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How to Compute the Probability of a Straight in Poker

The basic probability formula is the number of successful outcomes divided by the total number of outcomes. In poker, knowing the odds of making your hand is vital because it will help you determine whether it is worth staying in a hand or folding. A straight is any five cards in a row, such as 5-6-7-8-9, of the same suit. An ace can be high or low, but you cannot wrap around. For example, you could have a straight of A-2-3-4-5 or 10-J-Q-K-A, but not K-A-2-3-4. There are 10,200 possible straights and 2,598,960 possible five-card hands, so the odds of being dealt a straight are 1 in 255. Most likely, if you're search for a straight, you'll have four cards and just need that one more on your draw.

Things You'll Need

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Instructions

    • 1

      Count the number cards that can complete your straight. This is the number of possibilities for completing the straight. If you have an open-ended straight, your odds are twice as high as with a closed straight. For example, if you have 9-10-J-Q, either an 8 or a K could complete your straight, so it is open-ended. You have eight ways to complete the straight because you could draw any of the four eights or kings. However, if you have 9-10-Q-K, you would only have four ways to complete the straight because you could only draw one of the four jacks.

    • 2

      Count the number of cards you could draw, which are the number of possible outcomes. For example, if you have five cards in your hand, there are 47 cards remaining in the deck.

    • 3

      Divide the number of cards that could complete your straight by the number of cards remaining in the deck to find the probability of getting your straight in poker. If you have an open-ended straight, with eight possible cards, divide 8 by 47 to get a probability of 0.17, or 17 percent. If you have a closed straight, divide 4 by 47 to find the probability equals 0.085, or about 8.5 percent.

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