The Probability of Flopping Straight Flush

FAQ

While playing poker, knowing the odds of certain occurrences can prove beneficial. This article will discuss the odds of flopping straight flush. In other words, you will understand what is the probability that the following 3 cards (flop) will belong to the same suit, given that you already have 2 same suit cards.

Calculating The Odds Of Flopping Straight Flush

Now that you have already dealt 2 cards from a 52-card deck, there are a total of 50 cards left. Our answer depends on these 2 cards that you are holding. For instance, if you have 62s, you need to hit precisely a 3, 4, and a 5. Whereas if you have 76s, you’ll be able to hit T98s, 854s, 985s, 543s, and so on. 

This means the answer is dependent upon which 2 cards you may be holding. This is because we are presuming to begin with 2 cards capable of making a straight flush. So, there are just 1, 2, 3, or 4 flops resulting in a straight flush. 

Consequently, we have 50C3 or 19600 possible flops. Here, the odds will be 1, 2, 3, or 4, based on the two starting cards you pick. This means the probability can be 1/(50C3), 2/(50C3), 3/(50C3), or 4/(50C3), based on your first two cards.

A Common Mistake Which You Must Avoid

Since 50C3 signifies the total number of different combinations representing the flop, you may mistakenly assume that since you possess 2 same suit cards, just 11 cards are left from this particular suit. This makes 11C3 the total number of possible combinations required to pick 3 such cards from the remaining 11-card pile. This way, you may conclude that the required probability comes down to 11C3/50C3.

Let’s understand the problem with this assumption now. Here 11C3 represents the possible methods from which you can withdraw the required 3 cards from the 11 same suit cards. However, there is no guarantee that any 3 cards of this suit ensure a sure-shot straight flush. 

For instance, if you hold the 2h4h, the resultant combination covered by 11C3 would be 9hAhTh. However, this flop will not lead to a straight flush. This way, you just calculated the odds of flopping a flush, and not straight flush, when you are dealt with two suited cards.

Summing Up

The probability that you’ll flop a straight flush after being dealt two cards of the same suit depends on these two cards themselves. You can flop a straight flush in only some specific ways – 1, 2, 3, or 4 ways, making the required probability either 1/(50C3), 2/(50C3), 3/(50C3), or 4/(50C3).

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