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MyPokerOdds

How often does a pocket pair make four of a kind by the river?

A pocket pair makes quads 0.816% of the time by the river — about 1 in 122 hands.

Probability
0.816%
about 1 time in 122
Exact. Both remaining cards of the rank must be among the five board cards.

Both of the two remaining cards of your rank have to land among the five board cards. Choose the other three board cards freely from 48: C(48, 3) boards out of C(50, 5). Under 1% — a hand you will see a handful of times a year.

  1. Boards containing both remaining cards17,296C(48, 3)
  2. All five-card boards2,118,760C(50, 5)
  3. Probability0.82%17296 / 2118760

Try it

Change any card; the numbers recompute from the same engine that produced the answer above.

Click any hand. Suited above the diagonal, offsuit below, pairs on it.

Shading: brighter green is higher equity. Monte Carlo simulation, seeded xoshiro128**, 500,000 trials per hand, seed 20260901.

Pocket pair

Pocket Eights

Combinations
6
of 1326
Dealt
0.45%
about 1 time in 221
Odds against
220 : 1

Equity against random hands

69.2%
vs 1
50.0%
vs 2
37.6%
vs 3
23.9%
vs 5
15.8%
vs 8

Multi-way, a hand’s share of the pot falls even when it is the favourite: a fair share against 8 opponents is 11.1%.

Head-to-head, exact

Every one of the 1,712,304 possible boards, enumerated for each matchup.

  • vs Pocket aces…
  • vs Pocket queens…
  • vs Ace-king offsuit…
  • vs Pocket sevens…

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