Omaha Poker Probabilities
Thursday, 25 September 2008 03:37

With Omaha poker the probabilities are very different from Texas Hold’em because of the fact of having four cards instead of just two in your starting hand. This increases the chances of more strong hands being created for all players, resulting in an alteration in the way you play Omaha.

To give you a better idea of what you’re up against, here are some of the mathematical probabilities associated with Omaha using the high hands.

Starting at the top, the probability of obtaining a Royal Flush from 42807600 possible combinations is just
0.000092. A Straight Flush has a probability of 0.000795 from 368486160 combinations, whereas a Four of a Kind comes in at 0.0048 from 2225270496 combinations.

Lower hands have higher probabilities and are as follows:

 Full House 29424798576  combinations  0.063475 probability 
 Flush 31216782384  combinations 0.067341 probability
 Straight 52289648688  combinations  0.112799 probability
 Three of a Kind 40712657408  combinations 0.087825 probability
 Two Pair 170775844104  combinations  0.368398 probability
 Pair 122655542152  combinations  0.264593 probability

Knowing the pot odds are an important part of understanding the game of Omaha poker. They do not have to be so complicated that you want to give up and chance it all to luck, as that will cost you a lot of money. It is especially important to know the pot odds when playing online, as the more acceptable methods of reading and judging the intentions of the other players is not available to you.

The pot odds are best described as the relationship between the amount of money in the pot and the amount you must put on your next bet to stay in the hand. As an example, if there was $50 in the pot and your next call is $10 then the pot odds are 5:1. From this you will see that the better the odds, the more attractive to call the bet.

It’s also important to know how many outs, or cards remaining in the deck, there are. By knowing this number in relation to the pot odds can influence your decision whether to continue or not with your hand.

You can also calculate the probability of certain hands being dealt from the start of each round. As many starting hands have an identical value in play, the actual number of possible hands obtainable from a single deck is 16,432. This figure can be reduced to a mere 16 hands when considered as shapes in the following:

Four of a Kind has a single shape and produces 13 distinct hands with odds of 20,824:1 of you being dealt it
Three of a Kind has two shapes and produces 312 distinct hands with odds of 107:1
Two Pair has three shapes and produces 234 distinct hands with odds of 95:1
One Pair has five shapes and produces 5134 distinct hands with odds of 2.3:1
No Pair has five shapes and produces 10725 distinct hands with odds of 0.48:1

In addition to the above, here are some probabilities for a nine-handed game of Omaha Hi-Lo:

Chance of getting A-2-X-X = 6.5%
Chance of getting A-2-3-X = 1%
Chance of other player having A-2 same as you = 36%
Chance of other player having A-2 when you have A-3 = 52%
Chance of other player having A-2, A-3, or A-4 when you have A-4 = 86%
Chance of other player having A-2 or A-3 when you have A-3 = 70%

The last piece of advice is that whatever the probabilities, you almost always need to have the strongest hand you can make to stand a good chance of taking the pot.

 
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