KK vs 99 vs 33, flop hits K93: How low is this probability?

Recently, a player on Reddit's r/poker shared a jaw-dropping hand: in a daily $1 buy-in tournament, three players went all-in preflop holding pocket pairs KK, 99, and 33. The flop came K, 9, 3 — each player flopped a set, creating an extreme scenario of "top set vs set vs set."

The player commented: "At first I saw a 9 and a 3, then I noticed the K." This sparked lively discussion in the community: just how rare is this?

According to poker probability (using a standard 52-card deck): Given six known hole cards (two each of KK, 99, and 33), there are 46 remaining cards. The flop must consist of exactly one K, one 9, and one 3. There are 2 remaining kings, 2 nines, and 2 threes, so the number of valid combinations is 2×2×2 = 8. Total flop combinations from 46 cards are C(46,3) = 15,180. Probability = 8/15,180 ≈ 0.0527%, or about 1 in 1,898.

Even more unusual is that all three players happened to hold the same pair types, and the flop perfectly matched each pocket pair. Considering all possible starting hands, the probability of this specific scenario is astronomically lower. Usually, three players holding three different pocket pairs and the flop hitting all three sets simultaneously is a sight reserved for dramatic tournament highlights.

Although this hand would create a massive pot in a cash game, the player did not reveal the outcome or pot size. One commenter joked: "If this happened online, take a screenshot immediately — you might not see it again for a decade."

How Rare Is It?

• Extremely low probability: The calculation above only applies given the three known pairs. If we consider random dealing, the chance of three players specifically getting KK, 99, and 33 is about 1 in 160 million. Multiplying by the flop probability of K93 gives roughly 1 in 300 billion.
• Visual impact: A flop that gives everyone a set is often called a "perfect flop" or "soul flop" in poker.

Takeaways for Players

Such scenarios are almost impossible to avoid through skill — pure luck. If you encounter it once in your lifetime, consider it a poker anecdote rather than a strategy template.

FAQs

Q: Is this hand a "bad beat" or a "full house"?

A: Strictly speaking, it's not a typical bad beat because sets are very strong, and since all players were all-in preflop, there was no chance to draw out. But it is indeed extremely rare.

Q: Should online poker platforms guard against this?

A: Random number generators are rigorously tested and theoretically allow any legal board combination. Such extreme cases actually demonstrate randomness and need no special intervention.

Q: What should I do if I encounter a similar hand?

A: Just enjoy the moment. If it's in a tournament, save the hand history and share it with friends. Statistically, most players will never experience this even once in their lifetime.