Omaha Odds Question

What are the odds of a board showing up that is unpaired and does not contain a flush or straight possibility in Omaha.


What I'm trying to figure out is if the flop is say 2-4-9, and you have a set of 9's, how often will that set be good?


Thanks.


Mathematically challenged,

Dear tootight,

Your posted question is very broad and and miandering. The 2-4-9 in your post is the flop. The consists of three stages: flop, flop + turn, and flop + turn + river (of course you know that).


I think you should ask a more specific question. There are many people on 2+2 who could give you very accurate answers. Even if I had the various answers to your questions, it would be too time comsuming to post them using the keyboard. I mean questions....

What I think you should do is purchase some good software which is readily available on the market. I suggest you buy Wilson's Turbo Omaha High Only program. Then you could take your time to get all the answers to your questions. Also in California most people only play Omaha 8 (HiLo) -- you didn't specify what type of Omaha, in OM8 flopped sets when the flop is 2-4-9 will be lucky to get half the pot....


Your post implies all of the below and then some:


When the flop is 2-4-9, what you inply is what are the chances that the flop is all one suit, what are the chances that a flush draw will occur on the flop, what are the chances that a back door flush can occur via the turn and river, what are the chances that a straight will occur on the turn or river....


Buy Wilson's software, take the time to learn how to use all of it's tricks -- you will learn a lot....

Assuming you don't hold any of the flop cards other than your set, I calculate that the board will pair 36.5% of the time. The easiest way to calculate this is to determine the chances of not pairing on the turn and the river and multiplying the two, i.e.


37/45 times 34/44 equals .635 which is the probability that the board will not pair. 1-.635 is .365 which is the probability that the board will pair.


You would need to modify the odds if you happen to hold one or more of the board cards other than your set. You should also modify the odds if the betting indicates that there is another set out, which reduces your out cards by 3 since the other player holding a set holds two of your cards which pair the board and also makes the third card no good for you since it would make the other player's set into quads. Obviously if the other set out is higher than yours, your only out is to make quads.


If the betting indicates that someone likely holds the top two pair and you hold the lower set, your hand can only win if you make quads, the turn card pairs, or if the board does not pair and also does not make a flush or straight.

tootight - Omaha hands are four card hands and it is necessary to know all four cards to make calculations or estimations. A pair of nines, taken alone, is a very poor Omaha-8 holding. What other two cards would make a pair of nines playable, pre-flop? Depending on the game and the situation, perhaps a pair of bullets, a pair of kings, maybe a pair of queens, acey deucy, or ace-trey, all with some suitedness might make a playable hand.


Let's make the cards more specific. Suppose you hold As-2s-9s-9c and the flop is 2c-4d-9h.


You want the board to pair so that you will have a full house or quad nines. Yet, as I understand it, your question regards how often your flopped set of nines will remain the nuts on the river and that is the question I will answer.


There are 39 two-card combinations yet to come that do not pair the board, flush the board or straight the board. They are:


7c-Qd, 7c-Qh, 7c-Qs, 7c-Kd, 7c-Kh, 7c-Ks,

7d-Qc, 7d-Qh, 7d-Qs, 7d-Kc, 7d-Kh, 7d-Ks,

7h-Qd, 7h-Qc, 7h-Qs, 7h-Kd, 7h-Kc, 7h-Ks,

7s-Qc, 7s-Qd, 7s-Qh, 7s-Qs, 7s-Kc, 7s-Kd, 7s-Kh, 7s-Ks,

8c-Kd, 8c-Kh, 8c-Ks,

8d-Kc, 8d-Kh, 8d-Ks,

8h-Kd, 8h-Kc, 8h-Ks,

8s-Kc, 8s-Kd, 8s-Kh, and 8s-Ks.


All the other 951 two-card combinations yet to come enable a better high than a set. Thus the odds are 951 to 39 or about 24.4 to 1 that a set will not be the nuts on the river when your hand is As-2s-9s-9c and the flop is 2c-4d-9h. Since all of these 39 two-card combinations enable a higher set (kings or queens) to win for high on the river, there is no chance your flopped set of nines will be the nuts on the river. No chance at all. Zero.


However, don't despair. When you hold As-2s-9s-9c and the flop is 2c-4d-9h, although the flop is not ideal, it still is good for you.


If you're in one of those loosey-goosey games where everyone sees all five cards on the board before folding, you almost surely will need to improve to win and when you do win it will almost surely be for only half the pot. That's the bad news. The good news is those pots are huge.


If the field is sufficiently reduced before the flop, or if you are able to reduce the field sufficiently after the flop, opponents who were originally dealt hands that might have ended up winning for high will have folded before the river. In that case your set of nines, although not the nuts, will often be the best high hand on the river. In addition, you also have a good chance to improve your set of nines (to a full house/quads), and some chance (albeit slim here) to have your other two cards back into a fit with the final board.


(There even is a slim chance, if the next two cards are both low, and if the field is sufficiently reduced, that your live ace will be good for low, possibly making a scooper for you).


Hope that, along with what the other responders to your post have written, is what you wanted.


Buzz