What are the odds of a royal flush?

In the five cards available on the flop it is 4 out of 2,598,960 — about 1 in 649,740 (0.000154%). Using the best five of seven cards by the river, it improves to about 1 in 30,940 (0.0032%).

What are the odds of quads?

Four of a kind appears in about 0.168% of hands, roughly once every 594 hands.

How often do you flop a set with a pocket pair?

About 11.8% of the time — roughly once every 8.5 hands.

How do I calculate odds quickly while playing?

Use the rule of 2 and 4: multiply your outs by 4 with two cards to come, or by 2 with one card to come, to estimate your percentage chance.

What is the most common poker hand?

One pair, at roughly 43.8% of hands. That is why a single pair is often not strong enough in a large pot.

Poker Probability — Every Number Worth Knowing

Poker is a game of probability, not luck alone. Once you know the odds of each hand and the quick way to count outs, you stop guessing and start making decisions grounded in maths. The tables below show the exact probability of every five-card hand.

Royal flush: about 1 in 30,940
Quads: 0.168% of hands
One pair is the most common hand at 43.8%
Rule of 2 and 4: outs × 2 for one card, × 4 for two

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The short answer — exact numbers and how we calculated

Royal flush in the five cards available on the flop: 4 / 2,598,960 = 0.000154% — 1 in 649,740.

Holding two fixed Broadway cards of the same suit (A♠K♠) and needing the flop to bring exactly the three missing royal cards: 1 / C(50,3) = 1 in 19,600 ≈ 0.00510%.

Full house in the five cards available on the flop: 3,744 / 2,598,960 = 0.1441% — about 1 in 694.

How we calculated. Each figure counts the five-card combinations that make the hand and divides by all C(52,5) = 2,598,960 five-card combinations of a standard 52-card deck. On the flop a player has exactly five cards available (2 hole + 3 board). The chart further down uses the seven-card distribution instead (2 hole + 5 board by the river), which is why its percentages are higher — the same hand has more five-card combinations to be made from.

Figures verified on 15 September 2026 by direct combinatorial calculation.

Probability chart — best hand out of seven cards (by the river)

Hand	Odds	Percentage
Royal Flush	1 in 30,940	0.0032%
Straight Flush	1 in 3,590	0.0279%
Four of a Kind	1 in 594	0.168%
Full House	1 in 37.5	2.60%
Flush	1 in 32.1	3.03%
Straight	1 in 20.6	4.62%
Three of a Kind	1 in 19.7	4.83%
Two Pair	1 in 3.26	23.5%
One Pair	1 in 1.28	43.8%
High Card	1 in 4.74	17.4%

The rule of 2 and 4

You do not need a calculator at the table. Count the cards (outs) that make your hand a winner, then:

On the flop with two cards to come: outs × 4 ≈ your chance to complete.
On the turn with one card to come: outs × 2 ≈ your chance to complete.
Example: a flush draw has 9 outs — roughly 36% on the flop, 18% on the turn.

Preflop odds worth memorising

Being dealt any pocket pair: 5.9% (about 1 in 17).
Being dealt aces specifically: 0.45% (1 in 221).
Being dealt two suited cards: 23.5%.
Flopping a set with a pocket pair: about 11.8%.
AK versus a lower pair (the classic coin flip): roughly 43% to 57%.

Poker Probability — Every Number Worth Knowing

The short answer — exact numbers and how we calculated

Probability chart — best hand out of seven cards (by the river)

The rule of 2 and 4

Preflop odds worth memorising

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