Poker Hand Probabilities: A Complete Mathematical Reference
In a 52-card deck there are 2,598,960 distinct five-card hands. Every poker probability begins with this number. Here is the complete reference with odds, outs, and pot odds.
In a standard 52-card deck, there are 2,598,960distinct five-card hands. Every poker probability begins with this number. The relative rarity of each hand type follows directly from combinatorics — rarer hands beat more common hands because rarer hands are harder to make.
Five-card hand frequencies
| Hand | Combinations | Probability | Odds |
|---|---|---|---|
| Royal Flush | 4 | 0.000154% | 649,739 : 1 |
| Straight Flush | 36 | 0.00139% | 72,192 : 1 |
| Four of a Kind | 624 | 0.0240% | 4,164 : 1 |
| Full House | 3,744 | 0.1441% | 693 : 1 |
| Flush | 5,108 | 0.1965% | 508 : 1 |
| Straight | 10,200 | 0.3925% | 254 : 1 |
| Three of a Kind | 54,912 | 2.1128% | 46 : 1 |
| Two Pair | 123,552 | 4.7539% | 20 : 1 |
| One Pair | 1,098,240 | 42.2569% | 1.37 : 1 |
| High Card | 1,302,540 | 50.1177% | 0.995 : 1 |
More than 50% of all random five-card deals are high-card hands. One pair covers another 42%. If you have a pair, you are already beating the majority of random five-card combinations.
Texas Hold'em starting hand probabilities
There are C(52, 2) = 1,326possible starting hands.
| Starting Hand Type | Combinations | Probability |
|---|---|---|
| Any specific pair (e.g. AA) | 6 | 0.45% |
| Any pair | 78 | 5.88% |
| Ace-King suited | 4 | 0.30% |
| Ace-King offsuit | 12 | 0.90% |
| Any two suited cards | 312 | 23.5% |
Outs and the rule of 4 and 2
After the flop (two cards to come): Win probability ≈ (number of outs) × 4% After the turn (one card to come): Win probability ≈ (number of outs) × 2% Common out scenarios: Flush draw → 9 outs → ~36% (flop), ~18% (turn) Open-ended straight→ 8 outs → ~32% (flop), ~16% (turn) Gutshot straight → 4 outs → ~16% (flop), ~8% (turn) Two overcards → 6 outs → ~24% (flop), ~12% (turn)
Pot odds and calling decisions
Required win% = Call Amount / (Pot Size + Call Amount) Example: Pot = $100, Opponent bets $50, you call $50 to win $200 total. Required win% = 50 / (100 + 50 + 50) = 50/200 = 25% Flush draw win% ≈ 36% > 25% required → CALL is profitable Gutshot draw win% ≈ 16% < 25% required → FOLD is correct
Our Poker Evaluator calculates this for you: enter your pot size and call amount after running a simulation, and the tool tells you whether a call is profitable given your current win percentage.