Poker Odds Calculator
Why a Royal Flush Is 500,000 Times Rarer Than a Pair
A five-card poker hand comes from one of exactly 2,598,960 possible combinations dealt from a 52-card deck. Every hand ranking — from a lowly high card to a royal flush — is really just a count of how many of those combinations qualify, divided by the total. This calculator runs that combinatorial count directly rather than relying on memorized odds tables, so the percentage and the "odds against" figure are exact, not rounded approximations.
The Formula
P(hand) = (Number of ways to make hand) / Total 5-card hands
Odds against = (Total hands − Ways to make hand) / Ways to make hand
Each hand type has its own combinatorial count — for example, four of a kind is C(13,1) × C(48,1), because there are 13 ranks to choose for the quad and 48 remaining cards for the kicker.
Every Hand Ranking, Exact
| Hand | Ways to make it | Probability | Odds against |
|---|---|---|---|
| Royal Flush | 4 | 0.00015% | 649,739 : 1 |
| Straight Flush | 36 | 0.00139% | 72,192 : 1 |
| Four of a Kind | 624 | 0.02401% | 4,164 : 1 |
| Full House | 3,744 | 0.14406% | 693 : 1 |
| Flush | 5,108 | 0.19654% | 508 : 1 |
| Straight | 10,200 | 0.39246% | 254 : 1 |
| Three of a Kind | 54,912 | 2.11285% | 46 : 1 |
| Two Pair | 123,552 | 4.75390% | 20 : 1 |
| One Pair | 1,098,240 | 42.25690% | 1.37 : 1 |
| High Card | 1,302,540 | 50.11774% | 1.00 : 1 |
These ten counts add up to exactly 2,598,960 — every possible 5-card hand is covered once.
Where This Matters
- Learning hand strength intuitively — seeing that one pair shows up in roughly 1 of every 2.4 hands, while a full house shows up in fewer than 1 in 690, explains why post-flop betting is shaped the way it is.
- Evaluating home-game side bets — a payout structure that pays even money on "any pair or better" is a very different proposition from one that pays even money on "flush or better."
- Teaching combinatorics — poker hand frequencies are a standard, concrete example for explaining combinations (nCr) in a probability course.
How to Use This Calculator
- Select a hand type from the dropdown — Royal Flush, Straight Flush, Four of a Kind, Full House, Flush, Straight, Three of a Kind, Two Pair, One Pair, or High Card.
- Select Calculate to see the exact probability and odds against being dealt that hand in a single 5-card draw.
Related Calculations
Working out live-hand odds instead of a static deal? Use the Texas Hold'em Equity Calculator for outs-based equity, or check Deck Shuffle Randomness Calculator to see how many possible shuffles a deck actually has.