ROYAL FLUSH ODDS IN POKER GAME

All poker players around the world dream of achieving this extremely rare poker hand, but why? Why make a royal flush when you can make several other hands with less hassle?

For a quick breakdown of the royal flush, consult this dedicated blog post about what is a royal flush in poker.

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 royal flush represents for every poker player out there. We’ll also dig into the mathematics to discover different ways to make a royal flush to help you better understand how grandiose this hand truly is!

HOW TO CALCULATE THE PROBABILITY OF HITTING ROYAL FLUSH ON THE POKER TABLE?

Here’s a general guide to calculating how you can make a royal flush:

• Identify the Required Cards: Royal flushes are made in only one distinct way: a ten to ace straight, all from the same suit.
• Count the Possible Combinations: In a standard deck with a total number of 52 cards, there are four suits (hearts, diamonds, clubs, and spades), meaning that there are four ways to make a royal flush (four suits).
• Calculate Total Possible Combinations: Determine the total number of possible five-card combinations from a standard deck.
• Apply the Probability Formula: Use the probability formula: Probability = (Number of Favourable Outcomes) / (Total Number of Possible Outcomes).
• Plug in the Numbers: Insert the number of ways to make a royal flush as the favorable outcomes. Then, 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.

WHAT IS THE PROBABILITY OF HAVING A ROYAL FLUSH IN THE FIRST FIVE CARDS?

The probability of getting a royal flush in the first five cards of a poker hand is quite slim. To understand this, we look at the specific requirements for a royal flush: having the 10, jack, queen, king, and ace, all from the same suit.

Since there are four suits in a standard deck (hearts, diamonds, clubs, and spades), there are only four possible ways to make a royal flush — one for each suit. When you calculate the probability, you consider the total number of possible five-card combinations from a standard 52-card deck.

The odds come out to be a fraction, where the number of ways to get a royal flush is the numerator, and the total possible five-card combinations is the denominator. This fraction simplifies to a decimal or percentage, revealing the rarity of getting a royal flush in the initial five cards.

Skilled poker players are aware of this low probability but may use strategic gameplay to increase their chances of hitting this highly coveted five-card hand.

ODDS OF A ROYAL FLUSH IN A SEVEN-CARD HAND

When dealing with a seven-card hand, the calculation involves the total number of possible combinations. Using the combination formula, the numerator represents the number of ways to get a royal flush, and the denominator is the total possible combinations with seven total cards from a 52-card deck.

The resulting fraction or percentage signifies the likelihood of obtaining a royal flush in a seven-card hand. Similar to the five-card scenario, the odds remain relatively low, emphasising the rarity of achieving this exceptional hand. Nevertheless, just like all five-card hands, drawing a royal flush isn’t impossible.

ROYAL FLUSH ODDS IN TEXAS HOLD’EM POKER GAME

Before diving into the odds of making a royal flush, 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 royal flush, you need the 10, jack, queen, king, and ace of the same suit, but here’s the catch — these cards must come from the community cards, as you only get two private cards.

The odds of landing a royal flush in Texas hold’em are quite rare because you’re relying on specific community cards. With only four distinct hands to create a royal flush (only one distinct way for each suit), players face a challenging probability.

ROYAL FLUSH PROBABILITY PRE-FLOP

Seeing as making a royal flush depends on community cards, it isn’t possible to draw a royal flush pre-flop.

A royal flush requires five community cards, including the flop, turn, and river, in addition to the player’s two cards. This means that poker players must pass through these rounds before having a chance of making royal flush poker hands.

ROYAL FLUSH ODDS ON THE FLOP

Naturally, the probability of earning a royal flush also changes with each stage. Let’s look at the different ways of getting a five-card royal flush with the same hand during Texas hold’em:

With 19,600 different possible flops, flopping the royal flush is quite rare (1 in 19,600), which equals 0.05%.

ODDS FOR ROYAL FLUSH HANDS ON THE TURN OR RIVER

The chances of making this hand on the turn are 1/47, which is roughly 2.1%. When it comes for an open-ended royal flush, this rises to 2/47, which is roughly 4.3%.

Open-ended royal flushes are simply situations where the player has four consecutive cards to a royal flush and is only one card away from completing the desired hand.

For example, if a player holds the 10, jack, queen, and king of hearts, they have an open-ended royal flush draw. In this scenario, they would need the ace of hearts to complete the royal flush — the best hand in poker. Their hand is thus called an open-ended royal flush.

When it comes to the river, the chance of making a royal flush stands at around 7.69%, seeing as there is an extra card in play compared to the turn.

COMPARISON OF ROYAL FLUSH ODDS AND STRAIGHT FLUSH ODDS

Royal flushes and straight flushes are sometimes confused in the world of poker. Although these are both high-value hands and you could safely win the pot with both hands, they are very different.

If you want to find out more about the straight flush in poker, check out our dedicated post about the straight flush poker hand.

Here are the odds of making these hands on the flop, turn and river.

Stage	Royal Flush Odds	Straight Flush Odds
Flop	0.08%	0.27%
Turn	0.20%	0.54%
River	0.30%	0.81%

It’s important to note that the odds provided are based on specific assumptions and calculations, and actual odds can vary based on the specific context and cards dealt.

IS ACE HIGH STRAIGHT FLUSH THE SAME AS ROYAL FLUSH POKER?

No, an A-high straight flush is not the same as a royal flush in poker, although they share similarities. Both poker hands involve having five consecutive cards of the same suit. In an A-high straight flush, the sequence starts with an A and continues through the 2, 3, 4, and 5, or it could be higher, like 10, jack, queen, king, and ace.

On the other hand, a royal flush is a specific type of A-high straight flush, where the sequence is the 10, Jack, Queen, King, and ace—all from the same suit. So, while an A-high straight flush is a strong hand, a royal flush is the highest-ranking hand in poker and holds a special status due to its unique combination of cards.

ODDS AND PROBABILITY OF WINNING A ROYAL FLUSHES IN TEXAS HOLD’EM

In conclusion, landing a royal flush in Texas Hold’em is like hitting the jackpot—a rare and exciting feat in poker. Understanding the odds and probability adds a strategic edge to your game. Remember, while the chances are slim, the thrill of pursuing that ultimate hand is what makes poker so exhilarating.

It’s worth noting that some variations, with the introduction of wild cards, can alter the dynamics and enhance the possibilities of hitting this superb hand.