In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands. The following enumerates the frequency of each hand, given all combinations of 5 cards randomly drawn from a full deck of 52 without replacement. Wild cards are not considered. The probability of drawing a given hand is calculated by dividing the.
Poker Variations Probability Definition
- Poker games have many variations, some of which will be investigated here. One such variation is 'stud' poker in which a player must hold all the cards he/she is given. This is opposed to 'draw' poker in which a player can draw any number of replacement cards after being dealt an initial five in the attempt to improve his/her hand.
- A 'poker hand' consists of 5 unordered cards from a standard deck of 52. There are 52 5 = 2,598,9604 possible poker hands. Below, we calculate the probability of each of the standard kinds of poker hands. This hand consists of values 10,J,Q,K,A, all of the same suit. Since the values are fixed, we only need to choose the suit.
- The probability of forming any given hand is the number of ways it can be arranged divided by the total number of combinations of 2,598.960. Below are the number of combinations for each hand. Just divide by 2,598,960 to get the probability.
In this type of poker, each player has some private cards, sometimes known as 'hole' cards, concealed from the other players, and there are some 'shared' or 'community' cards dealt face up to the centre of the table or board. These face up cards are available to all players, and each player makes up a five-card poker hand from a combination of private and shared cards. The most famous game of this sort is Texas Hold'em, which became popular as a tournament and online game at the end of the 20th and start of the 21st century, and is now played by many poker players to the exclusion of all other variants. Omaha is another well-known but somewhat less played variant, and there are numerous home poker games based on simlar principles and with various enhancements.
Poker Variations Probability Games
The index below includes both traditional shared card poker variants and invented variants (listed in italics). The game type column shows other categories to which some games also belong. See also the full index of poker variants, which includes an explanation of the categories.
#ABCDEF G HIJKLM N OP Q RST U VW X YZ
Variant | Game type |
---|---|
2-11 | |
4-2-3 | |
5 Card Omaha | shared |
6 Card Omaha | shared |
43 | |
Aces, Straights and Flushes | |
Big O [= 5 Card Omaha] | shared |
Binglao | shared |
Blue Beacon | |
Boise | |
Box | |
Breaker | shared |
Buddys Game | |
Chowaha | |
Church [= Iron Cross] | |
Cincinnati | |
Circle Jerk | |
Cold Omaha | |
Courchevel | shared |
Crazy Blind Man | |
Crazy Pineapple | |
Crazy Pineapple Hi-Lo | |
Criss Cross [= Iron Cross] | |
Criss Cross [= Tic Tac Toe] | |
Cucamonga | |
Delaware Stud | |
Depot | shared |
Doogie | |
Double Elevator | |
Double Trouble | |
Double-Edge Trim-Saw | |
Egyptian Hold'em | shared |
El Dorado Hold'em | |
Elevator | |
Five Card Omaha [= 5 Card Omaha] | shared |
Forty-Three | |
Four-Two-Three [= 4-2-3] | |
Fred Potato | shared |
Hearts Poker | |
Hollywood Hold'em | |
Indian Chief | shared |
Irish | shared |
Iron Cross | |
Island Pineapple | |
Jersey Holdem | |
Kansas Tornado | shared |
King's Pot | |
KRG | shared |
Kryky | |
Lame Brain Pete | |
Loco | shared |
Mutual of Omaha | |
Odds and Ends | |
Off-Road Stud | shared |
Oh Shit | |
Omaha | shared |
Omaha Hi-Lo Eight or Better | |
Omaha High | |
Omaha/8 [= Omaha Hi-Lo Eight or Better] | |
One Man's Trash | shared |
Pass'Em | |
Piles | |
Pineapple | shared |
Privacy Poker | |
Pyramid | |
Pyramid (2) | |
Rails | shared |
Real Poker | |
Round the World | shared |
Royal Hold'em | shared |
Ruby Run | shared |
Russian Roulette | shared |
Same'Em | shared |
Six Card Omaha [= 6 Card Omaha] | shared |
Skyscraper Elevator | |
Slam-aha | |
Southern Deuce Hold'em | |
Spit in the Ocean | |
Spots | |
Stop, Drop and Roll | shared |
Strobe | shared |
Suicide Swiss Hold'em | |
Sviten Special | |
Swiss Hold'em | |
Tapiola Hold'em | shared |
Texas Dozen | shared |
Texas Hold'em | |
Texas Reach Around | |
Texas Tornado | shared |
The Bluffs | |
The Game Called 'The' | shared |
Three-Hole Poker | shared |
Tic Tac Toe | |
Two Eleven | |
Vancouver Stud | |
Waiting for Godot | |
Woodstock | shared |
Wraparound | shared |
Yukon Hold'em | shared |
Z |