the villain wouldn't risk 75% of his stack unless he was very confident he was ahead. 2) it was conceivable the villain would limp with 99. 3) the hero felt he could wait for a better situation against a softer opponent.

Answer 1

I think all-in is definitely the best move here in a cash game, where the hero is most surely ahead.

The villain, being in dealer position, would most likely have raised with QQ or 99 pre-flop. Without knowing about your table image, the villain could have been playing Q-x, 10dJd, or could have 2 pair.

So of the likely holdings for the villian there are far more possible hand combinations that leave the hero ahead. In addition, the hands in which the villain is ahead don't suit the betting pattern pre-flop.

Now the holding that gives the villain the most number of outs is 10dJd. Even with this holding, the hero has a 60% chance of winning according to PokerStove Calculator (this is because you also have outs, if the board pairs, or if a 2 comes up.)

Therefore in a cash game, the worst scenario is he has 10dJd, but you are still ahead, so you should definitely call.

If you are short stacked in a tournament, again you should definitely call. You have to be prepared to take more risks if you are short stacked, because you will get less of these opportunities.

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Further Mathematical Analysis of the Situation:

In the table below, I have a table of the hands that a villain would reasonably bet all-in on. The "raw probability" column gives the chance of a villain being dealt these hands given the card information we have. (i.e. hero's hand and the flop.)

The "relative probability" column, gives the probability the villain is dealt the corresponding hand, given that he is dealt one of the combinations listed (Raw prob/total).

Finally "Winning Prob" column tells us the probability the hero's hand will beat the corresponding hand given the flop. The chance of winning can be determined by multiplying "relative probability" by "winning probability" for each card and adding together. The end result is approximately 62% in favor of the hero.

| Raw Prob         | Relative Prob | Winning Prob |
|:-----------------|--------------:|:------------:| 
| (Q9)  0.0083     |      0.419    |     81    
| (Q2)  0.0028     |      0.140    |     90    
| (92)  0.0028     |      0.140    |     90    
| (99)  0.0028     |      0.140    |      5      
| (QQ)  0.0028     |      0.140    |      4    
| (J10d)0.0005     |      0.023    |     60

Expected Value 61.6744186

This analysis doesn't however take into account the chance that villain's probability of QQ and 99 should be lower than that in the table, due to no pre-flop raise. It also excludes the fact that there is a lower probability of the villain going all in on straight-flush (54% based on 15 outs) than on a made hand such as 2 pair. Both of these considerations mean there should be an even greater chance than 61% for the Hero.

Answer 2

I tend to raise this spot preflop but if the guys behind you and in the blinds are passive limping behind can be ok.

The flop raise is a tad big, but standard, and yes, call the shove.

His shove is pretty large and if anything that's indicative of a big draw like A⋄K⋄ or J⋄T⋄. Sure he'll show up with better sets sometimes but this is a spot where I happily stack off.

Answer 3

@Silversana With a hand like AK, he would have raised preflop. The same with 99 or QQ (bigger set).

Smells like KQ, A9, medium flush draw, straight draw, something in that range; in which case I would fold. Yes, you have a good hand, but in my opinion it's not good enough to call an all-in with. If this was a tournament and you had a smaller stack (less than 40 - 50 BB), then calling the all-in would make sense. Otherwise, I wouldn't take the risk.

Answer 4

Qd-9c-2d is pretty much the most favorable runout you could hope for when you're holding a pair of deuces (other than quads). If you're not willing to get all-in on that board, you shouldn't even be playing 22 at all. This is my argument, if you are playing this tight (which you probably shouldn't be), your preflop play isn't aligned with your postflop decisions.

I think the correct play is to call.

EDIT: Your fold is based on a specific read of QQ or 99. I don't think you can justify this read, as his possible hands could be a variety of QX top pair hands, Q9 or Q2 two pair hands, or a variety of flush draws (and one decent straight draw, J10). The only information you have is that he limped in, and then started raising aggressively on the flop - based on that alone, he could have any of these other hands.

Answer 5

I don't think there is a standard answer as to whether your play was right or wrong. I am going to guide you through the process of thinking I would do in a similar situation and then you can judge your decision.

1) We take all previous action as granted (some people would disagree on your preflop and flop plays probably, but it is not our target at the moment). Let's get to the part where you have to take your final decision:

Your current stack is= Initial Stack-Preflop Call-Betting=410-3-48=359

In case you call and win you will double up your stack after flop plus the blinds, i.e. 407*2+25=839

So, you need at least 359/839~=0.43=43% equity to justify your call. In other words, you need to win at least 43% of the times you make similar calls to gain profit in the long run.

2) How to calculate your equity, i.e. the probability to win the pot. At first you do it via a tool such as pokerstove. After some time, you will do it with your experience. The important thing to bear in mind is that in all cases, even with the most advanced tools, it is your judgement (of the opponent, the situation, the dynamics) that will define your action. Maths are just your assistance.

3) Now what you do is think the hand from the start, keep in mind the dynamics (your history, if villain is tilted, your image etc.) and let's build some scenarios:

1. Scenario A: Opponent does that move only with QQ and 99.

Your Equity (from pokerstove)=4.3% You need at least 43% as shown before, so... auto-fold

2. Scenario B: Opponent does that move with QQ,99 and with AA,KK,AKd

Your Equity=60%>43% --> Auto-call

3. Scenario C: Oppoent does that move only with 99 and JTd

Your Equity=18% --> Fold

4. Scenario D: Opponet does that with 99, and occasionally with big flush draws (like KJd,KTd,AJd, etc)

Your equity=47% --> Marginal Call

and so on...

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As you can see, you can build an infinite number of scenarios depending on how you judge your opponent and then determine mathematically if you need to call or fold. As time goes on you will learn to do that quickly. Try to get into the habit of doing it often and try not to play automatically. The real essence of poker lies on how you react to these situations.

For the record, I would probably call in such a spot against a random opponent, or an opponent I don't know a lot, as most players will overplay flushdraws or big pairs or top pairs in low-stakes games. But that's just a thought, definitely not a rule ;)

Answer 6

Don't agree with that fold nor your epilogue

Thus, the hero decided the villain wouldn't risk 75% of his stack unless he was very confident he was ahead.

You put that much at risk when you need/want a fold. And it was 60%.

The only hands you are behind are QQ and 99

Those hands should have raised pre.

Those hands should just smooth called you for value on the flop. I think Q9 would also smooth call. If they wanted your stack in the pot they should smooth call the flop and hopefully get another $100 in the pot on the turn and get you pot committed.

Think about it. Would you push there with QQ or 99? You did not push 22 and you were basically in the same spot.

Even their strongest draw JTc you are 3:2.

You are 4:1 to Q9

OK you say they may just call with 99 I still say they should smooth call your raise on the flop for value.

Your big raise on the flop looks like you are trying to buy the pot or 1 pair 2 pair wanting to charge a flush draw. You should have raised pre with QQ 99 and would probably just smooth call the flop for value. You have the only hand that would (well should) call. I bet they had a nut flush draw. They had fold equity here and outs.