We did the math so you don't have to. Check it out.
Version 1.01
We wrote code to test every single combination of Omaha and Texas Hold'Em starting hand against a randomly drawn hand. Each Omaha hand was tested 20,000 times, and each Texas Hold'Em hand 100,000. The Omaha simulation took four months and the Hold'Em one took four hours.
A Simple Mapping
Card 1 is the 2♣, and card 52 is the A♠. A card has an index, x, a rank z and a suit suit.
20,000 Tests per Data Point
There are 270,725 starting hands in Omaha. That is 5,414,500,000 tests! But still, we only explored < 10% of the hand space per data point. The numbers started to converge after 10,000 trials, so we did 20,000.
Please let us know on social media if you would like to see us rerun the Omaha experiment.
A Graph
The vertical red lines divide the chart into quartiles. These results are rather interesting as they appear to be a linear trasformation of a logistic curve, something found throughout the natural world.
Results From Each Quartile
The worst hand we tested was 2♣ - 2♦ - 2♥ - 2♠ And the top hand from each quartile.
| Quartile | Hand | Equity |
|---|---|---|
| 1 | T♦T♥A♦A♥ | 72.41% |
| 2 | 4♦7♠J♦Q♠ | 51.75% |
| 3 | 5♠6♠J♠A♣ | 47.85% |
| 4 | 4♦5♥7♥J♥ | 44.33% |
The Best, and the Worst
And the 10 hands in the middle. The 10 best hands all have PF equity greater than 70% vs a random hand. The hands in the middle are all a little worse than a coin flip vs a random hand. And the 10 worst hands can expect to lose more than 70% of the time.
Here some interesting patterns emerge. Double suited aces with a JJ or TT are the nuts. Low quads and trip dueces with a mid rank rainbow are the worst. The worst hands are significantly worst than the best hands are good.
| Rank | Hand |
|---|---|
| 1 | T♦T♥A♦A♥ |
| 2 | T♦T♠A♦A♠ |
| 3 | T♣T♥A♣A♥ |
| 4 | J♣J♦A♣A♦ |
| 5 | J♦J♥A♦A♥ |
| 6 | 9♠T♠A♣A♠ |
| 7 | K♦K♥A♦A♥ |
| 8 | J♣J♥A♣A♥ |
| 9 | T♦T♠A♦A♠ |
| 10 | Q♥Q♠A♥A♠ |
| Rank | Hand |
|---|---|
| 135,358 | 4♣6♠T♦J♣ |
| 135,359 | 4♣9♦Q♣K♠ |
| 135,360 | 6♥7♣T♠K♦ |
| 135,361 | 7♥9♦T♣J♠ |
| 135,362 | 5♠6♠J♠A♣ |
| 135,363 | 4♠9♠J♠A♣ |
| 135,364 | 3♦4♦7♦7♥ |
| 135,365 | 2♥9♠H♦K♠ |
| 135,366 | 3♦3♥6♥K♦ |
| 135,367 | 2♣8♥J♠A♠ |
| Rank | Hand |
|---|---|
| 270,716 | 2♣2♥2♠9♣ |
| 270,717 | 2♣2♦2♥7♠ |
| 270,718 | 2♣2♥2♠8♦ |
| 270,719 | 2♣2♦2♠7♥ |
| 270,720 | 2♣2♦2♥9♠ |
| 270,721 | 5♣5♦5♥5♠ |
| 270,722 | 2♣2♥2♠7♦ |
| 270,723 | 4♣4♦4♥4♠ |
| 270,724 | 3♣3♦3♥3♠ |
| 270,725 | 2♣2♦2♥2♠ |
Find a Hand
Enter a ranking, an integer greater than 0 and less than 270,726 and the site will return the corresponding hand
Find a Ranking
Enter a hand and we will return its ranking.
Texas Hold'Em Database
Each of the 1,326 starting hands in Texas Hold'Em were tested 100,000 times which, assuming an even sampling, explored the entire hand space more than 75 times.
Find a Hand
Enter a ranking, an integer greater than 0 and less than 1,327 to find the corresponding hand
Find a Ranking
Enter a hand and we will return its ranking.