(most recent edit: January 2, 2005)

A solitary PAIR

This the hand with the sample AABCD,where A, B, C and also D space from the unique "kinds" of cards: aces,twos, threes, tens, jacks, queens, and kings (there are 13 kinds,and 4 of each kind, in the conventional 52 map deck). The number ofsuch hands is (13-choose-1)*(4-choose-2)*(12-choose-3)*<(4-choose-1)>^3.If all hands space equally likely, the probability that a single pair isobtained by dividing by (52-choose-5). This probability is 0.422569.

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TWO PAIR

This hand has the sample AABBC whereby A, B,and C are from distinct kinds. The variety of such hands is(13-choose-2)(4-choose-2)(4-choose-2)(11-choose-1)(4-choose-1).After splitting by (52-choose-5), the probability is 0.047539.

A TRIPLE

This hand has actually the sample AAABC wherein A, B,and C space from distinct kinds. The variety of such hand is(13-choose-1)(4-choose-3)(12-choose-2)<4-choose-1>^2. The probabilityis 0.021128.

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A full HOUSE

This hand has actually the pattern AAABB whereA and also B are from distinct kinds. The variety of such hand is(13-choose-1)(4-choose-3)(12-choose-1)(4-choose-2). The probabilityis 0.001441.

four OF A kind

This hand has actually the sample AAAAB whereA and also B room from distinctive kinds. The number of such hand is(13-choose-1)(4-choose-4)(12-choose-1)(4-choose-1). The probabilityis 0.000240.

A straight

This is five cards in a sequence (e.g.,4,5,6,7,8), through aces allowed to be one of two people 1 or 13 (low or high) andwith the cards permitted to it is in of the exact same suit (e.g., all hearts) orfrom some different suits. The variety of such hand is 10*<4-choose-1>^5.The probability is 0.003940. IF YOU typical TO EXCLUDE straight FLUSHESAND royal FLUSHES (SEE BELOW), the variety of such hand is 10*<4-choose-1>^5 - 36 - 4 = 10200, through probability 0.00392465

A flush

here all 5 cards are from the exact same suit(they may also be a straight). The number of such hands is (4-choose-1)*(13-choose-5). The probability is about 0.00198079. IF YOU mean TO EXCLUDE right FLUSHES, SUBTRACT 4*10 (SEE THE following TYPEOF HAND): the number of hands would then be (4-choose-1)*(13-choose-5)-4*10,with probability about 0.0019654.

A straight FLUSH

every 5 cards are from the exact same suitand they form a right (they may likewise be a imperial flush). The number of such hands is 4*10, and theprobability is 0.0000153908. IF YOU typical TO EXCLUDE imperial FLUSHES, SUBTRACT 4(SEE THE NEXT kind OF HAND): the number of hands would then be 4*10-4 = 36, with probability approximately0.0000138517.

A royal FLUSH

This consists of the ten, jack, queen,king, and also ace of one suit. Over there are 4 such hands. The probabilityis 0.00000153908.

none OF THE above

We have actually to select 5 distinctive kinds(13-choose-5) but exclude any kind of straights (subtract 10). We can have anypattern of suits other than the 4 trends where all 5 cards have actually thesame suit: 4^5-4. The total variety of such hand is <(13-choose-5)-10>*(4^5-4). The probability is 0.501177.