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Below shows the probabilities of obtaining at least three of a specific card for both pocket pairs and non pocket pairs. The calculations include anything at least trips (4ofAKind or FullHouse) and exclude community trips. Flushes and Straights are not taken into consideration.

You can see that pocket pair hole cards have more than a 4x better chance of getting trips than non pocket pair hole cards. (C(n,r) choose function)

Pocket pair hole cards: 1 - [C(48,5) / C(50,5)] = 19.184%

Non pocket pair hole cards: 1 - [(C(44,5) + 6*C(44,4) + 9*C(44,3))/ C(50,5)] = 4.675%

The table below shows the trip draw probabilities while holding pocket pair hole cards. Note that the calculations only include trips that complete your pocket pair not for community trips. Flushes and Straights are not taken into consideration.

Draw Probabilities for obtaining trips with pocket pair hole cards

Complete on Flop Complete on Turn Complete on River
11.755% 4.255% 4.348%

Below shows the probabilities of obtaining at least three of a specific card for both pocket pairs and non pocket pairs. The calculations include anything at least trips (4ofAKind or FullHouse) and exclude community trips. Flushes and Straights are not taken into consideration.

You can see that pocket pair hole cards have more than a 4x better chance of getting trips than non pocket pair hole cards. (C(n,r) choose function)

Pocket pair hole cards: 1 - [C(48,5) / C(50,5)] = 19.184%

Non pocket pair hole cards: 1 - [(C(44,5) + 6*C(44,4) + 9*C(44,3))/ C(50,5)] = 4.675%

The table below shows the trip draw probabilities while holding pocket pair hole cards. Note that the calculations only include trips that complete your pocket pair not for community trips. Flushes and Straights are not taken into consideration.

Draw Probabilities for obtaining trips with pocket pair hole cards

Complete on Flop Complete on Turn Complete on River
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