Catching a Small Piece

So I wanted to examine another difficult spot in PLO cash games. It's a pretty straightforward odds calculation scenario, but there are a ton of variables that make knowing the precise odds very difficult.

Although PF 3-betting has increased in frequency in 6-max PLO games as more regulars settle in and figure out how profitable it is, you will still often find villains who are only 3-betting AAxx hands.  Oftentimes, the same type that is 3-betting with only AAxx also has no intention of ever folding that hand.  So, although strong hands like suited rundowns actually fare very well equity-wise against AAxx, it seems wiser to me to take advantage of the playability of suited rundowns postflop, rather than shipping it in PF.

The goal is to flop a big piece and get it in, but what constitutes a big piece and what do we do when we only catch a small piece?

Well, the big piece part is easy.  Any two pair, any sort of wrap, any pair + flush draw.  The small piece part is a bit tougher.  What do you do with just top pair on a 2-flush board?  What about on a rainbow board?  Not a trivial question to answer.

Here's the hand I played that prompted the investigation: 

Full Tilt Pot-Limit Omaha, $0.25 BB (6 handed) - Full-Tilt Converter Tool from FlopTurnRiver.com
UTG ($29.03)
MP ($20.20)
Hero (CO) ($31.93)
Button ($16.30)
SB ($23.45)
BB ($15.90)
Preflop: Hero is CO with Q, 9, J, 10
2 folds, Hero bets $1.15, Button calls $1.15, SB raises to $5.15, 1 fold, Hero calls $4, Button calls $4

Flop: ($16) 10, 3, 5 (3 players)
SB bets $16, Hero?

Time to run some odds.

To simplify, let's assume our villain is holding an AAxx hand.  How are we sitting, knowing we are behind with just 1 pair, but that we have a lot of 2-pair outs and some backdoor straight draws?

Against a rainbow, poorly-connected hand (As-Ad-9h-5c), we get about as good as it gets at about 40-60:

Against a slightly better AAxx hand (single-suit, some connectedness), it comes down to 35-65:

That's the good news.  It gets bad (22-78) when villain has a diamond draw:

My guess is that it averages out somewhere around 33%.  So then it becomes a simple matter of pot odds.  Villain bets $16 and leaves $2 behind, so essentially, I need to call $18 to win $34.  So the pot is giving me 1.9-1.  33% is 2-1, so that means it's just barely a fold.

Pretty interesting result IMO.  All you have to do is shift that 33% up to 35%, and the odds are right on.  Holding just a pair, you can get your stack in against AAxx - the key is how much goes in PF, and with 100BB stacks and a pot-sized 3-bet, it will usually come out just about even.

In the hand in question, I suppressed my gambling itch, but next time, I'll probably do it differently:

...

...

Hero folds, 1 fold

Total pot: $16 Rake: $0.80
Results:
SB didn't show
Outcome: SB won $15.20