Omaha Hi-Lo Probability Math – How Often Will You Make A Low?

Knowing the Omaha Hi-Lo probability and math is a key step in ensuring that your Omaha Hi-Lo, whether PLO8, NL08 or the fixed limit version, is maximally profitable. There are several aspects of this math, one of the keys being how often you will make a low hand should you hold 2, 3 or 4 low hole cards. This article outlines the key Omaha Hi-Lo probability concepts concerning the low side and provides links to many other quality o8 articles.

Omaha Hi-Lo Probability Key Concept #1: In any given deal there is a 60% chance of a low being possible by the river – that is to say there will be 3 or more different cards 8 or lower on the board.

Now, notice that this concept says ‘possible’. This is because many community card boards will contain the same low cards as you hold. Just because a low is possible it does not mean that you made it! Since you are required to play 2 from your hand and 3 from the board, whether you make your depends on you having different low cards to those shared via the board.

Omaha Hi-Lo Probability Key Concept #2: The chances of an individual player making a low are directly proportional to the number of different low cards in their 4-card starting hand.
With just 2 low cards in your starting hand pairing either one could ruin your low (you would then need an additional low on the board to even qualify for a low). With 3 low cards you would need to pair 2 of them to find yourself in the same situation, and with 4 you have greatly increased low potential – here are the raw numbers which take into account the fact that 40% of boards will be high-hand only:

2 Low Cards (example A-2-J-Q), probability of making a low by river = 24%
3 Low Cards (example A-3-4-K) probability of making a low by river = 40%
4 Low Cards (example 3-4-7-8) probability of making a low by river = 49%

So far we have looked at the probability for all 5 community cards. However during a hand you will normally make most important decisions long before you see the river. One of the most useful Omaha Hi-Lo probability concepts concerns how often you will make a low hand when the flop comes with 1 or 2 low cards:

Key Omaha Hi-Lo Probability Concept #3: While making a low on a 2 low-card flop can have a high probability, it is important to understand that this is only to make ‘a low’, this is not necessarily the ‘nut low’.

Probability of Making A Low By The River With 1 Low-Card Flop:
2 Low Card Hand (A-2-J-Q), probability of making a low = 16%
3 Low Card Hand (A-2-6-9), probability of making a low = 26%
4 Low Card Hand (3-4-6-7) probability of making a low = 24%

Probability Of Making A Low By The River With 2 Low-Card Flop:
2 Low Card Hand (A-2-J-Q), probability of making a low = 59%
3 Low Card Hand (A-2-6-9), probability of making a low = 72%
4 Low Card Hand (3-4-6-7) probability of making a low = 70%*

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