What is the probability of being dealt two pairs in a 5 card hand?
How to Compute the Probability of Equal-Rank Cards in Stud PokerIn this lesson, we explain how to compute the probability of being dealt two or more cards of equal rank in stud poker. (For a brief description of stud poker, click here.) Show
Hands With Equal-Rank CardsIn stud poker, there are five types of hands that include two or more cards of equal rank.
In this lesson, we will compute probabilities for each of these hands. How to Compute Poker ProbabilitiesIn a previous lesson, we explained how to compute probability for any type of poker hand. For convenience, here is a brief review:
So, how do we count the number of ways that different types of poker hands can occur? We recognize that every poker hand consists of five cards, and the order in which cards are arranged does not matter. When you talk about all the possible ways to count a set of objects without regard to order, you are talking about counting combinations. Luckily, we have a formula to do that: Counting combinations. The number of combinations of n objects taken r at a time is nCr = n(n - 1)(n - 2) . . . (n - r + 1)/r! = n! / r!(n - r)! 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. Probability of Four of a KindLet's execute the analytical plan described above to find the probability of four of a kind.
The probability of being dealt four of a kind is 0.0002400960384. On average, four of a kind is dealt one time in every 4,165 deals. Probability of a Full HouseWe follow a similar process to find the probability of a full house.
Based on these results, we can project that a full house will be dealt, on average, approximately one time in every 694 deals. Probability of Three of a KindWe use the same general approach to find the probability of three of a kind.
In stud poker, players get three of a kind about one time in every 47 deals. Probability of Two PairTo find the probability for two pair, we execute the same analytical plan that we've used to compute the other probabilities.
On average, players get two pair about one time in every 21 deals. Probability of One PairTo find the probability for one pair, we can use the same, general approach that we've used to compute each of the other probabilities for this lesson.
In stud poker, on any given hand, there is about a 42% chance that a player will be dealt one pair. What is the probability of drawing 2 pair from one deck of cards?Now our grand total possible number of ways to draw two pair in 5 cards is 2802 * 44 = 123.552. The probability, then, of getting two pair is 123,552/2,598,960 = 0.04754, which is about 1 in 21.
What is the probability of getting a 55-card poker hands. How many combinations of 5 cards are there?5! = 2598960 different ways to choose 5 cards from the available 52 cards.
How many two pairs are there?A straight flush is completely determined once the smallest card in the straight flush is known. There are 40 cards eligible to be the smallest card in a straight flush. Hence, there are 40 straight flushes.
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