Poker Hand Odds Calculator
Calculate the exact probability and odds of being dealt any specific poker hand from a standard 52-card deck (5-card draw).
Select a hand and click Calculate.
Formulas Used
Total 5-card combinations: C(n, 5) = n! / (5! × (n−5)!)
Probability: P = Favorable Combinations / C(n, 5)
Odds Against: (Total − Favorable) / Favorable
Key hand combination counts (52-card deck, 5-card hand):
- Royal Flush: 4 × 1 = 4
- Straight Flush: 4 × (ranks−4) = 4 × 9 = 36
- Four of a Kind: C(13,1) × C(4,4) × 48 = 624
- Full House: C(13,1)×C(4,3) × C(12,1)×C(4,2) = 3,744
- Flush: C(13,5)×4 − straight/royal flushes = 5,108
- Straight: 10×4⁵ − 40 straight flushes = 10,200
- Three of a Kind: C(13,1)×C(4,3) × C(12,2)×4² = 54,912
- Two Pair: C(13,2)×C(4,2)² × 44 = 123,552
- One Pair: C(13,1)×C(4,2) × C(12,3)×4³ = 1,098,240
- High Card: Total − all above = 1,302,540
- Total: C(52,5) = 2,598,960
Assumptions & References
- Standard poker hand rankings apply (Royal Flush is highest).
- 5-card hand formulas are exact combinatorial calculations.
- 7-card hand probabilities represent the best 5-of-7 cards (Texas Hold'em style) and use published statistical tables.
- Non-standard deck sizes use the same combinatorial formulas scaled to the new rank count (deckSize / 4 ranks assumed).
- Suits are always assumed to be 4 (♠ ♥ ♦ ♣).
- References: Sklansky, D. The Theory of Poker; Perez, R. Poker Probability Tables; Wikipedia — Poker probability.