The Odds of Making Three of a Kind in Poker

The odds of flopping Three of a Kind when holding a pocket pair are 10.8% or 1 in 9.3

Definition of  Three of a Kind  –

Three of a Kind – We hold three cards of identical rank.

Example – AAAKQ

3-of-a-Kind can be Sets (where we hold a pair and match it) or Trips (where we match one hole card with a pair on the board).

Although Three of a Kind Aces is the best 3-of-a-Kind hand, kickers will come into play if more than one player has the same Three of a Kind with Trips.

Odds of Making Three of a Kind on the Flop

The odds of making Three of a Kind on the flop will vary depending on the type of preflop hand we have.

Odds of making Three of a Kind with a random starting hand – 1.9%

Odds of making Three of a Kind with a pocket pair – 10.8%

Odds of making Three of a Kind with an unpaired starting hand – 1.35%

We can hence see that making Three of a Kind on the flop is unlikely, but our odds increase, dramatically, when starting out with a pocket pair preflop.

What about the odds of flopping Three of a Kind or better?

Odds of making Three of a Kind plus with a random starting hand – 2.66%

Odds of making Three of a Kind plus with a pocket pair – 12%

Odds of making Three of a Kind plus with an unpaired starting hand – 2.08%

Not only do our odds of making Three of a Kind improve, dramatically, when holding a pocket pair, but our odds of making any premium holding (Three of a Kind plus) also increase significantly.

The odds of making Three of a Kind don’t change depending on the type of unpaired starting hand we have, but the odds of making Three of a Kind plus do.

Odds of making Three of a Kind with AKo – 1.35%

Odds of making Three of a Kind plus with AKo – 1.78%

Odds of making Three of a Kind with T9s – 1.35%

Odds of making Three of a Kind plus with T9s – 3.58%

All pocket pairs make Three of a Kind with an equivalent frequency, but the higher pocket pairs have better odds to make Top Set as opposed to middle/bottom set.

Odds of Making a Three of a Kind on the Later Streets

There are two main types of postflop draw that can result in Three of a Kind.

1. Having a pair with the board. (2 outs to make Three of a Kind).
2. Having an unimproved pocket pair. (2 outs to make Three of a Kind).

While the number of outs is identical, it’s worth remembering that we have additional three two-pair outs when we make a pair with the board.

We hence have 5 outs to make two pair or trips.

From Flop to Turn

2 out of 47 cards make us Three of a Kind. 2/47 = 0.0426 or roughly 4.2%

5 out of 47 cards make us two pair plus. 5/47 = 0.1064 or roughly 10.6%

From Turn to River

2 out of 46 cards make us Three of a Kind. 2/46 = 0.0435 or roughly 4.3%

5 out of 46 cards make us two pair plus. 5/46 = 0.1087 or roughly 10.9%

Note that there is a slightly higher chance of spiking from turn to river due to the smaller pool of available cards we are drawing from.

From Flop to River

To calculate this, we first enumerate the possibility of not hitting at all by the river and then subtract from 100%.

Probability of not hitting Three of a Kind on the turn = 45/47

Probability of not hitting Three of a Kind on the river = 44/46

Probability of not hitting two pair or trips on the turn = 42/47

Probability of not hitting two pair or trips on the river = 41/46

Probability of not hitting Three of a Kind on the turn or river = (45/47 * 44/46) = 0.9158 or roughly 91.6%

Probability of not hitting two pair or trips on the turn or river= (42/47) * (41/46) = 0.7965 or roughly 79.7%

Therefore -

Probability of hitting Three of a Kind from flop to river = roughly 8.4%

Probability of hitting two pair or trips from flop to river = roughly 20.3%

Implied Odds Analysis of Three of a Kind

Three of a Kind is typically considered a monster in Hold’em and is very often strong enough to play for stacks with assuming 100bb effective.

However, it is essential to make a distinction between Sets and Trips.

Both Sets and Trips are a type of “Three of a Kind”, but they are formed in different ways. Trips are created with one of our hole cards along with two cards from the board. A Set is formed using a pocket pair in the hole along with one card from the board.

In terms of implied odds, Sets are more valuable than Trips.

The reason is simply that Sets are disguised; there is no obvious indicator for our opponent that we have hit a monster. Trips are generally more transparent because it means the board will be paired.

If, for example, there are two Tens on the board, it doesn’t take a rocket scientist to figure out that if someone has a Ten in the hole, they will have made trips.

Also, Sets are exclusive. If we make Three of Kind Tens with a Set, it means no-one else at the table could ever make Three of a Kind Tens. There simply aren’t enough cards in the deck.

If we make trips with the board; however, it’s possible that our opponent can make the same trips with a better kicker.

Basic Strategy Advice

Most of the time, we will try and avoid folding Three of a Kind, but the board texture still needs to be considered.

Three of a Kind is the most valuable when there are no possible Straights and Flushes on the board. In situations where both are possible, we will occasionally need to make tight folds with Three of a Kind when playing 100bb effective.

On dry textures, we’d seldom fold a set. There may occasionally be exceptions when a) facing action from an overly tight opponent and b) playing with deeper than usual stack depth. (It can start to be a mistake to stack off with bottom set when the stacks are 150bb plus for example.)