Pot-Limit Omaha: Flopping Two Pair Part 1

Nasr El Nasr

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 cannot 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.

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?

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.

Gus Hansen
Some players' playing style is well-suited for Omaha.

In reality, the odds of flopping two pair in an Omaha game are over five times 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 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%.

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

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

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

Bill Chen
If you want to know more about poker math, ask Bill Chen.

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 mean 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.

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.

(PS: If you're interested in the math, it's almost identical to the math used for this Yahoo! answer.)

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 from this article is the inherent vulnerability of an Omaha hand. In Omaha, you almost never have it made until after the river has fallen.

Part 2 of this article will put the math we saw here into practice, as we explore blockers and focus on the importance of redraws.

Related 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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