Royal flush is the greatest possible straight flush with an ace high. This combination consists of all suited cards, such as A-K-Q-J-T without jokers. In the games with jokers, the hand that consists of 4 cards of the same rank and the joker can be beaten only by the royal flush without joker. In this type of game, the royal flush that is completed without jokers is called a “natural” royal flush. Often, it is called "royal" because such combination is the rarest one and it is difficult to hit it.
That is why many casinos even offer rewards for such a hand (from the little gifts to the monetary reward).
Obviously, if you play with jokers your chances increase. If the number of jokers increases, the odds of hitting the royal flush also increase.
There are 4 variants of royal flush in the classic poker, where the combinations consist of 5 cards:
- A♥ K♥ Q♥ J♥ T♥
- A♦ K♦ Q♦ J♦ T♦
- A♣ K♣ Q♣ J♣ T♣
- A♠ K♠ Q♠ J♠ T♠
Basic assumption and probability
Let's assume that the player is dealt 5 cards from a standard 52-card deck. There are no jokers. In order to calculate the probability of royal flush, you need to know 2 figures:
- Total number of possible poker hands.
- The likelihood that a royal flush will be dealt.
Once we find out these two numbers, then it won’t be difficult to calculate the probability of royal flush. All you need to do is to divide the second number by the first one.
The number of poker hands
Combinatorial techniques or calculation methods can be used for calculating the total number of poker hands. It is important to note that the order of cards' dealing is of no importance. If the deck of 52 cards is used in the game, then you can hit 2 598 960 of different combinations (that consist of 5 cards).
The probability of hitting a royal flush
In a seven-card game such as Hold’em, or seven-card stud, you will hit the royal flash 1 time for every 30 940 hands. It means that you will have 0.003232% chances for hitting a royal flush for every particular hand. Also note that you can fold some “royal” cards during the play, because you won’t play each hand until the river. It means that in reality you will hit flash even more often.
Obviously, if you play with jokers, your chances for royal flush increase. If the number of jokers increases, the odds of completing a royal flush also increase.
Considering all of this, we can see that probability for completing a royal flash is too small. Out of 2.6 million hands, only 4 of them will hit this combination. Let’s note again that the formula for calculating the probability of hitting a royal flush is as follows: divide the number of royal flushes by the total number of poker hands. 4/2 598 960 = 1/649 740 = 0.00015% for completing this combination (for 5 card draw poker).
It follows that if the player plays 20 hands every day, then he will hit the strongest nut only 1 time in 7 300 hands, which is once every 89 years!
Since the royal flush is a rare combination, it often becomes an object of advertising. The poker rooms can grant you some clothes or hats with a logo in the case of hitting a royal flush.
In most poker games, the difference in suits of the same strength hands won’t be taken into account. For example, if two players hit a royal flush of different suits in a seven-card stud, then their hands will be considered equal in strength and they will split the pot. However, the situation when both players hit identical flushes or straight flushes during one hand in a seven-card stud is very rare.
In the games with flop and common cards, it is impossible for two or more players to hit the flushes or straight flushes of the same rank. Therefore, such situations never happen.
Rank of cards
The traditional classification of suits starts from the lowest to the highest one: clubs, diamonds, hearts and spades. Since the spades are considered the highest suit in the classification, we can often see the picture with a royal flush that consists of spades. The spades, in turn, symbolize the strength, power, wealth and exclusivity.
Royal flush in the movie industry and everyday life
Of course, according to the aesthetic point of view, the royal flush is an incredible performance. This combination is displayed in many pictures. It is shown in the movies, books, etc. For example, the main character hit the royal flush in the film “Maverick”. The agent 007 completed a straight flush in the film “Casino Royale”, but this combination was translated as a royal flush.
However, you shouldn’t believe the Hollywood films, because we found out that the probability of hitting this combination is too small. But there are players who were able to complete a royal flush, and luck is the reason for that. We wish you to hit the strongest combination and good luck!