Poker Variations Probability
There are only 10 distinct poker hand ranks, but if you randomly deal 5 cards from a deck of 52 cards there are exactly 2,598,960 possible card combinations. Poker Hand Odds for 5-Card-Poker. The poker hand ranking charts are based on the probability for each distinct hand rank. More unlikely combinations are ranked higher. Chinese Poker is the fourth most popular variations of poker and is played all over the world. As the name suggests, it was originated from China and is very popular among Chinese. The final hand won is decided by the poker hand rankings similar to Texas Hold’em Poker. This variation of poker is a bit different from the others but super fun.
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.
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 |
On This Page
Introduction
Rules
Poker Variations Probability Calculator
- Six Card Poker is a poker variant game played heads up against the dealer. The object of the game is to win by having a better five-card poker hand than the dealer using six cards.
- The game is played using one standard 52-card deck. The game uses standard poker rules for scoring and comparing hands.
- To begin, the player makes an Ante Bet.
- The dealer deals six cards face down to the player. The dealer deals to himself, three cards face up and three cards face down.
- The player examines his cards and must either fold the hand, losing his Ante, or raise by making an additional wager that is equal to his Ante. Players may not share information about their cards with other players.
- The dealer reveals his hole cards and compares his best five-card hand to the player’s best five-card hand. The dealer must qualify with ace-king or higher.
- If the dealer does not qualify, then the player’s Ante bet is a push. The raise bet is resolved as follows:
- If the dealer's hand beats the player's hand, then the player loses his raise bet.
- If the player's hand beats the dealer's hand, then the player is paid 1 to 1 on his raise bet.
- In the event of a tie, the player’s raise bet is a push.
- If the dealer does qualify:
- If the dealer's hand beats the player’s hand, then the player loses his Ante and raise bets.
- If the player's hand beats the dealer’s hand, then the player is paid 1 to 1 on his Ante and raise bets.
- In the event of a tie, the player’s Ante and raise bets push.
- There are also two optional side bets, the Aces Up and Two-Way Bad Beat, which are explained below.
Analysis
The game was analyzed through brute force, combinatorial analysis. The following table summarizes the analysis results. The bottom left cell shows the house edge of 1.2717%. With an average bet size of 1.6987, the element of risk is 0.7486%.Ante Bet Analysis
| Outcome | Dealer Qualifies | Net Win | Combinations | Probability | Return |
|---|---|---|---|---|---|
| Player Wins | yes | 2 | 1,040,023,036,938,350 | 0.272693 | 0.545387 |
| Player Wins | no | 1 | 755,514,209,224,548 | 0.198095 | 0.198095 |
| Ties | yes | 0 | 210,847,746,240 | 0.000055 | 0.000000 |
| Ties | no | 0 | 50,992,983,876 | 0.000013 | 0.000000 |
| Fold | - | -1 | 1,149,186,512,820,950 | 0.301316 | -0.301316 |
| Dealer Wins | no | -1 | 2,937,744,249,924 | 0.000770 | -0.000770 |
| Dealer Wins | yes | -2 | 865,968,968,971,212 | 0.227056 | -0.454113 |
| Total | 3,813,892,312,935,100 | 1.000000 | -0.012717 |
Strategy
Two basic playing strategies are presented below.
Poker Variations Probability Rules
Intermediate basic strategy:
- Fold if dealer has a higher ranked hand using his three up cards alone. This rule supersedes all other rules.
- Fold with ace-10 or lower.
- Raise with ace-king or higher.
- With ace-queen, fold if the dealer is showing an ace or king.
- With ace-jack, fold if the dealer is showing an ace, king, or queen.
Poker Variations Probability Definition
Simple basic strategy:
- Fold if dealer has a higher ranked hand using his three up cards alone. This rule supersedes all other rules.
- Raise with ace-king. Fold otherwise.
- With optimal play, the house edge is 1.27%.
- Using the intermediate basic strategy, the house edge is 1.48 %.
- Using the simple basic strategy, the house edge is 1.63%.
Aces Up
Aces Up is a side bet based on the poker-value of the player's hand only. The following table shows what each hand pays, the probability, and contribution to the return. The lower right cell reflects a house edge of 3.30%.
Aces Up Analysis
| Event | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal flush | 500 | 188 | 0.000009 | 0.004617 |
| Straight flush | 100 | 1,656 | 0.000081 | 0.008134 |
| Four of a kind | 30 | 14,664 | 0.000720 | 0.021609 |
| Full house | 10 | 165,984 | 0.008153 | 0.081530 |
| Flush | 8 | 205,792 | 0.010108 | 0.080867 |
| Straight | 6 | 361,620 | 0.017763 | 0.106576 |
| Three of a kind | 4 | 732,160 | 0.035963 | 0.143853 |
| Two pair | 2 | 2,532,816 | 0.124411 | 0.248821 |
| Aces | 1 | 751,332 | 0.036905 | 0.036905 |
| Loser | -1 | 15,592,308 | 0.765886 | -0.765886 |
| Total | 20,358,520 | 1.000000 | -0.032973 |
Two-Way Bad Beat
The 'Two-Way Bad Beat' pays if either you or the dealer has at least a pair of aces and loses. The higher the losing hand, the more the bet pays. In other words, it pays based on the worse hand between you and the dealer, as long as they don't tie.
The following table shows all the odds. The zeros for the probability and return of a losing straight flush are not a mistake. The probability of that is about 1 in 25 trillion. Such a situation was the basis of the movie Honeymoon in Vegas, but I'm getting off topic. The lower right cell of the table below shows a house edge of 10.84%.
| Two-Way Bad Beat Analysis | |||
|---|---|---|---|
| Event | Pays | Probability | Return |
| Straight Flush | 10000 | 0.000000 | 0.000000 |
| Four of a Kind | 5000 | 0.000001 | 0.006250 |
| Full House | 500 | 0.000099 | 0.049370 |
| Flush | 200 | 0.000307 | 0.061440 |
| Straight | 100 | 0.000972 | 0.097168 |
| Three of a Kind | 35 | 0.004056 | 0.141965 |
| Two Pair | 10 | 0.034513 | 0.345127 |
| Pair of Aces | 9 | 0.015036 | 0.135328 |
| Loser | -1 | 0.945016 | -0.945016 |
| Total | 1.000000 | -0.108367 | |
Acknowledgments
Usually, I like to do my own math. However, in this case ShuffleMaster, who is marketing the game, kindly provided the math report by mathematician Cindy Liu, which the Ante bet analysis is based on. The Two Way Bad Beat is based on the work of Elliot Frome. I did the analysis of Aces Up.
Written by:Michael Shackleford