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Omaha Odds and Probabilities

When playing Omaha, your odds are significantly altered in comparison with Texas Hold’em because you have four cards (instead of two) in your starting hand. Naturally, because of the additional cards, you will see many stronger hands in Omaha, which, in turn, alters the way you must play the game. As with any form of poker, the mathematical expectancy of different scenarios occurring in a game of Omaha poker can be precisely calculated to give you a valuable edge. Below, you can find some of the more commonly-considered probabilities, in both variations of the game: standard Omaha and Omaha Hi-Lo.

Here are some basic numbers for some of the various scenarios in Omaha Hi-Lo, starting with the probability for each type of hand.

Omaha High Hand

Hand

Combinations

Probabilities

Royal Flush 42807600 0.000092
Straight Flush 368486160 0.000795
Four of a Kind 2225270496 0.0048
Full House 29424798576 0.063475
Flush 31216782384 0.067341
Straight 52289648688 0.112799
Three of a Kind 40712657408 0.087825
Two Pair 170775844104 0.368398
Pair 122655542152 0.264593
All others 13851662832 0.029881
Omaha Low Hand
Hand

Combinations

Probabilities

5 High 7439717760 0.016049
6 High 25832342400 0.055726
7 High 51687563904 0.111501
8 High 76415359104 0.164843
9 High 90496557312 0.195219
10 High 87800751360 0.189404
J High 68526662400 0.147826
Q High 39834609408 0.085931
K High 13835276928 0.029845
Pair or Higher 1694659824 0.003656

In Omaha, cards are usually referred to as either low (8 or less) or high (9 or more). Consider the following scenario: You hold a hand such as A-2-3-4, and you want to know the likelihood of what you might see on the flop. Here are a few of the figures you may want to commit to memory: You have a 6% chance of not seeing another low card on the flop, a 32% chance there will be one low card, a 46% chance there will be two low cards, and a 16% chance the flop will contain all low cards.

Omaha Pot Odds

Understanding pot odds is crucial in the development of every poker player, particularly in the game of Omaha. If you are playing online, knowing the percentages is vital since, really, you have at your disposal none of the traditional methods of learning more about your opponent’s hand, such as the ability to read tells and recognize other visual clues. Many new players are overwhelmed by the thought of having to crunch numbers while concentrating on other things, such as maintaining composure and deciphering their opponent’s intentions. They feel that applying pot odds is something to be left to the pros. However, you do not have to be a math wizard in order to utilize pot odds. This section is an attempt to simplify the concept and hopefully you may begin using the advice to your advantage straight away.

First off, there are a few terms that you need to be familiar with before any real learning can take place:

Outs – The number of cards remaining in the deck, which will improve your hand. Your outs are the unseen cards that will complete or improve your hand to make it the winning hand. By determining the number of outs in relation to your pot odds, you can decide if it is worthwhile to continue with the hand.

Pot Odds – To put it as simple as possible, pot odds are the relationship between the size of the pot and the money you must place on your next bet, in order to stay in the hand. For example, if there is $20 in the pot and your next call is $4, your pot odds are 5:1. Clearly then, the better the odds are, the more attractive it becomes to call the bet.

The following table illustrates the odds of drawing your needed card for each number of outs you have.

Outs

Turn & River

Turn %

River %

21 69.9% 44.7% 45.7%
20 67.5% 42.6% 43.5%
19 65.0% 40.4% 41.3%
18 62.4% 38.3% 39.1%
17 59.8% 36.2% 37.0%
16 57.0% 34.0% 34.8%
15 54.1% 31.9% 32.6%
14 51.2% 29.8% 30.4%
13 48.1% 27.7% 28.3%
12 45.0% 25.5% 26.1%
11 41.7% 23.4% 23.9%
10 38.4% 21.3% 21.7%
9 35.0% 19.2% 19.6%
8 31.5% 17.0% 17.4%
7 27.9% 14.9% 15.2%
6 24.1% 12.8% 13.0%
5 20.4% 10.6% 10.9%
4 16.5% 8.5% 8.7%
3 12.5% 6.4% 6.5%
2 8.4% 4.3% 4.4%
1 4.3% 2.1% 2.2%
Omaha Starting Hands

It is possible to calculate with absolute certainty the probability that certain hands will be dealt at the start of each round. You may choose to think about it this way in order to grasp the idea: The first card you are dealt could be one of any of the 52 cards in the deck, the second could be one of any of the remaining 51 cards, and so on and so on. What this essentially means is that there are 270,725 possible starting hand combinations. Yes, that’s an awful lot indeed, but since many of these hands can have an identical playing value, and therefore no different from each other, we are left with 16,432 distinct starting hands. Luckily for you, these again can be reduced to a much more manageable 16 hands, which we will call shapes. Have a look at the example table below, which will hopefully make this clearer:

Rank

Example

# of Shapes

Distinct Hands

Odds

Four of a Kind 4444

1

13

20,824 : 1

Three of a Kind 777K

2

312

107 : 1

Two Pair 88QQ

3

234

95 : 1

One Pair 37AA

5

5134

2.3 : 1

No Pair 8KQ4

5

10725

0.48 : 1

You may have heard people refer to Omaha as a game of “the nuts”, which just means that you usually need the strongest hand in order to win the pot. This is a bit different from no-limit Texas Hold’em, in which the psychological aspect of the game is much more apparent.

Pre-flop Probabilities

Here are some important probabilities for a nine-handed game of Omaha Hi-Lo:

Chance of being dealt A-2-X-X = 6.5%
Chance of being dealt A-2-3-X = 1%
Chance that another player has A-2 when you do = 36%
Chance that another player has A-2 when you have A-3 = 52%
Chance that another player has A-2, A-3, or A-4 when you have A-4 = 86%
Chance of another player having A-2 or A-3 when you have A-3 = 70%

Flop Probabilities

Here are some important probabilities for the flop in a nine-handed game of Omaha Hi-Lo:

Chance of flopping a low with A-2 = 7%
Chance of flopping a low draw with A-2 = 37%
Chance of seeing an ace and another low card when you have 2-3 = 13%
Chance of seeing a deuce and another low card when you have A-3 = 13%
Chance of flopping a two and a three when you have A-4 = 3.8%

 


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