The Math of Omaha High/Low

Analysis of the Important Math & Odds for Omaha Hi-Lo Poker
This text has been prepared by The Eureka Kid, on behalf of TheOmahaSplit.com

Low Cards In Your Starting Hand
Zero or one unpaired low card = 18.9%
Two unpaired low cards = 42.1%
Three unpaired
low cards = 32.4%
Four unpaired low cards = 6.62%

A random starting hand has an 81.1% chance of having at least two low card ranks

Chances Of Making A Low
Your Hand
Pre-Flop %
Flop: Two Low Cards
Flop: One Low Card
Two Low Cards
24%
60%
16%
Three Low Cards
40%
72%
26%
Four Low Cards
50%
70%
24%

Important Numbers For A-2, A-3, A-4, 2-3 and A-2-3 Combinations
Pre-Flop

Probability of being dealt A-2-X-X = 6.5%
Probability of being dealt A-2-3-X = 1%
Probability of someone else having A-2 in a nine-handed game when you do = 36%
Probability of someone having A-2 in a nine-handed game when you have A-3 = 52%
Probability of someone having A-2, A-3 or A-4 in a nine-handed game when you have A-4 = 86%
Probability of someone having A-2 or A-3 when you have A-3 = 70%

The Flop
Probability of flopping a low with A-2 = 7%
Probability of flopping a low draw with A-2 =  37%
Probability of an ace and another low card flopping when you have 2-3 = 13%
Probability of a deuce and another low card flopping when you have A-3 = 13%
Probability of a deuce and trey flopping when you have A-4 = 3.8%

Hand Equity Match-Ups

Example Situations
Description
Hands
Equity
Any A-2 vs. Any A-A
A-2-X-X vs. A-A-X-X
40.58%
A-A vs. A-2 both with mid-high
A-A-M-N vs. A-2-M-N
56.43%
A-A with mid-high vs. A-2-3
A-A-M-N vs. A-2-3-N
54.58%
A-A with mid-high vs. Bad Low
A-A-M-N vs. 3-4-5-6
50.09%
Any A-2 vs. Random Hand
A-2-X-X vs. X-X-X-X
56.72%
Any A-2 vs. Top 20%
A-2-X-X vs.Top 20%s
56.72%
DS AA23 vs. Trash
AcAh2c3h vs. Ks9s9h6d
76.49%
DS Ace-Low Hand vs. Top 20%
As3s5c7c vs. Top 20%s
48.3%
Bad Low vs. No Low
K983 vs. N-N-N-X
52.01%
Any Ace vs. Random Hand
A-X-X-X vs. X-X-X-X
56.21%
99 vs. Random Hand
9-9-X-X vs. X-X-X-X
47.12%
Big vs. Middle vs. Small Cards
B-B-B-B vs. M-M-M-M vs. Z-Z-Z-Z
32.31%/23.86%/43.84%

Top X% - The top X% of hands | B = any four big cards (A,K,Q,J) | M = any four middle cards (T,9,8,7) | Z - any four small cards (6,5,4,3,2) | L = any four "low" cards (A,2,3,4,5,6,7,8) | N = any four "no-low" cards (K,Q,J,T,9) | W = any four wheel cards (A,2,3,4,5)

Outs Table

Outs
Turn & River %
Turn & River Odds
Turn %
Turn Odds
River %
River Odds
21 69.94% 2.326 to 1 44.68% 1.238 to 1 45.65% 1.19 to 1
20 67.53% 2.080 42.55% 1.35 43.48% 1.3
19 65.03% 1.860 40.43% 1.474 41.3% 1.421
18 62.44% 1.663 38.3% 1.611 39.13% 1.556
17 59.76% 1.485 36.17% 1.765 36.96% 1.706
16 56.98% 1.325 34.04% 1.938 34.78% 1.875
15 54.12% 1.179 31.92% 2.133 32.61% 2.067
14 51.16% 1.047 29.79% 2.357 30.44% 2.286
13 48.1% 1.079 27.66% 2.615 28.26% 2.538
12 44.96% 1.224 25.53% 2.917 26.09% 2.833
11 41.72% 1.397 23.4% 3.273 23.91% 3.182
10 38.39% 1.605 21.28% 3.7 21.74% 3.6
9 34.97% 1.86 19.15% 4.222 19.57% 4.111
8 31.45% 2.179 17.02% 4.875 17.39% 4.75
7 27.85% 2.591 14.89% 5.714 15.22% 5.571
6 24.14% 3.142 12.77% 6.833 13.04% 6.667
5 20.35% 3.914 10.64% 8.4 10.87% 8.2
4 16.47% 5.073 8.51% 10.75 8.67% 10.5
3 12.49% 7.007 6.38% 14.667 6.52% 14.333
2 8.42% 10.879 4.26% 22.5 4.35% 22
1 4.26% 22.5 2.13% 46 2.18% 45

The Rule of Four – Two
With two cards to come after the flop you multiply your number of outs by four. With one card to come after the turn, you multiply your number of outs by two. This will give you a quick figure to work with, this is a percentage figure.

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