A Strange Spot with AQs

I sat down at a shorthanded $1/$2 ame today and found myself in the following strange spot on my first hand. A totally random player made it $47 (23.5BBs!!!) from the CO and I found myself in the BB with AQs.

PokerRoom No-Limit Hold'em, $2 BB (5 handed)
SB ($342.20)
Hero ($200.00)
UTG ($80.00)
MP ($195.20)
Button ($150.50)

Preflop: Hero is BB with Ah, Qh.
1 fold, MP bets $47, 2 folds


This is a weird spot and I wasn't really sure what to do. After the fact, I asked a couple of people I know about this and even posted this scenario on 2+2, and everyone seems to think it's an obvious fold. It's not so obvious to me, so let's do some analysis. Remember, I know nothing about the villian in this hand.

Let me start by saying that I'm well aware of thet fact that I'm probably behind the raiser's range. But that doesn't necessarily mean this is a fold because we probably have at least some fold equity. I haven't actually run the numbers, but I think that it will at least be a close decision (not the totally obvious fold that everyone else seems to think it is).

Now let's assign him several canonical raising/calling (calling if I jam, that is) ranges and see how AQs does.

1) "Medium range" -- Raise {99+, AQ+, AJs+}, Call {QQ+, AK, AKs}

We now need to count the number of ways he can have each hand in his range:
- there are 6 ways for him to have 99, TT, JJ, KK.
- there are 3 ways for him to have QQ, AA.
- there are 3 ways for him to have AJs, AQs, AKs.
- there are 9 ways for him to have AQo.
- there are 12 ways for him to have AKo.

This means that there are 60 hands in his raising range and 27 hands in his calling range. Against his calling range, here's how AQs does.

equity (%) win (%) tie (%)
Hand 1: 28.6074 % 27.30% 01.31% { AhQh }
Hand 2: 71.3926 % 70.09% 01.31% { QQ+, AKs, AKo }

Then 55% of the time, he fold and we win $50. The other 45% of the time, he calls. Of these times, we win $198.20 28.6% of the time. We also lose $193.20 72.4% of the time.

So out equity is (33/60)($50) + (27/60)(0.286)($198.20) - (27/60)(0.724)($193.20) = 27.50 + 25.50 - 62.94 = -$9.94

2) "Loose range" -- Raise {22+, AT+, A8s+}, Call {99+, AQ+, AJs+}

There are 135 hands in this range, while there are 60 in his calling range. Here's how we do against the calling range:

equity (%) win (%) tie (%)
Hand 1: 40.7085 % 32.50% 08.21% { AhQh }
Hand 2: 59.2915 % 51.08% 08.21% { 99+, AJs+, AQo+ }

So our equity is then (75/135)($50) + (60/135)(0.407)($198.20) - (60/135)(0.593)($193.20) = 27.78 + 35.85 - 50.92 = $12.71

3) "Tight range" -- Raise {JJ+, AK, AKs}, Call {KK+}

There are 33 hands in this raising range and only 9 in the calling range. Here's how we do against {KK+}:

equity (%) win (%) tie (%)
Hand 1: 25.4101 % 25.06% 00.35% { AhQh }
Hand 2: 74.5899 % 74.24% 00.35% { KK+ }

So our equity against this range is (24/33)(50) + (9/33)(0.254)(198.2) - (9/33)(0.746)(193.2) = 36.36 + 13.72 - 39.31 = $10.77


So we can see that the only "canonical" range we shouldn't jam against is the meduim range.

But I don't think any of these ranges will apply in this situation because the raise is so large. Given this, I think we can safely remove AA and KK (and maybe even AK) from the villian's range because these hands are sort of universally thought of as being big hands that you need to get action with. And it's tough for them to get action by raising it to 23 BBs. In fact, the range I gave the raiser is {TT-QQ, AJs+, AQo+}. I also was pretty sure I'd only get a call from the strongest parts of his range, which is {JJ, QQ, AKs}. Let's see how things look against this more realistic range.

There are 45 hands in his range and he calls with 12 of them. Here's how we look against his calling range:

equity (%) win (%) tie (%)
Hand 1: 38.6917 % 37.90% 00.79% { AhQh }
Hand 2: 61.3083 % 60.52% 00.79% { QQ-JJ, AKs }

Our equity here is (33/45)(50) + (12/45)(.387)(198.2) - (12/45)(.613)(193.2) = 36.67 + 20.45 -31.58 = $25.54

Note that most of this comes from the fact that he's folding a lot of hands. If we don't have fold equity, we shouldn't move in. For example, if he calls with AKo this becomes -EV by about $10. Of course, all of this depends on his actual raising and calling ranges.

I think it's safe to conclude that it's not really a clear fold. Folding is certainly a safer play, and jamming here is going to be highly variant. But I don't like passing up on a perceived edge, no matter how much variance it brings (another good reason to play with a very large bankroll for your game). Given the tendencies of all players out there and the analysis I've just given, I would venture to say that this play is probably around EV neutral, tending towards having positive expectation.

And I like gambling. So I jammed and the villian folded. What did he have? I have no idea, but it really couldn't have been AA or KK. Obviously he doesn't need to have a big hand here as some people have been telling me. In fact, I think it's extremely unlikely for him to have a big hand.

One freind I asked even said he would fold AKs here. AKs! Needless to say, I woulda jammed {AKs, AKo, QQ+} here as well. I also think that it's probably marginally correct to jam with AQs and JJ here as well, as long as you have the bankroll to handle some swings.

You might be saying to yourself right now "if this play is based entirely on fold equity, why not jam with any two cards??" Why not indeed! If I knew the player and was sure he would be folding hands like AKo, I would definitely move in with any two here (this is not a play you could make very often of course). AQs is good enough in case you run into a player who will call you with medium pairs and big aces, since you need to have some outs against these loose ranges. The point is, this is never *that* bad of a play against any range with AQs.

I had a good time thinking about this hand today, and I really think that the classic way of thinking (i.e., needing a REALLY big hand to take action here) misses out on some profit in this spot.