Omaha Money Traps: The rundown on overcalling a 3-bet

“Those skilled at making the enemy move do so by creating a situation to which he must conform; they entice him with something he is certain to take, and with lures of ostensible profit they await him in strength.”
Sun Tzu, The Art of War

This article discusses a common spot in which there is no clear consensus on the correct course of action. I have regulars in my database overcalling a 3-bet with as tight a range as 2% and as wide as 10% of their starting hands. For the purpose of this article we are going to focus on the situation where a player opens from UTG/MP with a tight range, faces a 3-bet from an aggressive BT and we are contemplating a cold-flat in the blinds

1. The reason this situation is particularly interesting is because both of our opponent’s ranges are quite well-defined, which makes for some interesting behavior in the relative strength of our pre-flop hands.

A concept that seems to elude many players is that hand strength is fluid pre-flop in PLO.

JJT4ss is a top 10% hand against all hands, yet it doesn’t approach the best 10% of hands to continue with once our opponent opens UTG. Similarly, I saw a post recently by a player holding AKKJds, a worthy 3-bet “for value” even against a tight range. This player was now agonizing after facing a 4-bet. The poor soul was still blinded by the ‘strength of his hand’ after the deal rather than focusing his attention on the change in relative range strength. If he had instead reminded himself that now he would rather hold 9874r against his opponent’s Aces than AKKJds, his plight would vanish.

Flop hand strength in three-way pots

For the purpose of this article we are going to give both the pre-flop raiser and the 3-bettor the same range of the top 10% of hands. There are some complications relating to 4-betting that will be discussed at the end of the post. Before I drop a table in front of you, I want to discuss the strength of some common post-flop hands in this situation:

1) Pair + non-nut FD

Players who love to call double-suited hands are likely to overvalue the strength of {Pair + non-nut FD} on the flop. The problem with this draw is that one of our opponents flops {Nut FD, 2NFD, 3NFD, set} around 64% of the time. Even if they just stack off with this range against our open-shove, we have only 28% equity when called. With an SPR of 2.5 we would require 44% folds, so the 36% is falling short2.

2) Pair + OD on high flops

As an entrenched member of the ‘fight fire with fire’ school of poker3 I love to pitch the high rundowns in spots most players consider ‘standard’ continuations. Nevertheless the weakness of QJT8, no FD on a KT6d flop surprised me. It has only 23% equity 3-ways against the given ranges and runs into {High FDs, sets, top two} a jaw-dropping 75% of the time. Many players would no doubt believe this is a ‘good flop’ for their hand and count themselves unlucky when they get snap-called in one or even two spots. Most {Pair +OD} are not sufficient to shove on duochrome {A,K,Q}-high flops.

3) Non-AA overpair + non-nut FD

Similarly the equity of {non-AA overpair + non-NFD} is a miserable 29% when called by a range of {top two+ and NFDs}. Our opponents will only hold these hands around 50% of the time, which makes them close to break-even when we do flop them. Nevertheless, mining for {OP + FD or a set} is a losing play when the equity of half of our ‘hits’ is so low.

Fun with Card Removal

Our enthusiasm for cold-flatting the ‘standard’ hands has been suitably curbed, so let’s get to the fun stuff. Those of you who have done coaching/seminars with me are by now well aware that I love to introduce +EV/0EV lines that look crazy wherever possible. The table below is a veritable goldmine for these ‘shark in fish clothing’ plays.

A word of warning, do not attempt to use this table to counter wider ranges, the card removal effect is important both for how often we flop well but also how rarely our mediocre flops are dominated. When we cannot count on both opponents’ ranges being Broadway-oriented we have to take a different approach.


Hand Equity f(Top two+) f(9+ out wrap) f(OD + pair/FD or
NFD no Ace on board}
Total Shoves
AKQJds 30.5% 12% (-5) 11% 12% 35%
KQJT$ds 30% 15% (-2) 14% 1.5% 30.5%
QJT9$ds 31.5% 17% (=) 18% 3% 38%
9876$ds 34% 16% (+2) 21% 7% 44%
7654$ss 33.5% 13% (+2) 23% 9% 45%
AKQJ$ss 26% 11% (-5) 9% 0% or 12% 20% or 32%
QJT9$ss 28.5% 16% (=) 18% 2% 36%
T987$ss 30% 16% (+2) 21% 5% 42%
KK83$ss 28% 13% (-1) 0% 0% 13%
KKQJ$ds 35% 16% (-3) 3% 5% 24%
JJ33$ss 27% 26% (+1) 0% 0% 26%
7766$ds 35.5% 29% (+2) 0% 10.5% 39.5%
QQJT$ss 29% 18% (=) 3% 11% 34%
JJT9$ss 29% 19% (=) 5.5% 12% 36.5%
TT87$ss 29% 19% (+1) 5.5% 8.5% 33%
7765$ss 31.5% 20% (+2) 7% 13% 40%
AK98$ds 30.5% 12% (-2) 0% 15% 27%
A876$ds 34% 14% (+1) 8% 25% 47%
JT97$ss 29.5% 16% (+1) 14% 7.5% 37.5%
7653$ss 33% 13% (+3) 17% 9.5% 39.5%
KJ97$ss 27% 14% (=) 4% 7% 25%
T864$ss 30.5% 13% (+2) 5% 10% 28%
5432$ds 32% 10.5% (+2) 17% 13% 40.5%
Q876$ds 32.5% 15% (+2) 8% 13% 36%
J876$ss 30% 15% (+2) 9% 14% 38%

By way of explanation, the table above indicates the 3-way equity of the hand; frequency of {top two+} and how that has changed from the base frequency4; frequency of 9+ out wrap; frequency of other likely ‘stack-off’s’; total shoves as a sum of the previous three columns.

Of course, all shoves are not created equal. As referred to above, the QJT combinations aren’t doing well on KTx boards whereas a 765 is delighted on 85x board. Similarly, {overpair+FD} is omitted from the shoves category, although they add some value to the respective hands. Finally, double pairs flop very strong hands when they do hit, although set-over-set becomes an issue on A/K high boards5.

First Impressions

How should we estimate a good ‘shoving threshold’. The pot will be 36.5 on the flop if we cold-flat and the PFR calls, and we will have 88 behind for an SPR of 2.5. Crucially, we are first to act post-flop and so get to shove some additional hands profitably that we would not be able to call off our stack with. We have paid 11BB (from the big blind) pre-flop for the privilege of seeing a flop. Whilst it’s hard to know the exact profitability of a shove, we can immediately set an upper bound. If our opponents fold every time we shove6, we pick up the 36.5 in the pot. If we check/fold the rest of the time, we have a simple calculation to find the ‘shoving threshold frequency’:

F(+25.5)-(1-F)(11) = 0

Solving, we find F = 30%.

There is an additional problem here, however, which is that we don’t get to see the flop every time when we call, at least not for the advertised price.

The 4-bet threat

We are not bothered by the 3-bettor having specifically AA, so much as the PFR having AA and then 4betting us. When we hold a random hand, the PFR will have AA around 22% of the time. Holding KK bumps it up a little to 25%, and either player to 50%! We would need 29% equity to stack-off 3-ways having cold-flat; even AKQJds only has 25% versus {AA, 10%}. This means that we expect to divide hands into 3 categories:

1) Fold pre-flop
2) Call 3-bet, fold to 4-bet
3)Call 3-bet, continue to 4-bet

Since we would be putting up half our stack pre-flop, the third category is quite small.

Hand 3-way equity versus {AA} and {10%}

























The second table above demonstrates the consequences of facing a 4-bet from EP and a call/shove from the initial 3-bettor. Unsuprisingly, broadway cards fare very poorly and low connectors very well. Since the percentages seem close together, I’ll show a quick EV calculation to demonstrate the cost of stacking off with 29% equity 3-ways 100BB deep7:

0.29*(300.5)-99= -11.9BB

Despite being ‘only 4% short’ you end up dropping 12BB every time this occurs. The more curious among you might want to spend some time considering whether the initial 3-bettor constructing his 3-betting range well will make a 4-bet more or less frequent.


What to fold

Cold-flatting KKxx, as I see so often, is a dismal play. In fact I am reasonably comfortable saying that, if you are only 100BB deep, mediocre KKxx is a 4b/fold hand when faced with a raise and a 3-bet. It’s remarkable that KKQJds is not overwhelmingly strong; this hand will gain from flopping a large number of {OP + FDs}, so I won’t suggest folding it, but the blocker factor of our opponents’ broadway ranges weakens it considerably.

Most A-broadway hands fall into the ‘clear-fold’ category. Similarly, QJT-oriented hands fare pretty poorly. Gone are the days when {QQJT,QJT9ss} are autoflats.

Other woeful hands are those with multiple gaps, especially broadway-oriented. If you are a player who feels a temptation with AKJ5 or the like in this situation, then let that impulse rest. There’s always another hand.

What to call

Three-connectors below a ten are particularly powerful, since they gain from the interference effect of the two broadway-oriented ranges. Even with a pair in hand (or two), 7766ds and 7765ss are comfortable flats. The hilarious lower-connectors are also far more playable now than they would be in a HU single-raised pot. It does appear important that the 4th card is at most 1-gap away, or else the hand is double-suited. Curiously, even A876ds is a powerful hand, a testament to both the potency of a possible nut flush draw and the connectivity of the 876.

This article was originally featured as a subscriber-only post on my legacy site

QUESTION(S) OF THE WEEK: Check your database and see how often you cold-flat 3-bets. Are there any hand types costing you a lot of money at the moment? Share your flatting frequency and trouble hands in the comments below.

Show 7 footnotes

  1. We neglect the cold-flat OTB situation because it occurs less frequently. The most common spot, where the BT steals, SB 3-bets wide and BB is contemplating a call is also worthy of investigation.
  2. Although our opponents can stack off lighter with hands that we have better equity against, our average equity does not improve sufficiently to compensate for the reduced fold equity.
  3. This involves not just attacking wide ranges with a wide range but, equally important, nitting up against nitty ranges.
  4. So the +/- demonstrates the impact of adding two 10% hands to the frequency of us flopping a strong made hand.
  5. You are set-over-set with middle set 1/3rd of the time on a K high board
  6. Our opponent’s need around 41% equity against our range to stack off. If they have that, then we average 59% equity. 0.59*(88+88+36.5)-88 = 37.375. We can approximate this by saying that picking up the pot every time is the best possible result against strong players
  7. Assumes we are in the BB
By | 2017-04-10T13:22:54+00:00 February 24th, 2015|


  1. Matthias March 23, 2017 at 9:34 am - Reply

    Hey Phil,
    I’m not sure if you are still reading this. In the conclusion you said that three connectors below a Ten are particularly useful. Does this mean that a hand like 9872ds is a flat in your opinion? Could you otherwise specify these hand category a little more detailed please? You also state 7766ds as a cold call, is every double pair ds a coldcall in your opinion or also just those below a ten? What about 7744ds? What about the single suited ones?
    I also don’t quite get the hand strength of those double suited rundowns when openraising, E.g. is 9875ds an open from MP? Is JT86ds?
    Sorry for all those questions but I think you are the only one I could ask who I feel is competent enough to answer.
    Thanks for the great content.

    • Phil Rocquemore March 23, 2017 at 10:40 am - Reply

      Hi Matthias,
      The 4th card should play some role in the hand other than merely completing the second suit. In A876ds the disconnected A creates a nut feature and in 8764ds the 4 increases the low connectivity of the hand. 9872ds would not qualify.

      This article is about cold-calling a 3-bet. If you want to learn a comprehensive strategy for open-raising which answers all of your questions about EP/MP opens then I recommend you join my Poker Math 2020 course.


  2. 7th Lion May 22, 2015 at 10:02 pm - Reply

    Hello, in the part “flop hand strength” you said one of our opponent (with 10% top range in odds oracle i suppose) will have 64% of the time 3nfd+ and set. How did you come up with this strange number? I gave 10%6h (6handed ranking, tested also Th and 3h for the case) to a player and questioned “how often does player have four-to-flush OR flop hand category at least set” and the answer was ~26% , that means if there are 2 opponents, chance is 52% of them having this.. where does your 64% come from?

    • Phil Rocquemore May 22, 2015 at 10:38 pm - Reply

      Thanks for commenting. I’ve provided some help below:

      1) We need to exclude paired boards for the purpose of the example. To achieve this, constrain the board to three cards of different ranks with two cards of the same suit. You will then get a number in the low 60s IF you choose at least one player with two players’ ranges entered into your software.

      2) There is an error in your probability calculation above: since the events are not independent we cannot find the frequency of either player having a certain holding by simply doubling the frequency count for a single player. This is because when one player holds non-flush cards he increases the probability that the other player holds flushing cards as they are drawing from the same deck.

      That should clarify the method!

  3. SJ Lee May 5, 2015 at 2:47 am - Reply

    Thanks for sharing this! This article helped me a lot about cold-calling 3bet.
    I have a question: is there a reason that you don’t include the chance that we have trips or better?
    What program did you use to compute the first chart? I want to play with different ranges as well.

  4. A March 1, 2015 at 6:37 pm - Reply

    I am sad to report that i am a massive loser when i call 3bets. From 170k hands i called 3bets 2100 times and lose with them with about 90bb/100. I wasn’t even aware of that leak so thanks for this article!

    Besides the specific case mentioned here (cold calling OOP) I am not completely sure how to tackle this problem. If I raise and get 3bet i play mostly fit or fold – like most bad players – no matter if i am in position or not. So that sucks.

    When looking at the hand groupings it feels like a 170k hand database might be small for a correct analysis.

    The biggest group in HEM is ‘Other hands’ – 1027 hands and has -160bb/100.
    This includes hands like AKQ8ss, AQT5ss, AK93ds but also very bad ones like AK64ss, AQ96ss, 9543ds, AQ32s etc.

    The other groups have about 100 hands or less so i am not sure how reliable are the results there.
    Kings, middle GAP wrap, Ace GAP wraps are losing. High GAP wraps and High wraps are winning.

    Very interesting topic, thanks!

    • Phil Rocquemore March 1, 2015 at 11:51 pm - Reply

      Hi there, thanks for commenting. There’s an error in the analysis you describe here: to discover whether calling a 3-bet was on average a profitable decision, it only needs to be better than folding. So if you usually open to pot, as long as you are losing at less than -350bb/100 your call of the 3-bet was the correct play on average.

      That said, your -90bb/100 sample will be composed of some extremely profitable hands (hard to lose much with T987ds etc.) and some extremely unprofitable hands. You’ll want to dig a little deeper into those ‘Other hands’ to find which groups are costing you money.

      Good luck!

      • A March 2, 2015 at 2:58 pm - Reply

        Oh yes, of course. I forgot that calling and cold calling is two different things.
        I will look at them for sure and hopefully i will make some revelations 🙂
        Thanks again!

Leave A Comment

Click for Poker Course Details

New for 2014: Small Stakes Solutions!

The mathematics of in-position play in Pot-Limit Omaha from pre-flop to river explained in 5 interactive lectures.
Click for Poker Course Details