Notice that the circles do not intersect or overlap. From that, you can infer that a straight flush and ordinary straight are mutually exclusive events. To compute the probability of an ordinary straight, we rearrange terms, as shown below:.
From the analysis in the previous section, we know that the probability of a straight flush P sf is 0. Therefore, to compute the probability of an ordinary straight P os , we need to find P s. Here is how to find P s :. The number of ways to produce a straight Num s is equal to the product of the number of ways to make each independent choice.
Bottom line: In stud poker, even an ordinary straight is a pretty rare event. On average, it occurs once every deals. Probability Probability Basics About the tutorial What is probability?
Compared to the 10, ways to make a straight, three-of-a-kind occurs more commonly, making the straight the more rare and stronger hand.
The math of making a five-card hand out of seven cards puts three-of-a-kind much closer to a straight as far as probability. This is Dynamik Widget Area. Does Three of a Kind Beat a Straight? Now that you have an answer, let me explain why a straight beats three-of-a-kind. The Math Behind a Straight A straight is made when a player holds five cards in sequential order according to card rankings. Another straight example looks like this: The above qualifies as a seven-high straight.
Geoffrey Fisk Poker Rules Sep 1, About the Author. Geoffrey Fisk. Freelance writer and poker player based in San Diego, California. Take Poker Quizzes Now. Now that we have chosen the suits of the cards, we now have to choose the number for each card. In this case, we note that once we have chosen the lowest numbered card, the remaining cards must follow consecutively from the previous card.
Now, note that we can have a straight starting with ace through However, if it starts at a Jack, we will run out of cards to place in our straight, so there are only 10 options for the lowest card. We, therefore, have a total of ways to construct a straight. As we count the number of hands that are a straight or a flush, we will do so by noticing that we can do so by adding the number of straights to the number of flushes and subtracting the number of hands that are both.
Note we have to subtract off the hands that are both because we are counting them twice by adding the number of straights to number of flushes. We will therefore first need to find the number of hands that are both flushes and straight. Such hands would be called a straight flush and would be a hand in which you can rearrange the numbers so that they are consecutive and all the cards will be the same suit. If we follow the process we had above for choosing number and suit, we can find the number of such hands.
Since this hand will be a flush, we will have exactly 4 choices for suits. Also, since the hand is a straight, we will have 10 choices for the number. We, therefore, get that there are 40 total straight flushes. We were able to count the number of different ways to get a flush or straight in poker by combining our different counting techniques.
We could use these same counting techniques, with some modification in order to count the other types of hands as well. As we do so, make sure to determine how to construct each handing, noting whether or not order matter in each case. I hope you enjoyed and learned something from this post.
If you did, make sure to like it and share it on Social Media with anyone else that may find it useful. Albert received his Ph. He is currently an instructor at Virginia Commonwealth University. He has a passion for teaching and learning not only mathematics, but all subjects.
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