In poker, the probability of many events can be determined by direct calculation. This article discusses how to compute the probabilities for many commonly occurring events in the game of Omaha hold ‘em and provides some probabilities and odds[note 1] for specific situations. In most cases, the probabilities and odds are approximations due to rounding.

When calculating probabilities for a card game such as Omaha, there are two basic approaches.

Determine the number of outcomes that satisfy the condition being evaluated and divide this by the total number of possible outcomes.

Use conditional probabilities, or in more complex situations, a decision graph.

Often, the key to determining probability is selecting the best approach for a given problem. This article uses both of these approaches, but relies primarily on enumeration.

Chinese Poker

Chinese poker, also called Russian poker, is a card game that has been played in the Asian community for many years. It has begun to gain popularity elsewhere because it has many features of an “exciting” gambling game:

The rules are simple: only a basic knowledge of poker hand rankings is needed to get started.

There is a large element of luck involved, therefore a beginner has a good chance of winning in the short term, even against experienced opponents. Poor players may not be so easily deterred by losses as they can more easily attribute bad results to their cards rather than their plays.

More advanced players can still apply enough strategy to the game to give themselves a significant advantage over poor players.

The game format results in frequent unexpected wins and high ranking hands.

Only a few players are required to play the game.

Playing a hand

In Chinese Poker, each player receives a 13 card hand from a standard 52 card deck. Each player then has to divide his cards into three bitcoin casinos for us players hands (known as “setting”): two containing five cards each (known as “the middle” and “the back”), and one containing three cards (”the front”); the back must be the highest ranking hand, and the front, the lowest ranking hand (note that straights and flushes do not count in the three card hand). The back hand is placed face down on the table in front of the player, then the middle hand is placed face down in front of the back hand, and the front hand is placed face down in front of the middle hand. After all the players have set their hands, each player will announce in turn (clockwise, starting from the left of the dealer) whether or not he is playing his hand. All players then announce their royalties, before revealing their hands.

Scoring

The stakes played for in Chinese poker are known as units: an amount of money agreed on before the game starts. Basic scoring rules dictate that a player collects one unit from each opponent whose front, middle or back hand is beaten by his own corresponding hand. Thus, unlike most poker games, being second-best at the table is good enough to win money. In some variants players are also paid an additional unit if they win in two or three of the hands. In other variants players only get an additional unit if they win all three hands (known as a scoop). Also, due to the head-to-head nature of the comparisons, it is possible for different players to play for different stakes. For example, A and B could play for $10/unit, while all other pairs play for $1/unit. Many variations of scoring are in common use; refer to the external links for more information.

The two most common scoring systems used in Casinos today are the 2-4 scoring method, and the 1-6 scoring method.

In the 2-4 method you receive 1 unit for each of the three hands you win, and 1 unit called the overall unit is awarded to the player who wins two out of the three hands, or all of the three hands. In the event of a tie in one of the hands, then no money is exchange for this particular hand and one player either wins both of the other hands, and collects 3 units (1 for each hand, and 1 overall), or they each win one hand and no units are exchanged (each win 1 unit, and there is no overall).