# Probability of a poker hand...?

10 Date created: Mon, May 17, 2021 10:03 AM
Date updated: Mon, Jun 20, 2022 6:56 PM

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Video answer: Math 131 - calculating the probability of poker hands ## Top best answers to the question «Probability of a poker hand...»

#### Frequency of 5-card poker hands

HandDistinct handsProbability
Flush (excluding royal flush and straight flush)1,2770.1965%
Straight (excluding royal flush and straight flush)100.3925%
Three of a kind8582.1128%
Two pair8584.7539%

Video answer: Poker hand probability: full house After dividing by (52-choose-5), the probability is 0.047539.

Putting all of this together, we obtain the following ranking of poker hands: Poker Hand Number of Ways to Get This Probability of This Hand Royal Flush 4 0.000154% Straight Flush 36 0.00139% Four of a Kind 624 0.0240%

There are 2,598,960 many possible 5-card Poker hands. Thus the probability of obtaining any one specific hand is 1 in 2,598,960 (roughly 1 in 2.6 million). The probability of obtaining a given type of hands (e.g. three of a kind) is

So, the probability of being dealt any combination of hands in poker is 1/2652. However, this number represents that you get a King first and then a Queen . But do you really care about their order? Not really.

P = (1/52) * (1/51) P = 1/2652. So the probability of being dealt the A and then K is 1/2652. As you might be able to work out, this is the same probability for any two exact cards, as the likelihood of being dealt A K is the same as being dealt a hand like 7 3 in that order.

Add the three scenarios!: 1098240 (hand) + 6589440 (connected) + 3294720 (flop) = 10982400 cases. Recall the amount of whole cases: 25989600. Ratio: like 0.42 or 42%. Add the two scenarios if I don't want the in-table pair: 1098240 + 6589440 / 25989600 = like 0.29 or 29%.

Case 1 (7 is a pair): (3C1) (12C1) (4C2) (11C1) Case 2 (7 is not a pair): (12C2) (4C2)^2. So the probability is: ( (3C1) (12C1) (4C2) (11C1) + (12C2) (4C2)^2)/ (52C5) But I think I'm missing something. probability poker. Share. edited Sep 1 '20 at 21:48. RobPratt. 23.1k 3. 