Texas Hold’em Odds Dataset (downloadable)
Open dataset: exact combination counts and probabilities for the 10 Texas Hold’em hand categories, plus drawing equity for 1–20 outs. Computed by deterministic code (lib/poker-math.ts), CC BY 4.0 — free to cite.
Hand probabilities (out of 2,598,960 five-card hands)
| Hand | Combinations | Probability | Odds against |
|---|---|---|---|
| Royal Flush | 4 | 0.0002% | 649739.0 : 1 |
| Straight Flush | 36 | 0.0014% | 72192.3 : 1 |
| Four of a Kind (Quads) | 624 | 0.0240% | 4164.0 : 1 |
| Full House (Full Boat) | 3,744 | 0.1441% | 693.2 : 1 |
| Flush | 5,108 | 0.1965% | 507.8 : 1 |
| Straight | 10,200 | 0.3925% | 253.8 : 1 |
| Three of a Kind (Trips / Set) | 54,912 | 2.1128% | 46.3 : 1 |
| Two Pair | 123,552 | 4.7539% | 20.0 : 1 |
| One Pair | 1,098,240 | 42.2569% | 1.4 : 1 |
| High Card | 1,302,540 | 50.1177% | 1.0 : 1 |
Drawing equity (Rule of 2 and 4 vs exact)
| Outs | Flop approx | Flop exact | Turn approx | Turn exact |
|---|---|---|---|---|
| 1 | 4% | 4.26% | 2% | 2.17% |
| 2 | 8% | 8.42% | 4% | 4.35% |
| 3 | 12% | 12.49% | 6% | 6.52% |
| 4 | 16% | 16.47% | 8% | 8.70% |
| 5 | 20% | 20.35% | 10% | 10.87% |
| 6 | 24% | 24.14% | 12% | 13.04% |
| 7 | 28% | 27.84% | 14% | 15.22% |
| 8 | 32% | 31.45% | 16% | 17.39% |
| 9 | 36% | 34.97% | 18% | 19.57% |
| 10 | 40% | 38.39% | 20% | 21.74% |
| 11 | 44% | 41.72% | 22% | 23.91% |
| 12 | 48% | 44.96% | 24% | 26.09% |
| 13 | 52% | 48.10% | 26% | 28.26% |
| 14 | 56% | 51.16% | 28% | 30.43% |
| 15 | 60% | 54.12% | 30% | 32.61% |
| 16 | 64% | 56.98% | 32% | 34.78% |
| 17 | 68% | 59.76% | 34% | 36.96% |
| 18 | 72% | 62.44% | 36% | 39.13% |
| 19 | 76% | 65.03% | 38% | 41.30% |
| 20 | 80% | 67.53% | 40% | 43.48% |
Methodology and precision
Rule of 2&4 is the standard mental shortcut in Texas Hold'em: multiply your outs by 4 for a two-street equity approximation after the flop, or by 2 for a single-street estimate. The approximation works well when outs are few. With 4 outs, the Rule gives 16% against an exact figure of 16.47% — an error of just 0.47%. However, the underlying hypergeometric formula is nonlinear: the exact two-street probability equals 1 minus ((47 minus outs)/47) times ((46 minus outs)/46). As outs increase, the multiplicative structure of the miss probability diverges from the linear approximation at an accelerating rate. At 9 outs the error reaches 1.03%; at 12 outs it climbs to 3.04%; at 15 outs the gap widens to 5.88%. Spots with many outs — combination draws, flush draws plus overcards — are precisely where the approximation is least reliable, yet most consequential for calling decisions.
Every figure in this dataset is derived from deterministic combinatorial computation, not Monte Carlo simulation. The five-card hand space contains exactly C(52,5) = 2,598,960 equally likely combinations. Each hand category is counted precisely: royal flushes number just 4 (probability 0.000154%), while high-card hands account for 1,302,540 combinations. Drawing equity values are computed via the exact hypergeometric formula and presented alongside Rule of 2&4 approximations with per-outs error margins. The dataset is released under CC BY 4.0; all computation is encapsulated in lib/poker-math.ts and is independently verifiable without reliance on external APIs or language model inference.
How to cite this dataset
If you use this dataset in research, articles or tools, please cite it as follows (CC BY 4.0 attribution):
APA 7th
Pailiku Editorial. (2026). Texas Hold'em odds dataset [Data set]. Pailiku. https://pailiku.com/poker-odds-dataset
BibTeX
@misc{pailiku2026pokeroddsdataset,
title = {{Texas Hold'em Odds Dataset}},
author = {{Pailiku Editorial}},
year = {2026},
howpublished = {\url{https://pailiku.com/poker-odds-dataset}},
note = {Computed deterministically from lib/poker-math.ts; C(52,5)=2,598,960 exact enumeration; CC BY 4.0}
}All figures are computed exactly by deterministic code (not estimated); free to cite with attribution to Pailiku / lib/poker-math.ts.