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Table

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Hand Name Example Probability
Royal Flush
Ace Diamond
King Diamond
Queen Diamond
Jack Diamonds
10 Diamonds

Work

4
------
52 C 5

Answer

4 / 2598960 or 1.539077169E-6 or around .0002%
Straight Flush
10 Spades
9 Spades
8 Spades
7 Spades
6 Spades

Work

9 * 4
------
52 C 5

Answer

36 / 2598960 or 1.385169452E-5 or around .001%
Four of a Kind
Jack Diamonds
Jack Hearts
Jack Clubs
Jack Clubs

Work

13 * 4 C 4 * 13
---------------
52 C 5

Answer

169 / 2598960 or 6.50260104E-5 or around .007%
Full House
Ace Diamonds
Ace Hearts
10 Diamonds
10 Spades
10 Clubs

Work

13 * 4 C 3 * 12 * 4 C 2
-----------------------
52 C 5

13 * 4 * 12 * 6
---------------
52 C 5

Answer

3744 / 2598960 or .0014405762 or around .1%
Flush
Ace Diamonds
10 Diamonds
9 Diamonds
6 Diamonds
2 Diamonds

Work

13 C 5
------
52 C 5

Answer

1287 / 2598960 or 4.91980792E-4 or around .04%
Straight
Jack Spades
10 Diamonds
9 Clubs
8 Hearts
7 Hearts

Work

9 * 45
------
52 C 5

Answer

9216 / 2598960 or .0035460338 or around .3%
Three of a Kind
Ace Diamonds
Ace Hearts
Ace Clubs

Work

13 * (4 C 3) * (12 C 2) * 42
----------------------------
52 C 5

13 * 3 * 66 * 16
----------------
2598960

Answer

41184 / 2598960 or .0158463385 or around 1.6%
Two Pairs
7 Diamond
7 Heart
5 Spade
5 Diamond

Work

13 * (4 C 2) * 13 * (4 C 2) * 52
--------------------------------
52 C 5

13 * 6 * 13 * 6 * 52
--------------------
2598960

Answer

292032 / 2598960 or .112364946 or around 11.2%
Pair
9 Club
9 Diamond

Work

13 * (4 C 2) * (12 C 3) * 43
----------------------------
52 C 5

13 * 6 * 220 * 64
-----------------
2598960

Answer

1098240 / 2598960 or .4225690276 or around 42.3%

© Copyright 2001 Max Battcher/WorldMaker