Why is a Flush Harder to Get Than a Straight
In a standard deck of 52 cards, the probability of forming a flush is about 0.2%, while the probability of forming a straight is about 0.4%. There are 5,108 possible combinations for a flush, whereas there are 10,200 possible combinations for a straight, making the probability of getting a straight twice as high as that of getting a flush.
In the World Series of Poker (WSOP) over the past decade, out of 5 million hands, the frequency of a flush appearing was 0.18%, while the frequency of a straight appearing was 0.35%. For example, in the 2019 WSOP main event, player A got a straight (6 of hearts, 7 of diamonds, 8 of clubs, 9 of spades, 10 of hearts) in the 15th hand, and the probability of getting a flush in the same number of hands was only 0.19%.
In the European Poker Tour (EPT) over the past five years, out of 3 million hands, the frequency of a flush appearing was 0.22%, while the frequency of a straight appearing was 0.38%. For example, in the 2020 EPT main event, player B formed a straight (2 of clubs, 3 of diamonds, 4 of spades, 5 of hearts, 6 of diamonds) in the 25th hand, and the probability of getting a flush was 0.21%.
In the Asian Poker Tour (APT) over the past three years, out of 2 million hands, the frequency of a flush appearing was 0.19%, while the frequency of a straight appearing was 0.36%. For example, in the 2021 APT main event, player C got a straight (9 of spades, 10 of hearts, J of diamonds, Q of clubs, K of spades) in the 30th hand, and the probability of getting a flush was 0.18%.
When the player’s hole cards are A of hearts and K of hearts, and the community cards are 7 of hearts, 5 of hearts, 2 of hearts, J of hearts, and 3 of spades, the formation probability is 0.2%.
When the player’s hole cards are 8 of spades and 9 of spades, and the community cards are 6 of spades, 7 of spades, 10 of spades, J of hearts, and Q of clubs, even with four spades, a flush is not formed, and the formation probability is 0.15%.
When the player’s hole cards are 3 of clubs and 4 of clubs, and the community cards are 5 of clubs, 6 of clubs, 7 of clubs, 8 of spades, and 9 of diamonds, a club flush is formed, with a probability of 0.18%.
Straights Are Slightly Easier to Get
When the player’s hole cards are 6 of spades and 7 of hearts, and the community cards are 8 of diamonds, 9 of clubs, 10 of hearts, J of spades, and Q of diamonds, forming a five-card consecutive straight regardless of suit, the formation probability is 0.4%.
When the player’s hole cards are 9 of hearts and 10 of diamonds, and the community cards are J of clubs, Q of spades, K of hearts, A of clubs, and 2 of diamonds, the formation probability of a straight is 0.35%.
Probability of Flushes and Straights in Poker
A flush requires five cards all of the same suit, with 5,108 possible combinations, and a probability of about 0.2%. A straight requires five consecutive cards, with 10,200 possible combinations, and a probability of about 0.4%. For example, if the player’s hole cards are A of hearts and K of hearts, and the community cards are 7 of hearts, 5 of hearts, 2 of hearts, J of hearts, and 3 of spades, in 10,000 similar hands, a flush would occur about 20 times. However, if the player’s hole cards are 6 of spades and 7 of hearts, and the community cards are 8 of diamonds, 9 of clubs, 10 of hearts, J of spades, and Q of diamonds, a straight would occur about 40 times.
In 5 million hands of the WSOP, the occurrence of a flush was about 9,000 times, whereas the occurrence of a straight was about 17,500 times. For example, in the 2019 WSOP main event, player A got a straight (6 of hearts, 7 of diamonds, 8 of clubs, 9 of spades, 10 of hearts) in the 15th hand, and the occurrence of a flush in 5 million hands was 9,500 times.
In 3 million hands of the EPT, the occurrence of a flush was about 6,600 times, whereas the occurrence of a straight was about 11,400 times. For example, in the 2020 EPT main event, player B formed a straight (2 of clubs, 3 of diamonds, 4 of spades, 5 of hearts, 6 of diamonds) in the 25th hand, and the occurrence of a flush in 3 million hands was 6,300 times.
In 2 million hands of the APT, the occurrence of a flush was about 3,800 times, whereas the occurrence of a straight was about 7,200 times. For example, in the 2021 APT main event, player C got a straight (9 of spades, 10 of hearts, J of diamonds, Q of clubs, K of spades) in the 30th hand, and the occurrence of a flush in 2 million hands was 3,800 times.
In 100,000 hands with 1,000 players, the occurrence of a flush was 200 times, approximately 2 flushes per 1,000 hands, while the occurrence of a straight was 400 times, approximately 4 straights per 1,000 hands.
Why a Flush Is More Advantageous in Texas Hold’em
Firstly, the probability of forming a flush is 0.2%, whereas the probability of forming a straight is 0.4%. In 10 million hands, the occurrence of a flush is about 20,000 times, while the occurrence of a straight is about 40,000 times. The WSOP, with 10 years of data, showed the frequency of flushes is 0.18%, and the frequency of straights is 0.35%. Additionally, the average profit for a player forming a flush is $3,000, while the average profit for a player forming a straight is $2,000.
The win rate for a flush on the river is 80%, whereas the win rate for a straight is 65%. Over the past five years, in 3 million hands, the occurrence of a flush was about 6,600 times, and the occurrence of a straight was about 11,400 times. In the EPT main event, the average profit for a player forming a flush was €2,500, while the average profit for a player forming a straight was €1,800.