Introduction

• How to play against 3-bets and 4-bets
  
• When to 3-bet out of position
• When to 3-bet in position

Pre-flop play in Pot-Limit Omaha (PLO) is different from every other poker variant in many aspects. An essential difference is caused by the relatively close pre-flop equities, which leads to the widely held opinion that, in PLO, with appropriate post-flop skills, you can call and even 3-bet profitably with a lot of starting hands before the flop.

The following article demonstrates the playability of different hands in 3- and 4-bet pots, and analyzes the expected values for pre-flop decisions with simple math. The second part introduces you to the usage of the tool propokertools for your own analysis.

How do you play against 3-bets?

The recurrent term 'playability' refers to how far a hand can be played profitably on the flop regardless of its pre-flop equity. The site www.propokertools.com offers easy-to-use simulation software for free. The software also offers a graphing feature in addition to simple equity calculations. The graph shows how often your hand will have a given amount of equity against your opponent's hand. This shows how often a hand will be playable on the flop and how EV you can give yourself.

Pot-Limit Omaha Ring game $1/$2 (6 players)

Stack sizes:
UTG: $46.30
UTG+1: $296
CO: $95
Hero: $201
SB: $199.40
BB: $86.70

Pre-flop: (6 players) Hero is Button with 7 8 5 6
UTG folds, UTG+1 calls, CO folds, Hero raises to $9, SB raises to $31, BB folds, UTG+1 folds, Hero calls.

Flop: Q 5 6 ($66, 2 players)
SB bets $66, Hero raises all-in, SB calls.

Turn: K ($402.8, 1 player + 1 all-in - Main pot: $402.8)

River: 4 ($402.8, 1 player + 1 all-in - Main pot: $402.8)

Results:
SB shows 3 A A J
SB has A A Q K 6 a pair of aces.

Hero shows 7 8 5 6
Hero has 8 6 5 4 7 straight, eight high.

In this case, you had 74.51% equity on the flop with two pair and the straight draw against the opponent's aces, meaning you can go all-in right on the flop.

The opponent committed himself to the pot with his continuation bet and had to call your all-in raise. On a separate note, your opponent's mistake was made before the flop when he gave you the chance to play in position after the flop.

With the aid of the following graph, you can determine how often you have a given amount of equity on the flop against a specific hand.

Expected equity on the flop

The central point of the line lies at 25% and shows an average equity at 65%.

Logically, you always continue playing the hand on the flop when it has more than 40% equity. This is given in about 50% of the cases. By replacing the curve with a straight line, you can see that the hand has, on average, 65% equity in 50% of cases. You also have the advantage of position and will only invest when you have the needed equity.

If you call the 3-bet and invest another $22, your EV will be as follows:

• In 50% of the cases, you go all-in on the flop.
  • In 65% of the cases, you win $204.40 (actual pot + remaining stack from the SB)
  • In 35% of the cases, you lose $138.40 (amount to put the SB all-in)
• In 50% of the cases, you fold on the flop and lose $22.

EV = 0.5 * (0,65 * $234.40 - 0.35 * $168.40) - 0.5 * $22
EV = +$35.71

Compare this to the EV from the SB's point of view:

• In 50% of the cases, you fold after seeing the flop and he wins $66.
• In 50% of the cases, you are both all-in on the flop.
  • In 35% of the cases, he wins $234.40 (pot + your bet)
  • In 65% of the cases, he loses $168.40 (his remaining stack)

EV = 0.5 * 66 + 0.5 * (0.35 * 234.4 - 0.65 * $168.40)
EV = +19.29

As you can see, the pre-flop raise from the SB allows him to continue playing on the flop with positive expected value. However, he is putting you in an even better situation. If you calculate his expected value on the flop based on the pre-flop re-raise coupled with his relatively small fold equity, his expected value is considerably lower than that of a smooth call with his AAxx. A smooth call before the flop in a multi-way pot could have put him in a number of situations, in which he could play profitably after the flop without increasing the variance so significantly. He could then contibet any flop and commit himself in a heads up pot.

Things are considerably more difficult when your opponent can re-raise with a range of hands like JT97s and contibet/fold on the flop when his hand hasn't improved significantly. He would then have a better hand than you on some flops that you would continue to play and can also bluff on A and K high boards profitably at the same time. You need to know if your opponent can re-raise with hands other than AAxx out of position before you can choose a range for calling 3-bets. Opponents that only 3-bet out of position with AAxx certainly exist, but opponents able to 3-bet with a wider range need to be noted as post-flop play against them will differ significantly.

Further mathematical analysis would take too much time to cover in this article, but we will look at a few hands and their playability against AAxx.

• 8765s - an average equity of 65% on 50% of all flops.
• JT86s - a bit weaker than 8765s, but 50% of all flops will give you 40% equity, but usually only 60% at most.
• JJT9s - only 40% of the flops will provide more than 40% equity, usually about 60% on average.
• 9988s - also gives you more than 40% equity on more than 40% of all flops. The fact that you have well over 70% equity on 20% of all flops makes this hand very playable.

Experimenting with ProPokerTools will give you a better feel for your own starting hand selection and the playability of various starting hands against 3-bets from hands other than AAxx. You will also get a feel for the playability of your own 3-bets.

You should also pay attention to the following when choosing your starting hands.

Quite simply, the bigger the stack, the better. If your opponent check/folds on many boards, it will be profitable for you to call even when his stack isn't massive. If he overplays big overpairs, you have very good implied odds.

If there are other opponents in the hand who have called the 3-bet, make sure that you don't overplay hands with massive reverse implied odds. You can still profitably play a hand like 9764s heads-up on the flop against AAxx without a problem, but in three-way action, the danger grows as a possible hand like T987 could hit a considerably stronger draw on the flop. In this situation, try to stick with hands that draw to the nuts or are double-paired and can flop big sets. Pairs below 88 do not flop the best set often enough. For instance, holding 7744 on a Q97 board rarely gives you more than the 60% equity needed to justify the call before the flop.