Outline
I have developed a tool for Omaha Hold’em as well as Texas Hold’em, so I will post a link to it. As with Texas Hold’em and Short Deck Hold’em, the opponent is not human in the sense that they do not bluff, but it should have enough functionality to get a feel for the game. I intend to implement an NPC that executes a human-like strategy in the future.
While I’m linking to the tool, I’ll also briefly explain the rules and features of the game.
Rules and Features
The difference between Omaha Hold’em and Texas Hold’em is that you play with four cards in your hand, and when making a hand in Omaha Hold’em you must choose two cards from your hand and three cards from the community. The players make a hand from a total of
\[ \small {}_4 C_2 \times {}_5 C_3 = 6 \times 10 = 60 \]
possible combinations, and the player who makes the strongest hand wins. This is the only difference in the rules, and the rules are basically the same as Texas Hold’em. In Omaha Hold’em, the amount you can bet cannot exceed the total amount of the pot in the previous round, and there are also restrictions on the number of raises per betting round, so it is sometimes called Pot Limit Omaha (PLO).
The features of the game compared to Texas Hold’em are as follows:
- Compared to Texas Hold’em, it is easier to make strong hands, and hands stronger than three of a kind tend to be recognized as strong hands. It is not uncommon to be able to make the strongest hand from the common cards known as the nuts.
- The strength of hands is less likely to differ pre-flop, and players tend to play looser than in Texas Hold’em (tight aggressive players have a VPIP of around 30-40%).
- Hands that include AA and KK are some of the strongest hands in Omaha Hold’em, but they tend not to have as high a winning probability as in Texas Hold’em. AAKK, which does not include suited cards, has a winning probability of only about 65% even with two players (still close to the strongest hand that does not include suited cards). Because it is easy to make straights and flushes, the overall strength of the four cards in your hand becomes important.
Pot Limit Bet Amount
Unlike Texas Hold’em, Omaha Hold’em is often played with a pot limit rule that places a limit on the bet size. Specifically, the maximum bet amount is:
Maximum bet amount = Total pot amount,
and if the opponent has raised, it is calculated as:
Maximum bet amount = Total pot amount + Call amount x 2.
For example, in pot limit, you cannot go all-in right away from the preflop. The maximum raise amount for a preflop open-raise, 3-bet, or 4-bet is calculated as follows. An open raise is when the BB has raised to 1bb, so
Maximum open raise: 3.5bb = 1.5bb + 1bb × 2
can make the maximum raise. If the open-raise is the maximum raise (raise to 3.5bb, pot total is 5bb), then the maximum raise for a 3bet is:
Maximum 3bet reraise amount: 12bb ＝ 5bb + 3.5bb × 2.
If the 3bet is the maximum raise (raise to 12bb, pot total is 17bb), the maximum raise for the 4bet is:
Maximum 4bet re-reraise amount: 41bb ＝ 17bb + 12bb × 2.
The same restrictions apply after the flop, but although the pot amount is carried over from the previous round, the call amount is not carried over and is calculated using the amounts bet and raised in each round. Unlike Texas Hold’em, you should be aware that there may be restrictions on suddenly going all-in or betting over the pot. Bluffs that try to scare opponents with the size of their bets are less likely to go through, so you may need a good story if you want to bluff.
Omaha Hi-Lo
There is a game called Omaha Hi-Lo, which is a form of Omaha Hold’em. In one game, a winner is determined for two poker hands, a strong hand (high hand) and a weak hand (low hand), and half of the pot is allocated to the winner of the high hand and the other half to the winner of the low hand. The specifications for the high hand are the same as in regular Omaha Hold’em, but the low hand has a special specification, so I will explain it briefly.
For low hands, the strength of the rank is determined by \(\small A>2>3>\cdots>K \). Also, hands with a pair are invalid and are considered to not have a low hand. A low hand can be a straight or a flush, but it is not included in the strength of the hand and is determined only by the strength of the rank. For example, A2345 is the best low hand. If no player has a low hand (such as a four of a kind with the community cards), the low hand is invalid and the winner of the high hand wins the entire pot. Of course, it is possible for the same player to win both the high and low hands, in which case they will win the full amount of the pot.
Conclusion
Omaha Hold’em may be an interesting game for players who enjoy predicting the probability of getting a strong hand loosely (loose-passive players?). The calculation of the probability seems too complicated, so if you think about it intuitively, you may misevaluate the probability. In this sense, it may be a game where players with more experience are more likely to become strong. If I feel like it, I will also make a page on Omaha Hi-Lo, including the win rate calculation, hand range, and game.
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