Malaysian Games Convention

What Is the Probability of a Flush

Playing Cards Probability: Flush and Straight Flush Probabilities

At this point, we are already aware of the different hands in a poker game if you are playing you poker game as part of the togel online. One of the easiest ones to define is known as a “flush.” A flush is a hand that is composed of each card in the exact same suit.

To know the probability of drawing a type of hand in a poker game, certain counting techniques, or combinatorics, may be used.

What is the probability of dealing a royal flush? Well, this one is quite simple to decipher compared to finding the probability of getting a flush.

Assumptions

Let’s assume that 5 cards will be dealt from the standard deck of 52 cards. None of these cards are replaced, and no wild ones. The player can keep all cards dealt for him. Therefore, every hand has a 5-card combination.

The number of possible unique hands– 2,598,960. This particular hand set forms the sample space.

Flush

What is a flush? It is composed of 5 cards of the exact, same suit. All players must take note that the 4 suits in one standard deck have 13 cards each.

Therefore, flush is a mixture of 5 cards coming from a sum of 13 in one same suit. It can be done in 1,287 different ways.

Since 4 different suits exist, 5,148 flushes are very much possible. A few of these have already been regarded as hands with higher ranks.

The players should subtract the straight flush number and royal flush number from 5,148. This is necessary to get the number of flushes not included in higher ranks.

Straight Flush

It’s time to look for a straight flush’s probability.

What is a straight flush? It is a hand in which all 5 cards are of the same exact suit, and in sequential order. To precisely figure out the straight flush probability, we must follow certain stes.

A royal flush shouldn’t count as straight flush. Therefore, the highest-ranking straight flush is composed of a ten, nine, queen, jack and king—all of the same exact suit.

Take note that the ace can count a high or low card. The lowest-ranking straight flush is composed of 2, 3, 4, 5 and an ace—all of the same exact suit.

The ace, 2, 3, king and queen are not considered as straight, so these means that there are 9 straight flushes in any given suit.

4 separate suits make up 36 straight flushes. Thus, the straight flush probability is 0.0014%, around 1/72193. Players can expect this hand in the long run, once every 72,193 hands.

Computing for Card Probabilities and Rankings

As per the information above, every hand’s ranking highly depends on its probability.