The Chance of Achieving Four of a Kind while Playing Poker

Chances of Forming Four of a Kind on Later Rounds

The most frequent opportunity to make Four of a Kind arises when we already possess Three of a Kind in the current round. With only four cards of each value available in the deck, this means that we will have only one chance to complete Quads during each round.

The likelihood of completing Quads on the turn is 1 out of 47, equating to about 2.1%.

On the river, the odds of hitting Quads improve slightly to 1 out of 46, which is approximately 2.2%.

To figure out the chances of landing Quads on either the turn or river, we can apply a straightforward method.

We'll first calculate the probability of missing and then deduct that from 100.

The chance of not hitting Quads on the turn is 46 out of 47.

Similarly, the odds of not getting Quads on the river are 45 out of 46.

Thus, the probability of not achieving Quads on either the turn or river equals 46/47 multiplied by 45/46, which is about 95.7%.

Therefore, the probability of hitting Quads by the time we reach the river after flopping trips is (100 – 95.7) = approximately 4.3% .

Even after obtaining Three of a Kind, the numerical odds suggest that achieving Four of a Kind by the river remains unlikely.

Delving into Implied Odds for Four of a Kind

Four of a Kind is always associated with advantageous implied odds as long as one of our hole cards is utilized.

If the four matching cards are displayed on the board, it results in every player at the table having Quads, substantially diminishing the relevance of implied odds. When four cards of the identical rank are visible, the player holding an Ace in their hole card guarantees victory.

This situation makes it less likely for opponents to risk a significant portion of their stack with merely a King kicker, limiting our expectations for great implied odds.

Creating Quads using one of our hole cards while three matching cards appear on the board offers excellent implied odds. An opponent holding a large pair may often perceive their hand as a winning full house and will hesitate to fold.

Even if they suspect we might have Quads, it may not be in their best interest to lay down their hand unless we are involved in a deep-stakes game.

When we use both hole cards to form Quads (for instance, having two matching cards on the board), it creates a highly beneficial situation regarding implied odds, as our Quads can remain concealed, allowing us to potentially trap opponents with full houses.

However, this can vary based on the layout of the board. For instance, when two matching cards are already present on the board, opponents might credit us with trips and may not fully consider the possibility of us having Quads.

For example, if we hold 55 against a board showing 5-5-4-2, our opponent may decide to fold based on fear of us holding a 5x, knowing that they themselves cannot possess one due to card removal.

Conversely, possessing 55 when the board reads 5-5-6-6 renders the situation highly valuable, as our opponent is unlikely to part with their 6x overfull.

In essence, the specific implied odds of Quads formed by a pocket pair greatly depend on the structure of the board.

Basic Strategy Advice

Quads are essentially unbeatable. Never fold Quads when holding a stack of 100bb deep (unless at least one of your hole cards contributed to the Quads).

If the four matching cards are revealed on the board, it’s wise to proceed carefully unless we hold the Ace. In these cases, pushing for value betting is advisable, even if it’s improbable we will extract chips from weaker hands.

Since this particular situation doesn’t arise frequently, novice players might misjudge the strength of their hand, leading to unfortunate call downs. They might overlook that their QQ has been counterfeited by a KKKKx board and that any Ace will claim the pot.