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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.

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The answer depends on the table dynamics so far. The general case will be to call the shove because you should play 22 preflop with the intention to go all in if you hit a set. If you are planning to fold it dont play it pre. In your specific question the only extra information you provide that villan is a solid player. Is he agressive ? The only condition that should make you consider folding is if you have wached him for a while seeing he calls relatively strong hands and raises very rarely. If he is just an experienced palyer you should call considering he might have combo draw in his range –  Daniel Mar 13 at 13:31
    
There are very few situations in NLHE in which you should fold a set on the flop. This is definitely not one of them. Not even close. –  Andrew Brennan Mar 20 at 11:26

3 Answers 3

up vote 6 down vote accepted

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.


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.

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(via @Chris) "It's interesting to see that mathematically there is a 42% chance the villain was holding just Q9." –  Toby Booth Nov 28 '12 at 16:25

@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.

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Lots of $1/$3 players will limp AK preflop because they (very much incorrectly) claim it to be a "drawing hand." The range you assigned villain has no hands that are better than ours so we definitely shouldn't be folding vs that range. In fact, if I take the best hands in that range, it would be a huge mistake to fold: Board: Qd 2d 9c { 2c2s } Hand 0: 64.798% { Ad9d, KdQd, JdTd } Hand 1: 35.202% –  Silversana Nov 4 '12 at 20:22
    
@Silversana I guess I play more cautious than you... another example of how diverse and amazing poker is. I know that the villain has a worse hand most of the time... it's just... for me the risk of him hitting a straight or a flush on the following streets is a little too much in this situation... (I'm actually curious what the hero did here :D ) –  Radu Murzea Nov 4 '12 at 21:51
    
I appreciate all the feedback. I've updated the question with an epilogue that reveals what happened. –  Craig Nov 5 '12 at 2:47
1  
@SoboLAN You shouldn't make decisions based on being cautious - you should be playing low enough stakes to not be afraid of losing a few buy-ins due to running bad. Also, at the end of the day a decision is either +EV or not (or more +EV relative to other options) and that is all that matters. High variance situations can suck sometimes, but if the call is profitable, you should make the call. –  Silversana Nov 5 '12 at 4:56
    
+EV isn't always +EV. If you've got your opponent covered, I think a call is the best move here. You're probably leading as QQ or 99 are all that have you beat at this moment (with no preflop raise, I don't see anyone holding). If you can claim a knockout here with the best odd's, get it AI. But if you're short stacked/tournament life on the line, there are definitely better spots to pick (better than 2:3) if they have a straight+/flush draw(s). –  Chris Nov 10 '12 at 23:01

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.

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