The Odds of Making a Two Pair Hand in Poker

Odds of Making Two Pair on the Later Streets

Let’s imagine that we have flopped a pair and want to know the odds of making Two Pair by the river.

By the flop, there are 47 unknown cards left in the deck, and we have 3 outs to make Two Pair. We also have 2 outs to make Trips, which are very relevant, and we’ll account for those too.

From Flop to Turn

One pair with the board…

3 out of 47 cards make us Two Pair. 3/47 = 0.0638 or roughly 6.4%

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

From Turn to River

3 out of 46 cards make us Two Pair. 3/46 = 0.0652 or roughly 6.5%

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

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%.

One pair with the board….

Probability of not hitting Two Pair on the turn = 44/47

Probability of not hitting Two Pair on the river = 43/46

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 Two Pair on the turn or river = (44/47 * 43/46) = 0.8751 or roughly 88%

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 Two Pair from flop to river = roughly 12%

Probability of hitting Two Pair or Trips from flop to river = roughly 20.3%

Implied Odds Analysis of Two Pair

Making Two Pair often means we’ll benefit from a small amount of implied odds. We’ll usually have the best hand and can frequently either call down on the later streets or make additional value bets ourselves.

These hands are not invulnerable, however, and don’t carry the same implied odds that hands such as Straights and Flushes do. Two Pair can never be the stone-cold nuts since there is always the possibility that our opponent has a set.

Naturally, some Two Pair type hands are better than others. When making estimates regarding our implied odds we should usually think about the following -

- Do we have Top Two Pair? Top and middle? Two middle pairs? Bottom two?

Top two carries the best implied odds since our opponent might have made a dominated Two Pair.

- Is the board texture dry, or does it allow for completed draws?

Our implied odds suffer significantly on board textures where Straights and Flushes are possible. On extremely connected textures such as four-to-a-flush and four-to-a-straight textures, our Two Pair hands actually start to suffer from reverse implied odds.

Basic Strategy Advice

Two Pair is generally a strong hand in Hold’em and is frequently strong enough to play for stacks, assuming 100bb effective.

However, we should not blindly stack off with such holdings. On textures where possible draws have already completed, we will want to exercise caution. We should also look carefully at the absolute strength of our Two Pair. Top Two Pair is definitely more valuable than bottom Two Pair.