Hand analysis: AQ, do you make the call

I got involved in a debate on the following hand, and ended up doing enough work on the hand that I think its worth posting. This is really long, and has a lot of hand ranges and EV calculations in it. If you're just interested in a quick answer, I'd skip to the bold part at the bottom, and read that and from the rest of the way out...

Here's the original question as posed:

Just out of curiosity, I'd like to get anyone's opinion on what they'd do here in the following tournament hand. It is a $20 buy in, w/o rebuys or add ons. Just a good ol' freezeout style tourney.

You are UTG with AQ os. You have ~6000 in chips. Blinds are 50/100. You raise to 600. It folds to a short(er) stack w/~1350 in chips, who goes all in. SB, with ~5300 in chips goes all in as well.

FWIW, I know it is hard to give an opinion without knowing how the players have been etc, but in this example, YOU (with AQ) and the SB have been playing the same type of game. Semi-Tight/aggressive. Neither has done anything (seemingly) fancy, such as button raises when folded to and raising ridiculous amounts after several limpers in hopes to simply take down that pot right then and there. As for the already all in 1300 chip d00d, it's irrelevant, really, as he is all in, and you are facing a much bigger task of taking on someone with just a slightly smaller chip stack.

To ME, this seems like a no brainer. What would you do, if you were the UTG player with the original pf raise? A) Call, or B) Fold?

My response:

Really depends on your reads in this scenario, as you mentioned. But absent reads: As always, its about putting your opponents on a range of hands.

So let's look at it from just about every player's perspective:

Shorter stack with 1350: there's 750 in the pot to him, and he's guaranteed a call from the UTG raiser. Assuming he's in late position, and smart enough to realize he's going to want to get his money in the middle soon, i'd put him on a range something like any pair, any broadway. At least, I'd make this move with at least that range if not wider...

Small blind with 5300: Assuming he's a thinking straightforward player, he's doing one of two things here: he could be making a squeeze play here, trying to squeeze the UTG raiser and flip the shortstack with a good amount of dead money. Or, he's got a vulnerable hand that doesn't want multiway action.

Based on those two factors, I'd put him on a range like: pairs 77 - QQ, any ace, any two face cards. Either he's got a middle pair up to queens trying to protect it, or looking to flip for the dead money with a weak ace or two faces and doesn't expect to be too far behind. Based on moving in here, its really unlikely to see AA or KK here.

So if I'm the UTG raiser, here's the scenario: Its ~7350 in the pot, and ~4700 to call. Now, I'm not raising 6xBB UTG here, that's a leak unless for some reason that's the standard raise at this table, but when it comes back to making the call when the SB pushes, I'm making this call myself with AQ most of the time, given the information we've been given. If we're close to the end of the tournament or something I can probably find a fold, as I probably could if the SB is an uber-rock. But otherwise I'm making this call most of the time in this scenario, and most of the time, expecting the SB to turn over JJ-77 or a wide range of aces. But lets take a deeper look and see if this is correct...

Its ~7350 in the pot, and ~4700 to call. The small blind is all-in for 1350, meaning 4150 of 12,050 the pot is going three-way if we call. so we've got:

4150 chips with:

Hand 1: 32.8150% 29.99% 02.83% { QQ-77, ATs+, KTs+, ATo+, KTo+ }
Hand 2: 36.6925% 33.14% 03.55% { AcQd }
Hand 3: 30.4924% 28.58% 01.91% { 22+, A5s+, KTs+, QTs+ JTs+, A8o+, KTo+ }

So the SB in hand 1 has 1362 chips in equity out of the main pot.
UTG raiser has 1523 chips in equity out of this main pot.
the all-in player has 1265 chips in equity out of the main pot

and in the side pot: 7900 chips with:

Hand 1: 44.5159 % 40.02% 04.49% { QQ-77, ATs+, KTs+, ATo+, KTo+ }
Hand 2: 55.4841 % 50.99% 04.49% { AQo }

The SB has 3517 chips in equity out of this side pot
The UTG raiser has 4383 chips in equity out of this side pot.

In total, that gives us:

So the SB has 4879 chips in equity out of both pots together.
UTG raiser has 5906 chips in equity out of both pots together.
the all-in player has 1265 chips in equity out of the main pot

So from a pot odds perspective against those hand ranges, the UTG raiser is faced with calling 4700 chips with 5906 chips in pot equity, making this a very clear +EV call with AQ against the ranges given.

If I narrow the hand range for the small blind to just 77-QQ, AJs+, KQs, AJo+, KQo, lets see if it changes any. if you've got any suggestions as to other ranges (i.e. what you'd really come over the top all-in with, let me know)

4150 chips with:

Hand 1: 35.7275% 32.13% 03.60% { QQ-77, AJs+, KQs, AJo+, KQo }
Hand 2: 33.4292% 29.23% 04.20% { AcQd }
Hand 3: 30.8432% 29.24% 01.60% { 22+, A5s+, KTs+, QTs+ JTs+, A8o+, KTo+ }

So the SB in hand 1 has 1483 chips in equity out of the main pot. UTG raiser has 1387 chips in equity out of this main pot. the all-in player has 1280 chips in equity out of the main pot

and in the side pot: 7900 chips with:

Hand 1: 49.7223% 43.23% 06.49% { QQ-77, AJs+, KQs, AJo+, KQo }
Hand 2: 50.2777% 43.79% 06.49% { AcQd }

The SB has 3928 chips in equity out of this side pot The UTG raiser has 3972 chips in equity out of this side pot.

In total, that gives us:

So the SB has 5411 chips in equity out of both pots together. UTG raiser has 5349 chips in equity out of both pots together. the all-in player has 1280 chips in equity out of the main pot

This slightly narrower range means the SB has a slight equity edge across both pots, but its still a +EV call for the UTG raiser with an expected value of 5349 chips and 4700 to call.

In summary, to this point - if you put the players on the following ranges:

Small blind: { QQ-77, ATs+, KTs+, ATo+, KTo+ }
All-in shorty: { 22+, A5s+, KTs+, QTs+ JTs+, A8o+, KTo+ }

Then the UTG raiser is faced with calling 4700 chips with 5906 chips in pot equity, making this a very clear +EV call with AQ against the ranges given.

If you narrow the SB's range for moving in here to { QQ-77, AJs+, KQs, AJo+, KQo }, it becomes closer, but its still a +EV call for the UTG raiser with an expected value of 5349 chips and 4700 to call.

That being said, I wanted to see how much it would change if I included AA and KK in the SB's range: i.e. he's overbetting a monster here trying to suck me in to calling, basically third or fourth level thinking.

For the main pot: 4150 chips with:

Hand 1: 35.250% { 77+, ATs+, KTs+, ATo+, KTo+ }
Hand 2: 35.331% { AcQd }
Hand 3: 29.419% { 22+, A5s+, KTs+, QTs+ JTs+, A8o+, KTo+ }

UTG raiser has 1466 chips in equity out of this main pot if we include AA and KK.

and in the side pot: 7900 chips with:

Hand 1: 47.060% { 77+, ATs+, KTs+, ATo+, KTo+ }
Hand 2: 52.940% { AQo }

The UTG raiser has 4182 chips in equity out of this side pot.

In total, that gives the UTG raiser 5648 in expected value, still making it a call.

If we narrow the range of the SB as in the second set of numbers:

4150 chips with:

Hand 1: 38.973% { 77+, ATs+, KTs+, ATo+, KTo+ }
Hand 2: 31.777% { AcQd }
Hand 3: 29.250% { 22+, A5s+, KTs+, QTs+ JTs+, A8o+, KTo+ }

UTG raiser has 1319 chips in equity out of this main pot if we include AA and KK.

and in the side pot: 7900 chips with:

Hand 1: 52.727% { 77+, AJs+, KQs, AJo+, KQo }
Hand 2: 47.273% { AQo }

The UTG raiser has 3735 chips in equity out of this side pot.

In total, that gives the UTG raiser 5054 in expected value, still making it a call in pure +EV terms, albeit a much much closer call.

Speaking with a pair of top players I know, they both recommended assigning some significantly tighter ranges and running the numbers. Based on discussion with them, we came up with the following ranges:

Small Blind: { 99+, AJs+, AQo+ }
Short Stack: { 22+, A2s+, KTs+, QJs, A2o+, KTo+, QJo }

Which gives us a pretty dramatic difference in outcome:

Main pot, 4150 chips with:

Hand 1: 47.772% { 99+, AJs+, AQo+ }
Hand 2: 26.833% { AcQd }
Hand 3: 25.394% { 22+, A2s+, KTs+, QJs, A2o+, KTo+, QJo }

UTG raiser has 1114 chips in equity out of this main pot with this much smaller range.

and in the side pot: 7900 chips with:

Hand 1: 64.401% { 99+, AJs+, AQo+ }
Hand 2: 35.599% { AcQd }

The UTG raiser has only 2812 chips in equity out of this side pot.

In total, that gives the UTG raiser 3926 in expected value, still making it a -EV call of -774 chips.

If you really wanted to get technical, you could assign probabilities to each of the above scenarios and weigh the total EV. Arbitrarily as an example, say I think he's putting on a squeeze play 20% of the time so he has the larger range but without AA or KK, 60% of the time he has the tightest range, and 20% of the time he has the middle range with AA and KK . In which case you'd assign the probability to each EV and then weight the total: in that example, 20% of 5906 + 60% of 3926 + 20% of 5054. That's 1181.2 + 2355.6 + 1010.8, for a total weighted EV of 4547.6. This would mean the call of 4700 chips is slightly negative EV in that scenario, which means its probably a bad call. However, just playing with the numbers, if you thought he had the tightest range only 50% of the time and 30% of the time was trying the squeeze play, it would jump to a very narrowly +EV call.

So in a really really long summary, like almost every other decision in poker it comes down to your reads and the hand ranges you assign your opponents. If you think the SB is as tight as just some big pairs and big aces, then its going to be a -EV call. If you think the SB has a bigger range, including if they're making a squeeze play here, then its going to be a +EV call.

Do I do this math in my head at the table? of course not. Can some players? I guess its possible. But most top players I've talked to do the same thing:

You just have a gut feel, from running simulations, from playing for years, from analyzing and studying hands like this after the fact, and had the feeling when I first saw the hand that I'd call the push if I were the UTG raiser faced with calling 4700 chips here. But I also assigned the SB a wider range than some would. But based on that range i was able to run the numbers which showed that my first instinct against that range was correctly a +EV call.

So as usual, the answer's not a simple call or fold. Personally with my tournament style if its early I'm probably more likely to gambool and call here, as I tend to put my opponents on a wider range until they prove me otherwise. Essentially, this hand comes down to your read on the small blind. Any read on the small blind as loose and I think this is an easy call, any read on the small blind as tight and its a fold. More than anything, this should help to underscore the importance of reads and assigning hand ranges, and hopefully walk a few people through some of the thought process behind evaluating one of these close hands after the fact mathematically.