Probability of Poker Hands

Every poker hand ranking is really a probability ranking: the rarer the hand, the higher it beats. From a single random five-card deal there are exactly 2,598,960 possible hands, and dividing the ways to make each hand by that total gives its probability — from a royal flush at 1 in 649,740 down to a one pair that shows up 42% of the time. Here is the full table, each number counted from combinatorics rather than memory.

The full probability table

Ranked from rarest to most common, using a fresh five-card deal:

Hand	Combinations	Probability	Odds against
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	0.144%	693 : 1
Flush	5,108	0.197%	508 : 1
Straight	10,200	0.392%	254 : 1
Three of a kind	54,912	2.11%	46 : 1
Two pair	123,552	4.75%	20 : 1
One pair	1,098,240	42.26%	1.37 : 1
High card	1,302,540	50.12%	1.0 : 1

Those combinations sum to exactly 2,598,960 — a clean check that nothing is double-counted. (Straight flush here excludes the royal, and flush and straight counts exclude any that are also straight flushes.)

How the counts are built

Each number is a small combinatorics problem. Two examples show the pattern:

Four of a kind. Pick the rank (13 ways), take all four of its cards (1 way), then any 1 of the remaining 48 cards as the kicker:

13 × 1 × 48 = 624

Full house. Pick the trips rank (13), choose 3 of its 4 suits C(4,3) = 4, pick a different pair rank (12), choose 2 of its suits C(4,2) = 6:

13 × 4 × 12 × 6 = 3,744

One pair. Pick the pair rank (13), choose 2 of its 4 suits C(4,2) = 6, then pick 3 different kicker ranks C(12,3) = 220, each in any suit 4 × 4 × 4 = 64:

13 × 6 × 220 × 64 = 1,098,240

The same logic — choose ranks, then choose suits — produces every row. Subtracting hands that accidentally form a straight or flush is what separates a plain flush count from a straight-flush count, and it is why the flush total (5,108) already excludes the 40 straight flushes. For the full method of counting card combinations, see poker combinatorics.

Made hands vs. draws

These are the odds of being dealt a finished five-card hand at random. In Texas hold’em you build a hand from seven cards, so the practical frequencies differ — you make one pair or better far more often across seven cards than the 5-card figures suggest. The five-card probabilities are the pure foundation; the game applies them across multiple streets.

That is why drawing math matters more at the table than the raw deal odds, and why postflop decisions hinge on what a hand can become. You rarely start with quads, but you often start with a draw that has a countable chance of becoming a strong hand by the river.

The gap is large. Dealt five random cards, a full house shows up 0.144% of the time; made from the best five of seven cards in hold’em, full houses appear several times more often, and one pair or better covers the large majority of finished hands. The five-card table understates every strong made hand relative to what you will actually see at showdown, because two extra cards give many more chances to improve.

Odds against, and why the format matters

The rightmost column above lists odds against — the ratio of hands that are not this hand to hands that are. For a royal flush that is (2,598,960 − 4) / 4 ≈ 649,739 to 1. Odds-against is the form you will hear at the table (“about 4,000 to 1 for quads”) because it maps directly onto payout thinking: a hand that is 4,164 to 1 against is genuinely once-in-a-session rare, while one pair at 1.37 to 1 is barely against you at all. Both columns describe the same event; percentages suit equity math, ratios suit intuition.

Two numbers worth memorizing

• You will hold at least a pair about half the time. One pair (42.3%) plus everything better (~7.6%) means roughly 50% of random hands are a pair or better; the other ~50% is high card only.
• The straight-vs-flush gap. Straights (10,200) outnumber flushes (5,108) almost two to one, which is the entire reason a flush wins the straight vs flush clash.

The takeaway

The ranking chart and the probability chart are the same chart. A royal flush is the lowest-probability hand at 1 in 649,740, high card is a coin flip at 50%, and everything between is ordered by exactly how many ways it can be built. Once you see rankings as counts, the whole odds and math hub clicks into place.