Royal Flush is the rarest and most sought-after hand in poker. It’s the ultimate hand, ranking the highest in all poker combinations list. But how rare is it? And what is your chance to make a royal flush in a real game at least once in your life? Let’s dive into the math behind it and explore what it takes to get a royal flush in poker.
What Is a Royal Flush?
First, let’s understand what a royal flush is. A royal flush is the highest-ranking hand in poker. It consists of five cards in sequence, all of the same suit. These cards are the Ten, Jack, Queen, King, and Ace.
For example, if you have A♠ K♠ Q♠ J♠ T♠, you have a royal flush. There are only four possible royal flushes in a deck of cards (one for each suit: ♥ hearts, ♦ diamonds, ♣ clubs, and ♠ spades).
Calculating A Chance Of Getting A Royal Flush
Step 1. How Many Poker Hands Are There?
To understand the chances of getting a royal flush, you need to know how many possible poker hands can be dealt. A standard deck has 52 cards. To calculate the number of possible poker hands, we need to calculate the combinations of 5 cards out of 52.
The formula to calculate combinations is:
C(n,k)=n! / (k! × (n−k)!)
Where (n) is the total number of cards (52 in a deck), and (k) is the number of cards in the hand (5 in poker). So,
C(52, 5) = 52! / (5! × (52−5)!) = 2,598,960.
This means there are 2,598,960 possible 5-card hands in poker.
Step 2. How Many Royal Flushes Are There?
Now, let’s figure out how many royal flushes are possible. As mentioned, a royal flush is a sequence of five specific cards (Ten, Jack, Queen, King, Ace) of the same suit. Since there are four suits, there are 4 royal flushes.
Step 3. The Probability of Getting a Royal Flush
The probability of any event is calculated as:
P(A) = Number of favorable outcomes / Total number of possible outcomes
For a royal flush, the probability is:
P(Royal Flush) = 4 / 2,598,960 = 1 / 649,740
So, the chances of being dealt a royal flush in a 5-card poker hand are 1 in 649,740. It means that on average you will be getting a royal flush once every 650,000 hands.
Why Is It So Rare?
The rarity of the royal flush comes from the very specific combination of cards required. There are many other poker hands you can get, such as pairs, three-of-a-kind, full houses, and straight flushes, but the royal flush is the rarest. The odds of getting other hands are much higher, making them more common in gameplay.
How Often Will I Get A Royal Flush In Offline Games?
In offline tables, the speed of dealing is usually around 20 hands per hour. To make a distance of 650,000 hands you would need to dedicate 32,500 hours to playing poker. If you play for 8 hours 5 days a week (like a real job), you’d need more than 15 years to secure an achievement of 650,000 played hands.
But even then, there is no guarantee that you will see a royal flush even once. Much depends on luck. Some players encounter a royal flush many times, while others have never experienced the feeling of holding the strongest combination.
And What About Online Poker?
In online poker, your chances of getting a royal flush are higher due to the faster dealing process. In online games, players are usually dealt around 90 hands per hour. So if we do the same calculations here, to play 650,000 hands you’ll need 3,5 years of full-time grinding.
You can improve your odds even more by playing multiple tables at the same time, as many online pros do. In that case, you will likely see at least one royal flush in less than a year.
Comparing the Royal Flush to Other Hands
To put the rarity of the royal flush into perspective, let’s compare it to the probabilities of getting other poker hands:
- Straight Flush (excluding royal flush): 1 in 72,193
- Four of a Kind: 1 in 4,165
- Full House: 1 in 694
- Flush: 1 in 509
- Straight: 1 in 255
- Three of a Kind: 1 in 47
- Two Pair: 1 in 21
- One Pair: 1 in 2.4
- High Card: 1 in 1.3
As you can clearly see from these numbers, a royal flush is the rarest hand by far.
Odds in Different Poker Variants
The probabilities we’ve discussed apply to the classic 5-card draw poker. But poker has many variants, like Texas Hold’em, Omaha, and Seven-Card Stud. The odds of getting a royal flush can vary depending on the game.
- Texas Hold’em: In Texas Hold’em, each player is dealt two private cards, and five community cards are placed face up for everyone to use. The probability of getting a royal flush is slightly different because players have seven cards to make the best five-card hand. The odds are approximately 1 in 30,939.
- Omaha: In Omaha, players are dealt four private cards, and five community cards are shared. Players must use exactly two of their private cards and three of the community cards to make the best hand. The odds are roughly 1 in 108,290.
- Seven-Card Stud: In Seven-Card Stud, each player is dealt seven cards, and the best five-card hand wins. The odds of getting a royal flush are about 1 in 30,939, similar to Texas Hold’em.
These variations make the royal flush slightly more achievable in some games compared to others, but it remains an extremely rare hand.
What to Do If You Get a Royal Flush
If you’re lucky enough to get a royal flush, it’s a big deal. It’s a hand that cannot be beaten. The best strategy is to bet confidently but not too aggressively, as you want to keep your opponents in the game. If you scare them off with a big bet, they might fold, and you won’t win as much. A well-played royal flush can win you a significant pot. For offline games, you have another big challenge to hold a poker face in that hand 😅
Conclusion
The royal flush is the pinnacle of poker hands, rare and unbeatable. With odds of 1 in 649,740 in 5-card draw poker, it’s no wonder players dream of landing this hand. While the odds are slightly better in games like Texas Hold’em or Seven-Card Stud, it remains an elusive goal. If you ever get a royal flush, savor the moment and play it wisely. It’s a hand that doesn’t come around often, and when it does, it’s a moment to remember.