FOUR OF A KIND ODDS IN POKER GAME

One of the best possible hand combinations in poker is the four of a kind. Although this poker hand is the third-best hand, it usually ends up being the winning hand. This is the exact reason why one should know the possibilities of having a four of a kind dealt to them.

For a quick breakdown of the four of a kind, consult this dedicated blog post about what is a four of a kind poker hand.

Should you need a complete breakdown of all the poker hands out there, check out this dedicated blog post with all poker hands explained.

That said, in this post, we’ll be establishing what the four of a kind represents for every poker player out there. We’ll also dig into the probabilities to discover different ways to make a four of a kind to help you better understand how superb this hand truly is!

HOW TO CALCULATE THE PROBABILITY OF HITTING FOUR OF A KIND ON THE POKER TABLE?

Here’s a general guide to calculating how you can make a four of a kind:

• Identify the Target Hand: Four of a kind involves having four cards of the same rank (e.g., four 7s) but of different suits.
• Determine the Number of Ways: Count the number of ways to get this hand for each rank in the deck.
• Calculate the Total Possible Five-Card Hands: Use the combination formula (C(n, k)) to find the total number of five-card combinations from a standard deck.
• Apply the Probability Formula: Use the probability formula: Probability = (Number of Ways to Get Four of a Kind) / (Total Possible Five-Card Combinations).
• Plug in the Numbers: Insert the number of ways to get four of a kind as the favourable outcomes. Insert the total possible five-card combinations as the total number of outcomes.
• Simplify the Fraction: Simplify the fraction to obtain the probability as a decimal or percentage.
• Note: Understand that the probability of four of a kind varies based on the specific cards and the stage of the game.

FOUR OF A KIND ODDS IN TEXAS HOLD’EM POKER GAME

Before diving into the probability of making a four of a kind, let’s have a brief look at how the game of Texas hold’em unfolds.

In Texas hold’em, each player gets two hole cards, and five community cards are placed face-up on the table. To make a four of a kind, you need four cards of the same rank.

As one can assume, the chances of making a four of a kind poker hand depends on the variant you are playing. If you are playing 5-Card poker, for example, the significance of five cards in play will greatly make a difference when it comes to the probabilities compared to, for example, Texas hold’em.

FOUR OF A KIND PROBABILITY PRE-FLOP

Seeing as drawing a four of a kind poker hand depends on community cards, it is impossible to draw a four of a kind pre-flop.

Four of a kind poker hands requires at least four cards, so without the flop and turn, there is no point in trying to calculate an event that simply cannot happen.

FOUR OF A KIND ODDS ON THE FLOP

What cards is the player holding? Yes, this answer does matter. Having a pair greatly facilitates your chances of making Quads (a four of a kind poker hand).

If you have a pair in your hand (for example, two 7s), the chances of flopping a four of a kind are calculated as follows:

• You already have two of the same rank, so you need two more of that rank among the three comm. cards (the flop).
• The probability of the first card on the flop matching your pair is 2 in 50 (because there are 50 cards left after removing your two and the three on the flop).
• The probability of the second card matching is 1 in 49 (because there are now only 49 cards left).
• So, the overall probability is (2/50) * (1/49), which simplifies to 1 in 1225.

If you don’t have pocket pairs, the probability of flopping a four of a kind should be calculated differently:

• The probability of the first card on the flop matching any rank is 3 in 50 (because any card can match).
• The probability of the second card also matching the first is still 3 in 49 (because there are now 49 cards left).
• So, the overall probability is (3/50) * (3/49), which simplifies to 1 in 272.2.

ODDS FOR FOUR OF A KIND HANDS ON THE TURN OR RIVER

Calculating the probability for these situations requires precise information about the cards in play, both in your hand and on the board.

The specific ranks and suits of the cards are crucial factors in determining the probability accurately. Additionally, the probability to change dynamically as comm. cards are revealed.

For a comprehensive calculation, it’s advisable to use poker probability software or tools that can consider all possible combinations and variations based on the specific context of the variant.

COMPARISON OF FOUR OF A KIND ODDS AND ROYAL FLUSH ODDS

The royal flush is an unbeatable hand, one that can only be tied by another royal flush by some other player. With that said, the four of a kind poker hand is a similarly strong hand. Here are the differences between the chances of making Quads and making a royal flush.

Stage	Royal Flush Odds	Four of a Kind Odds
Flop	0.08%	0.24%
Turn	0.20%	0.49%
River	0.30%	0.73%

When we compare the odds of four of a kinds and royal flushes in poker, it’s like weighing the chances of two extraordinary events.

A four of a kind, where you get four cards of the same rank and the fifth card being a kicker, is more likely to happen compared to the ultra-rare royal flush, which is the highest-ranking hand in poker.

If you’d like to read more about the odds of a royal flush, you can do so by visiting our dedicated article about the royal flush odds.

FOUR OF A KIND OR STRAIGHT FLUSH – WHAT IS THE PROBABILITY?

In poker, landing a straight flush and a four of a kind is somewhat equally fantastic, but they come with different probabilities. A straight flush is a hand with five cards (consecutive) of the same suit, like 7, 8, 9, 10, and jack of spades.

The probability of getting a four of a kind is generally higher than that of a straight flush because there are many other possibilities to achieve it than just one — matching ranks can happen in various combinations.

In contrast, a straight flush demands a specific sequence of consecutive cards of the same suit, making it a rarer occurrence.

If you want to read more about the straight flush poker hand, have a look at our dedicated blog about the straight flush poker hand.

IMPLIED ODDS FOR FOUR OF A KIND POKER HAND

Understanding implied odds for a four of a kind poker hand involves considering potential future gains when deciding whether to continue with a hand. Implied odds go beyond the current pot odds and factor in the likely winnings from opponents if the desired card is drawn in subsequent rounds.

Let’s say that, for example, you have a draw to a four of a kind, and although the current pot odds may not justify calling, the implied odds take into account the additional chips you could win if you complete your hand and your opponents continue betting.

This strategic concept allows players to make more informed decisions by evaluating the potential long-term value of their hands rather than just the immediate situation in the poker round.