---
title: "Probability of Flopping a Pair"
url: "https://georgelipoker.com/flop-odds/pair.md"
canonical_url: "https://georgelipoker.com/flop-odds/pair"
last_updated: "2026-10-22"
type: "reference"
summary: "An unpaired hand flops at least a pair 32.43% of the time, 1 in 3.08. Exact counts over all 19,600 flops."
related: ["https://georgelipoker.com/flop-odds.md", "https://georgelipoker.com/flop-odds/two-pair.md", "https://georgelipoker.com/flop-odds/set.md", "https://georgelipoker.com/flop-odds/straight.md"]
---

# Probability of Flopping a Pair

An unpaired hand flops at least a pair 32.43% of the time, 1 in 3.08. Exact counts over all 19,600 flops.

An unpaired hand flops at least a pair with a hole card 32.43% of the time, 1 in 3.08, because one of the six cards that match your hole ranks must land on the flop.

- At least one card matches: 32.43%
- Both cards match: 2.11%
- Exactly one matches: 30.32%

## What is the chance of flopping a pair?

With two different ranks in your hand there are six cards that match one of them among the 50 unseen. The flop has at least one of the six on 6,356 of 19,600 flops, 32.43%. That is 1 - C(44, 3) / C(50, 3), where 44 is the number of cards that match neither hole rank.

How an unpaired hand pairs up on the flop:

| Event | Chance | Odds | Flops out of 19,600 |
| --- | --- | --- | --- |
| At least one flop card matches a hole rank | 32.43% | 1 in 3.08 | 6,356 |
| Both hole ranks appear on the flop | 2.11% | 1 in 47.3 | 414 |
| Exactly one of the two ranks appears | 30.32% | 1 in 3.30 | 5,942 |
| Neither rank appears | 67.57% | 1 in 1.48 | 13,244 |

## What if I hold a pocket pair?

A pocket pair already is a pair, so the question becomes how often it improves. It makes a set or better 11.76% of the time, and the rest of the time it stays a pair or becomes two pair when the board pairs (16.16% of flops).

## Where do these numbers get used?

The chance to flop a hand is the first number in a plan. The pages below turn it into prices: what a call can cost, how many outs a draw has, and how many ways a hand can be dealt.

Related pages:

- [All flop odds](https://georgelipoker.com/flop-odds.md)
- [Hand matchups](https://georgelipoker.com/equity.md)
- [Combination counts](https://georgelipoker.com/combos.md)
- [Flopping two pair](https://georgelipoker.com/flop-odds/two-pair.md)
- [Flopping a set](https://georgelipoker.com/flop-odds/set.md)
- [Flopping a straight](https://georgelipoker.com/flop-odds/straight.md)

## How were these numbers computed?

After two hole cards are dealt, 50 cards are unseen and the flop is any 3 of them, so there are C(50, 3) = 19,600 equally likely flops. For each starting hand we deal all 19,600, classify the five cards with our hand evaluator and count. Suits are symmetric, so one combination stands for every combination of the same hand. The closed forms on this page use binomial coefficients and give the same counts.

Source: GeorgeLiPoker's own exact count of the 52-card deck.

## Questions

**What is the probability of flopping a pair?**

With two unpaired hole cards, 32.43%, or 1 in 3.08, that at least one flop card matches a hole rank.

**What are the odds of missing the flop completely?**

67.57%, or 1 in 1.48: none of the three flop cards matches either hole rank.

**Does it matter which ranks I hold?**

Not for the chance of matching a rank. Every unpaired hand has six matching cards among the 50 unseen, so the figure is the same for all of them.

## Related

- [Flop Odds: Set, Flush, Straight and More](https://georgelipoker.com/flop-odds.md)
- [Probability of Flopping Two Pair](https://georgelipoker.com/flop-odds/two-pair.md)
- [Probability of Flopping a Set](https://georgelipoker.com/flop-odds/set.md)
- [Probability of Flopping a Straight](https://georgelipoker.com/flop-odds/straight.md)