Wednesday, September 27, 2006

Hand of the Week - Do You Know What Expected Value Is?

I am well into a single table S&G. Seven left. Blinds are 100/200, and I have about 2500 in chips. Chip leader is on my right and has 2700 in chips. The chip leader opens UTG for T600, and I look down at TT.

This is a pretty tough situation. I don't think calling is an option. You would be calling 1/4 of your chips, and are not getting any type of odds to draw to your set. If you raise, any raise would be for 1/2 of your chips minimum, pot committing you. It is a classic push or fold situation. So what do you do?

I thought it through like this. The chip leader is making this raise. An UTG open is pretty strong, but this guy has been accumulating chips somehow. I put him on a range of say 66-AA, AK, AQ, KQ, AJ. There are a lot of people behind me, but nobody has me covered. If I go ahead and push some one might wake up with a huge pair behind me, but I will still be alive. The key is that the initial raiser has me covered. AA-JJ has me dominated. I dominate 99-66. We are coin flipping with the rest. I would have the better side of the coinflip, and my push should get him to fold some of the coinflips (KQ, AJ). Also, the shorties behind me might call with any pair (99-22), or some coinflips. If I get called by the chip leader, and win the coinflip or have him dominated, I would be north of 5k in chips, and should get at least 2nd.

Given all this thought, I think it is still a very borderline decision. One of the famous authors said that when faced with a 50/50 type decision go with the call or push because it is more fun. Also, I am playing these S&Gs to open my game up, so I go ahead and push in over the top.

It folds to the initial raiser, who after a couple seconds thought calls with AA.

I spike a Ten on the flop and win the pot.

Then the following conversation breaks out.

UTG: Lucky
Blinders: That's what you get for the slow roll
UTG: What?, that was a horrible play
Blinders: Good play
UTG: All-in with TT vs. AA is a good play?
UTG: You donk
UTG: Don't you know what expected value is?
UTG: How much you expect to make.
Blinders: Do you know what fold equity is?
Blinders: It was +EV

I usually don't like to argue with the fish on the finer points of the game, but this was pretty funny. The decision was about as borderline as they get, but I thought it through and went with it. To me it was +EV or I would not have done it. I could have folded easily as well. When I made the decision, I did not put the raiser on AA or I would not have made the move. Expectation value for TT is negative specifically against AA, but not against a $10 S&G players range. If I check pokertracker TT is one of my higher +EV hands. Thank god it does not run up against AA all of the time. And thankfully, I can get out of those type situations safely most of the time.


At 8:05 PM, Blogger smokkee said...

n1 donk.

At 5:50 AM, Blogger Hammer Player a.k.a Hoyazo said...

Ha Smokkee.

Personally I would probably fold here. Since the leader was at 2700 chips, I'm assuming you were currently in second place with your 2500 chips, with 7 remaining at a 1-table sng. So you were in good chip position (ie you werent short or anything close to it). If you had been in last or second to last place way behind the other players at the table, I would almost certainly move in here. I would be hoping he has 77, or at least AK, and I would be happy to take the race there.

I agree it's a very borderline decision, no doubt. I can see the argument for either way, and I don't think either move is terrible.

With Kings or Aces, it's obviously fine to move in here. With Queens, maybe, because he could be raising with a hand like AQ or KQ. Once you get down to Jacks, I think this one gets real close to crossing the breakeven line with the push.

I agree 100% that the range of hands of a $10 sng guy is far different from Doyle Brunson's range at this point in a 1-table sng with 7 players remaining. Nonetheless, I still think his range is higher than maybe you do. I'd say he clearly makes that raise with any pair JJ-AA. He clearly makes that raise as well, even from UTG, with AK, AQ, or let's even say AJ or KQ just for good measure (I obviously have no clue what kind of player he is, I'm just making all this stuff up from perceived averages). I assume he also clearly makes this open-raise from UTG with pocket 9s, 8s, or 7s. Many players would choose to limp with 6s and under (or fold, for that matter, though not me as you know), so I'm not counting those hands as too likely.

So to me, you're looking most likely at a guy with 77, 88, 99, JJ, QQ, KK, AA, AK, AQ, AJ or KQ. I'm putting him on one of 11 hands to open raise from UTG as the chip leader like that, knowing the shorter stacks after him will all want a piece. Obviously that range is not 100% but that's where I have him with that move from up front like that.

Of the 11 hands, you are an 80% favorite against 3 of them (77, 88, 99), you are a 20% dog against 4 of them (JJ, QQ, KK, AA) and against the remaining 4 you are just a 52% favorite (AK, AQ, AJ, KQ). So, I'm thinking there is a 73% chance (8 out of 11 hands) that you are no better than a coin flip. 27% chance you're a 4 to 1 favorite, a 36% chance you're a 4 to 1 dog, and a 36% chance you're a 52% "favorite". That is 21.6% pot equity from the 4 to 1 favorite (27% times 80% chance of winning that hand), plus 7.2% equity from the 4 to 1 dog (36% times 20% chance of winning that hand), plus 18.7% pot equity from the coin flip situation (36% times 52% chance of winning that hand). Total pot equity then would be 21.6% + 7.2% + 18.7% which equals 47.5% of the pot equity. Less than half, so your "expected value" to me is slightly negative.

Now, of course if you add in some other hands he might open-raise UTG with like Ax suited (typical online donkey play for sure) or suited connectors, then this becomes a positive equity play to push pretty quickly given how close it is with my range above. But that's how I view it.

Keep in mind also that this is the chip leader. To me, with the Ms still relatively low for everyone including you and the leader, the fact that he has the biggest stack gives more credence to his open raise. And why would you want to take any kind of a close chance of going up against the chip leader when you're currently in second place? It all just adds up to me to be a slight folding situation. Either way as I said I agree this is a close one. Almost any other factor or circumstance changes even slightly for the better, and I would be willing to make the push.

At 8:46 AM, Blogger Blinders said...


Nice analysis. Thanks. Normally, I lean towards folding in that situation, but I think I was trying to talk myself into a push just to be more agressive. Getting over aggressive can be a huge leak, so I need to be careful. I think the only thing that makes it more borderline than what your analysis would suggest is that non paired hands are much more likely then paired hands. If his range is 11 hands, you need to overwieght the AK, AQ, KQ type hands which are easier to get delt.


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