How many flushes are possible

The number of combinations of n objects taken r at a time is. In summary, we use the combination formula to count a the number of possible five-card hands and b the number of ways a particular type of hand can be dealt. To find probability, we divide the latter by the former.

Let's execute the analytical plan described above to find the probability of a straight flush. The number of ways to produce a straight flush Num sf is equal to the product of the number of ways to make each independent choice.

The probability of being dealt a straight flush is 0. On average, a straight flush is dealt one time in every 64, deals.

The Venn diagram below shows the relationship between a straight flush and an ordinary flush. Everything within the rectangle is a flush, in the sense that it is a poker hand with five cards in the same suit.

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Active 3 years, 8 months ago. Viewed times. WhoopsBing WhoopsBing 2 2 bronze badges. Add a comment. Active Oldest Votes. So the highest ranking straight flush consists of a nine, ten, jack, queen and king of the same suit.

Since an ace can count a low or high card, the lowest ranking straight flush is an ace, two, three, four and five of the same suit.

Straights cannot loop through the ace, so queen, king, ace, two and three are not counted as a straight. These conditions mean that there are nine straight flushes of a given suit. So in the long run, we would expect to see this hand one time out of every 72, hands. A flush consists of five cards which are all of the same suit. We must remember that there are four suits each with a total of 13 cards.

Thus a flush is a combination of five cards from a total of 13 of the same suit. Some of these flushes have already been counted as higher ranked hands. We must subtract the number of straight flushes and royal flushes from in order to obtain flushes that are not of a higher rank. There are 36 straight flushes and 4 royal flushes. We must make sure not to double count these hands. So in the long run, one out of every hands is a flush.

We can see from the above that the ranking of each hand corresponds to its probability. The more likely that a hand is, the lower it is in ranking. The more improbable that a hand is, the higher its ranking. Actively scan device characteristics for identification. Use precise geolocation data. Select personalised content. Create a personalised content profile.