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%