Getting A Straight Flush
When you hear things about poker especially at the mobile casino malaysia, you might have already heard the term “flush”. A flush in the game of poker is simply where the player possesses every card having the same suit (for example, Ace, Queen King, Jack, and 10, also known as the Royal Flush).
If you can create a straight flush, you’ve essentially won the game. But, what are the odds of you getting a flush? In this article, we will try to see the actual probability of you getting one.
What Are the Assumptions?
To make it simple for you, we will just assume that we are using a standard deck of cards without any special cards in it (such as the Joker).
Let’s also not concern ourselves with the exact order to which the cards are drawn. Instead, we would focus more on the actual combination of five cards taken from the complete deck.
If we are to do the math, C(52, 5), there is a total of 2,598,960 possible hands that can be taken just from the standard deck of cards. Moving forward, this will now be known as our Sample Space.
What is the Probability of Getting a Straight Flush?
Before we get started, you have to know what a straight flush is. A Straight Flush is where you will get five cards all in sequential order. It is also important to remember that all of these cards should be of the same set.
For us to truly calculate the probability of getting a straight flush, we would have to make a few stipulations first.
One, we will not count the Royal flush as a straight flush. This is so that the highest ranking straight flush does not contain any aces (which means we are only limited to getting a 9, 10, jack, queen, and king cards of the same suit).
Now, the previous example would be to denote the highest possible value of a straight flush. But, since the Ace card can actually be deemed as the highest or lowest possible value card, we will just group the ace card with the lowest value cards, so it should look something like this: Ace, 2, 3 ,4 ,5 cards of the same suit.
These conditions will present us with nine possible straight flushes on any given suit. Since there are 4 different suits (Hearts, Spades, Diamonds, Clubs), that makes it a total of 39 total straight flushes.
Given that number, we can say that the probability of getting a straight flush would be 0.0014% if you follow this formula: 36/2,598,960. If we are to use that calculation, we would get a straight flush 1 out of 72,193 hands.
Regular Flush Probability
The regular flush is simply just five cards of the same set, even those that are not in sequential order.
We know for a fact that there are 13 cards in total and there are 4 suits. We also know that a flush is any combination of cards that amount to a total of 5 cards. So, using C(13, 5), we would have 1287 possible ways of getting a 5-card stack. And, since there are a total of 4 suits, there are 5148 flushes that are possible (using this formula: 1287×4).
Since we have already included the high-ranked cards in our previous calculation to determine the probability of getting a straight flush, we will slightly alter our calculation for us to get the regular flush.
There are 36 straight flushes and 4 royal flushes that a player can get. We must make sure that we do not get a double count. So, this means that there is a total of only 5108 regular flashes that do not include higher-ranked cards (5148-40).
Given that number, we can then proceed to calculate for the probability of getting a regular flush. The calculation would be 5108/2,598,960= 0.1965%. That number would give us the probability of 1/509, which means that we only get one flush for every 509 hands.