How to Play a Flopped Two Pair in Pot-Limit Omaha

Christian Handschuh 2707

Players new to playing Pot-Limit Omaha are often unsure about how to play two pair in the game - especially if they have experience in Texas Hold'em.

One of the first things you need to understand when trying to learn how to act in specific PLO situations is that you can't directly relate what you know of Hold'em to PLO and expect to succeed.

Every player who plays both games knows that the odds of hitting larger hands are higher in Omaha than in Hold'em. 

Many players greatly underestimate this disparity, which is a big mistake.

Odds of Flopping Two Pair in Omaha

The odds of flopping two pair in Hold'em are 2.02%. Without doing the math or looking it up, what do you figure the odds of flopping two pair in Omaha are?

pot limit omaha flopped two pair

To find out you need to use the following equation (this is with no pair on the flop):

( (12/48)*(9/47)*(40/46) ) + ( (12/48)*(38/47)*(9/46) ) + ( (36/48)*(12/47)*(9/46) ) = %

(0.25*0.191*0.87) + (0.25*0.809*0.156) + (0.75*0.255*0.156) = %

0.041 + 0.0312 + 0.0298 = 0.102

0.102 = 10.2%

The majority of people, poker players included, are less than proficient at math and probability. Because of this people tend to assume that having twice as many cards translates into exactly twice as great of a chance of hitting a specific hand in Omaha.

In reality the odds of flopping two pair in an Omaha game are over 5x greater than in Hold'em.

Although the math isn't exactly this simple it's a strong argument for thinking about two pair like this:

If you have 9 players at a table in Hold'em there's an 18% chance of someone having flopped two pair (2% per person * 9 people).

So if you flopped two pair the chances of someone having flopped better than you are fairly small.

Apply this simple formula (which, again, is not meant to be perfectly accurate, just to give you a general idea) to a nine-handed Omaha game, and the chance of someone having flopped two pair is almost 91%.

Related Reading:

What are the Odds You're Outflopped?

If you flopped two pair the chances of someone else having out-flopped you is significantly greater in Omaha than in Hold'em.

A simple test: Take a deck of cards and deal nine Omaha hands face-up. Burn one card and deal a flop.

pot limit omaha two pair strategy

Take a look at how many players connect with the flop. You'll see two pairs, trips, straights, flushes and plenty of draws.

Shuffle the deck and try it again: you may be amazed how often multiple players connect with the flop in Omaha.

Not only are the odds greater because more cards are in play, but in a typical Omaha game, you have more players seeing flops in an average hand than you do in Hold'em.

The more hands you have to the flop, the greater the chances of another player having connected with what has fallen.

Straight Draws in Omaha

Omaha is a game of redraws. Even if your flopped two pair is the best hand on the flop, chances are you're only slightly ahead - or even behind - in the hand.

Unlike in Hold'em, where the vast majority of all draws against a two pair will consist of eight or nine outs, Omaha draws can have 25 outs on the flop to a better hand.

Aside from the standard gut-shot and open-ended straight draws, Omaha has three more straight-draw possibilities:

13-out draw: You have three cards above or three cards below the connectors on board.

  • Hand: K-Q-J-x
  • Flop: T-9-x
  • Outs: 13

Wraparound: You have two cards above the connectors on board, and one below (or vice versa).

  • Hand: Q-J-8-x
  • Flop: T-9-x
  • Outs: 17

Double Wrap: You have two cards above and two cards below the connectors on board.

  • Hand: Q-J-8-7
  • Flop: T-9-x
  • Outs: 20

A player sitting with a double wrap with a single flush draw holds a total of 25 outs to either a straight or a flush. In a scenario with a player having 20+ outs, they are statistically ahead of a made hand on the flop.

Many beginners will think that they are ahead in such a context since the player with the draws has to hit a specific card to take the lead. Unfortunately there are only 45 cards left in the deck. If the player has 20 outs, that means they are 44% (20/45) to hit their hand on the turn.

If they miss on the turn, they are now 45% (20/44) to hit. The chances that they will hit their card on either the turn or the river are in the neighborhood of 68%.

To see the numbers for yourself, plug cards into our online poker odds calculator here.

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In Omaha You (Almost) Never Have It Made

The actual true math for finding the 68% involves binomial distribution, the Probability Mass Function and the Cumulative Distribution Function ... basically, unless you're John Nash or have actually studied calculus, the odds calculator is the way to go.

The upshot is, even if you flop two pair there's a chance you can be statistically behind a hand that hasn't even hit yet.

The most important idea to take away is the inherent vulnerability of an Omaha hand. In Omaha, you almost never have it made until after the river has fallen.

Related Reading:

Edges in Omaha are Razor Thin

So how do you begin evaluating the true strength of your two pair? If you ran the test above and dealt out nine Omaha hands with a flop, you'll have a firm understanding of how often multiple hands hit the flop in a nine-handed Omaha game.

So even if you go to the flop heads-up and flop top two pair, it's still possible to be behind another hand - even that of a player holding only a draw.

To evaluate the strength of your hand you need to take into consideration the number of outs your opponent may hold.

Equity is finite, meaning there are only 100 possible percentage points you can own. When multiple forces are competing for shares out of the same finite pool, the acquisition of a single unit is worth two units relative to your opposition.

In simpler terms, if you and your opponent are even, you each have 50% equity.

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If you gain one point of equity (bringing you up to 51%), you had to gain that point by forcing your opponent to lose it; your opponent now holds 49%. And 51%-49% = 2%. Your one percentage point gain has given you a two percentage point lead.

This concept is important in poker, especially in Omaha, where the edges in equity are razor-thin at best. Omaha is a very equity-liberal game, as opposed to Hold'em, in which one player will commonly hold a vast majority share.

What Are Your Blockers?

One of the strongest ways to acquire hidden equity is through blocker cards. The more blockers you have, the more equity you'll have in the pot. More importantly, the more blockers you have, the less equity your opponent will have.

Still more crucially, the more equity you hold from blocker cards, the more equity your opponent will falsely believe they hold.

A blocker is simply one of your opponent's outs. Here are two versions of an Omaha hand, one with blockers, one without. Take a look at how the equity changes between the two hands:

Flop:     

Hand 1:        

Hand 2:        

In this scenario, hand 1 holds top two pair with no draws. Hand 2 holds a 13-out straight draw and a flush draw.

This setup illustrates a situation in which hand 1 has almost no blockers. Unfortunately, Omaha hands are typically very intertwined, and hand 1 holds one blocker (K).

If hand 2 was to make his flush with the K, he would lose to a full house. This effectively lowers his outs to 18. Even though he's still drawing, his massive amount of outs brings his equity to a total of 63.07%. Even though hand 1 has flopped two pair, it holds no more than 36.93% equity in the pot.

Take the same example above, but substitute hand 1 for this hand:

       

With hand 1 now holding blockers to the straight and flush, it has gained almost five points of equity, bringing it up to 41.71%. That makes the hand worth a 10% equity shift to the player holding it.

Even though it may seem small - 36% or 41% is still behind - just imagine if your bank decided to raise the interest on your mortgage by 5%. This shift in equity will translate into thousands of BBs over a long-term sample of cards.

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The Redraw in PLO

Even more powerful than a blocker is the redraw. If you change the queen of diamonds in hand 1 to the Q (giving hand 1 the higher flush draw), you've now given yourself a strong redraw.

Since hand one does not have to improve to win this pot - it only has to stop hand 2 from improving - it's irrelevant whether hand 1 hits the flush or not. This means a redraw is not so much a draw as a super blocker.

Holding the Q in conjunction with the seven of hearts doesn't just give you one more blocker against your opponent; it effectively blocks all possible flush cards, meaning this Q is actually as strong as holding seven blockers in your hand.

When looking at your two pair, there is a very decent chance you're behind in equity, unless you're holding redraws and blockers. Omaha is a turn and river game: your goal is to play your hand for the future streets, not for the flop.

You need to be playing for draws, redraws and redraws on your draws. In fact, single points of equity are so valuable in Omaha that serious players will even consider blockers to rare hands such as straight flushes. For example, a player may say, "I had the nut flush redraw with a blocker to the straight flush."

If you want to be successful in Omaha, you need to play a strong drawing game. Play hands that will allow you to be ahead on the river, regardless of where they stand on the flop. Simply put, a naked two pair will rarely work out well for you in the end.

Related Omaha Strategy Articles

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Russell Bamberger 2017-02-23 19:52:04

you can still multiply but you multiply but you want to multiply the chances of not hitting. thus 89% for each player or .89 ( using 11% for each player) to the ninth power. gives you about a 35% chance of no one hitting. but ooops this assumes that there is an infinite deck . if the first 8 players don't match the board the last guy is more likely to. I don't know how much this changes the probability

Not_John_Nash 2013-07-25 06:17:24

"If you have nine players at a table in Hold'em, there is an 18% chance of someone having flopped two pair (2% per person * nine people). If you flopped two pair, the chances of someone having flopped better than you are fairly small.
Apply this simple formula (which, again, is not meant to be perfectly accurate, just to give you a general idea) to a nine-handed Omaha game, and the chance of someone having flopped two pair is almost 91%."

Please change this paragraph, it is so wrong I want to divide it by 0. It doesn't lack "accuracy", it's just wrong.

A better calculation would be: 1-0.98^x where x is the number of players. Luckily for the author the number he gives is approximately true (but the precise answer with the figures given is: 16.63%)

For omaha, we get 1-0.898^x, thus 62% for nine players, which is quite different from your "91%".

It does get trickier if the question is "what are the chances that someone flopped two pairs KNOWING that I did flop two pairs". Here, you may use some maths (7 cards left that could give pairs among 8x4=32 cards distributed, what are the odds that someone has two of them ? basic-boring maths)
Long story short, on a dry rainbow board you actually have real chances of being ahead (especially with two top pairs).
But yes, you often have even bigger chances that someone will hit a draw, or simply hit a set or bigger pairs.

And you don't need to have a math degree to know that 1-(1-0.44)*(1-0.45)=69% , your chances of hitting your draw by the river with 20 outs. It's like the absolute first lesson of any probability class.
So if you had math in high school, you know that (or you used to). If not, it's never too late.

conrad: AK in your hand and three aces on the flop and you have a quad with kicker K. No problem.

conrad lafond 2013-03-05 09:42:29

having to use 2 cards in OMAHA, is it possible to have 4 of a kind
without having a pair in your hand??
our players are always arguing this, 3on the board and 1 in your hand.

hard way to make a living 2012-03-08 10:54:52

if u hav a stronger hand than your opponants then this doent mean that by the river u will succeed in winnin the hand, the odd's are the main event in the matter but what happends if u come acroos a very loose player who is willin to bluff this means that your hand conseeds on reads and notes. for the best part is to know how many outs u have BUT in omaha more than likely often your opp's will have some off your outs which makes it u hav less outs most plo plays mistake this and calculate in correct.

Sk1llz 2010-05-09 11:13:32

The probability of flopping two-pair is 11.864% and not 10.2%. (You are not supposed to round your calculations before you've reached the end)

alex 2009-12-02 15:40:38

Nice article. I enjoyed reading it and especially liked the probability discussion. It can get really tricky when taking everything into account.

the slisz 2009-06-20 13:47:00

Maths is simply a guideline in poker, an expectation, board analysis and betting patterns and a better source of information, I have folded 2 pair plenty of times knowing that I can easily be outdrawn, not to mention being an underdog already, with say, bottom 2 pair

Sean Lind 2009-05-19 18:40:00

Hey PokerDude,

When it comes to probability, especially compounding probability, the equations are never simple.

The most obvious way you can tell that the actual answer isn't as simple as multiplication is that 2% from two cards isn't half of the 10% from 4 cards. If you can't just multiply when adding cards, you can't multiply when adding players.

I'm not going to pretend I'd know where to start to get the exact numbers for one of 9 players having flopped two pair from 4 cards, but luckily for me it's not crucial.

I mentioned in the article that the calculations are not accurate, but a general idea of the actual numbers.

2% versus 10% doesn't seem like a really big deal until you point out that every player you add amplifies the difference between the numbers. Using simple multiplication cements this idea, without distorting the numbers too much to make it an invalid argument.

The idea is to note how much more likely it is for someone to have flopped two pair from 4 cards, than from 2.

For those of you who can't wrap your head around why the numbers aren't simply multiplied, here's a quick explanation:
Every time you add more cards into play, there are less possible cards that do NOT make a pair in someone's hand. The problem is we're dealing with a finite number of cards.

If you look at the cards left in the deck as cards that will pair player's cards (X) versus cards that won't (Y) you'll notice that when you add another player, you have to remove 4 cards from the deck (total number of deck cards goes down), the value for X goes up, and the value for Y goes down.

You have less options total, and the balance of cards that hit versus cards that don't becomes vastly more one-sided.

Then you also have to take into account players taking each other's outs.

The math is never as simple as you may like.

PokerDude 2009-05-18 02:16:00

Hey man, nice article, but I saw a flaw. You cannot just multiply the percentages by the number of players to get the chance. It is not a straight line proportional algorythm, it is a parabola, meaning even if there were 10,000 players (if it were possible) in the hand with a 10.2% chance of a two pair, it is still not 100% that someone has two pair. Sorry if this is too complicated, but my point is there is another forumla (one I do not know) to figure out the chance of someone have that two pair with more players, you don't multiply.

I Don't Need a Job 2009-03-30 19:21:00

I am learning the ropes with Omaha and finding it a great relieft from boring holdem nit fests!

A great article about playing a tricky hand in Omaha.

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