How often somebody has it
In a bomb pot every player sees the flop with random cards, so the chance that someone holds a set on a king-high flop is exactly the chance on a seven-high flop. What changes everything is how many players and how many hole cards. This is the table we play by.
Read this first
- Each cell is the chance that at least one opponent holds the hand, on the flop named in the row, with the number of opponents in the column.
- Hole cards are random for every opponent. That is the bomb pot: nobody folded before the flop.
- Evaluation is exact Omaha: two cards from the hand, three from the board. A pair in the hand plus a board card is not a set unless two hand cards are used, and the script enforces that.
- 20,000 deals per cell, so a cell can be off by about a point. The direction never changes.
Eight-handed with four cards (seven opponents): someone has a set 28% of the time, a flush when three of a suit flop 82%, the nut straight on a connected flop 43%. With five cards: 43%, 96% and 62%. That is why a middle set or a king-high flush is not a hand to pay a raise with.
Four hole cards
| Somebody at the table holds | 1 opponent | 2 | 5 | 7 | 9 |
|---|---|---|---|---|---|
| Overpair (AA on K-8-3) | 3% | 6% | 14% | 20% | 25% |
| Two pair or better (K-8-3) | 15% | 28% | 60% | 75% | 86% |
| Any set (K-8-3) | 5% | 9% | 21% | 28% | 35% |
| Top set (K-8-3) | 1% | 3% | 8% | 11% | 13% |
| Trips (K-8-8, holds an 8) | 16% | 30% | 65% | 82% | 93% |
| Any straight (9-8-7) | 19% | 35% | 68% | 81% | 89% |
| Nut straight (J-T on 9-8-7) | 7% | 14% | 33% | 43% | 54% |
| Any flush (three of a suit on the flop) | 18% | 33% | 69% | 82% | 92% |
| Nut flush (A of the suit + one more) | 4% | 8% | 19% | 27% | 35% |
| Full house or better (K-8-8) | 5% | 9% | 22% | 32% | 39% |
| Nut full house (A-K on A-A-K) | 3% | 6% | 14% | 19% | 24% |
| Quads (8-8 on K-8-8) | 1% | 1% | 3% | 4% | 5% |
Five hole cards
| Somebody at the table holds | 1 opponent | 2 | 5 | 7 |
|---|---|---|---|---|
| Overpair (AA on K-8-3) | 5% | 10% | 22% | 32% |
| Two pair or better (K-8-3) | 22% | 40% | 78% | 91% |
| Any set (K-8-3) | 8% | 14% | 33% | 43% |
| Top set (K-8-3) | 2% | 5% | 12% | 17% |
| Trips (K-8-8, holds an 8) | 20% | 37% | 77% | 92% |
| Any straight (9-8-7) | 28% | 49% | 84% | 94% |
| Nut straight (J-T on 9-8-7) | 11% | 22% | 47% | 62% |
| Any flush (three of a suit on the flop) | 27% | 48% | 86% | 96% |
| Nut flush (A of the suit + one more) | 6% | 12% | 29% | 41% |
| Full house or better (K-8-8) | 8% | 15% | 35% | 48% |
| Nut full house (A-K on A-A-K) | 5% | 9% | 22% | 30% |
| Quads (8-8 on K-8-8) | 1% | 2% | 4% | 6% |
No ten-player column here: ten players with five cards each is fifty cards, and two boards need ten more. The deck has fifty-two. Eight players is the practical ceiling for five-card double board.
What to do with it
- Against seven opponents, "somebody has a set" is a coin flip with five cards and a one-in-three with four. A set that is not top set on a wet board is a hand to see the turn cheaply with, not to raise with.
- A nut straight on a connected flop is held by someone else more than half the time eight-handed with four cards. Two nut straights split that board. Raising with it on one board buys you a quarter of the pot at best.
- Three of a suit on the flop and you hold a non-nut flush: with seven opponents and four cards, a flush is out there most of the time and the nut flush about one time in four. A king-high flush can bet into checks and should not pay a raise.
- The numbers drop fast with fewer opponents. Heads up on the turn, a middle set is a real hand again. That is the whole argument for betting the flop to thin the field.
Reproduce it: the script is research/freq_sim.cjs in our repository and uses the same evaluator as the trainer. Change the flop, the hand class or the deal count and run it. If you find a cell that disagrees with yours, write to us; we will rerun it in public.
THE 30-DAY COURSE
A plan for your next game.
One lesson. One drill set. A little more clarity at the table.