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Probability of holding
First betting interval
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EXAMPLE BASIC OMAHA GAME

 Bets and raises are one to three chips for the first two betting interval and three to ten chips for intervals  three and four.  Player 1 is dealer , and there is an ante of five chips.

First betting interval

Player 2 speaks first, and bets two chips.  All players call.  There are 15 chips in the pot.

Flop

The flop comes up 9, ♠ 3, and ♥ J.

1ST BETTING INTERVAL  At this stage all the poker players are content to remain in the game.

Second betting interval

  • Player 2, if all cards could count, would have a straight, but must ‘discard’ two of his hole-cards.  He nevertheless can fill a straight with any 8 or 10 and has other possible straights, including a straight flush.  Player 2 bets two chips.
  • Player 3’s hand has not improved much, as the 9 in his hole will probably not help him, but he has four chances of a straight, especially with an 8.  Therefore he calls.
  • Player 4 folds.  He is not helped by the flop.
  • Player 5 is not helped, but also calls.  He has his two 8s, and three spades towards a flush.
  • Player 1 still has his pair of Queens, and Queen is the highest card he can see, so he also calls.

Four players are left in and the pot is 23 chips.

2ND BETTING INTERVAL  The flop has not actually helped any of the players much

The turn

Next comes the turn, the ♠ 9.  This changes the nature of some poker hands.

Third betting interval

  • Player 2 now has triple 9s.  He has a good chance of a full house on the river, needing a K, Q, or 10, and he still has chances of a straight.  He decides to bet the limit of ten chips.
  • Player 3 is in a similar situation, having three 9s and wanting a 10 or 7 for a full house.  He calls.
  • Player 5 has two pairs, 9s and 8s and can fill a full house with another 9 or 8 – he also has four spades, and another on the river would give him a flush.  He calls.
  • Player 1 also has two pairs, Queens and 9s, and decides to call, too.  He reckons if  either turns up, he will have a good chance of winning.  He calls.  The pot is 63 chips

3RD BETTING INTERVAL  The ♠ 9 has improved most player’s hands, but they need to

 bear in mind that everyone now has at least a pair of 9s.

  • Player 1 and 5 are being a trifle optimistic with their two pairs, because if a 9 appears on the river, all players will hold three 9s, with the possibility that an opponent is holding four.  Player 5, however, still has the chance of a winning flush.
  • Player 2 has most options of significant improvement with the outstanding 9 ( called the ‘case 9’) providing four of a kind, any of three remaining three Kings, three Queens and three 10s providing a full house and any of three 8s providing a straight.  Thirteen of the unknown cards will improve his hand.  (Remember all players can see only eight cards, their hole-cards and the four communal cards turned so far.)
  • Player 5 needs a 9 for a full house, or any of nine spades for a flush, so has ten chances to improve his hand.
  • Player 3 can get the case 9 for a set of four, or one of two 10s or three 7s for a full house, making 6 chances to improve his hand.
  • Player 1 can get the case 9 for a full house or one of two Queens for a full house, Queens up; only three chances to improve his hand significantly.  Improving to a better two pairs has not been considered.

With sight of al four hands, plus the discarded hand, we can see that there is no chance of four 9s, as all four 9s are accounted for.
            We can work out all players’ chances, bearing in mind that player 2 has the best hand at the moment, triple 9s, K, J.

  • Player 1 can beat this with ♠ Q (full house, Queens, 9s) or ♦ J, or ♣ J (triple Jacks) – 3 chances in 28.
  • Player 3 can beat this with ♣ 10 (full house, 10s, 9s) or ♠ 7, or ♥ 7 (full house, 9s, 7s).  He has 4 chances in 28.
  • Player 5 can beat this with, ♠ A, ♠ 6, ♠ 5, ♠ 4, or ♠ 2 for a flush (not ♠ Q, which wins for player 1 or ♠ 7, which wins for player 3) or ♦ 8, ♣ 8, (full house 8s, 9s).  Note he does not win with ♥ 3, because to get a full house of 3s, 8s, he would need to use three of his hole-cards.  He has 7 chances in 28.
  • All other cards (14) win for player 2, whether he improves his hand or not.

Thus player 2 has exactly an even chance of taking the pot, player 5 is 21 to 7, or 3 to 1 against, player 3 is 24 to 4, or 6 to 1 against, and player 1 is 25 to 3, or more than 8 to 1 against.
            If all of them knew these odds (and they don’t because, unlike us, they cannot see the other player’s five card), player 2 would bet the maximum of ten chips again.  Player 3, seeing he would need to put in ten chips to win a pot of 73 would call, as his chances are only 6 to 1  against.  Player 5, with a pot now of 83, is offered odds of 8 to 1 for 3 to 1 chance and would call, or even raise, and player 1, with a pot now of at least 93 chips could just about justify calling, too.
            Thus the pot would stand at 103 chips or more when the river is turned over.  Who wins?  Justice would say player 2, but luck also plays a part in poker.

Strategy

Much of the skill in Omaha comes in recognizing what constitutes a good hand. Unlike Texas Hold’Em, in which efforts have been made to grade the two-card hands held before the flop, the rules of Omaha make the four-card hands- of which two cards only, no more, no fewer, may be used impossible to evaluate precisely.  One can only know what a good hand, as opposed to a poor one, is.
            A good hand consists of four cards that work with each other, giving opportunities to develop hands with the flop in many directions.
            For example, see the hand below.  With this, depending on the flop, you have a range of chances:

  • Triple or four Aces.
  • Two cards to six straights from different flops: Q, 9.8 –9. 8. 7 –K. Q, J –A, K, Q – K,Q, 10-K, Q, 9.
  • Two cards to Ace flushes – in fact these will be nut flushes because there cannot be two flushes of different suits in Omaha poker , since a flush requires three suited cards among the community cards, and there cannot be sets of three suited cards among five cards in two different sets.

*  Betting hard

A good hand in Omaha requires aggressive betting.  Getting opponents to fold and picking up pots is generally a better policy than checking in the hope of persuading others to put in more chips.  The more opponents who get more cards the more likely it is that one of them will hit an even better hand than yours.

Obviously the best holding the flop involves two cards of one suit and two of another, with all four cards connected or pairs, with potentials for runs.  The hand below is a good example of this.  If you have one or two cards unconnected to the others by suit or rank, clearly the hand is not so good.  Because you can use only two of your hole-cards in making your hand, two Aces is actually better than three.  With three Aces, one cannot be used, and there is only one left in the pack to achieve a triple with the remaining two.
            After the flop you must look at your possible trips, full houses, flushes and straights in the same manner.  Work out roughly, if not exactly, how many ways you can achieve these hands, without forgetting that communal cards are exactly that.  If two Queens among the five common ones give you triple Queens, remember an opponent might well have triple Queens, too.  If you have two Aces to go with them, fine.  If your best to accompany them, fine.  If your best to accompany them is, say, Jack on the board and 7 in hand, beware.