Online Poker Forum - Community Card pairs

Timinane · High Card Joined: 02 Aug 2009 Posts: 14

I'm rather new to Omaha Hi prefering Omaha8.

I haven't yet worked out the maths behind Omaha so if anyone can link to anything that'll help me there I'll be thankful.

As part of a rather annoying string of events I'm wondering one thing about Omaha

How often do you expect pairs to be part of the community cards.
ie. the cards being something like xxxTT.

tracysanders · Posted: Thu Aug 13, 2009 1:49 am Post subject:

xxxTT- that would be a full house not a pair.

Just kidding, but seriously- I fail to see the relevance in this question as your opponents can also use the same pair.

If I had to guess, you are thinking if you have trips in your hand - how often will the board pair to give you a full house. If this is correct you need to know that you can only use 2 cards from your hand and you HAVE to use 3 from the board.

As far as the exact maths I cannot help you there, but it seems to me you are misunderstanding the rules.

Timinane · High Card Joined: 02 Aug 2009 Posts: 14

I asked because it seems every hand I get involved in pairs and in several cases it has cost me a tournament when a nut flush or nut straight gets cracked by a full house.

I think it's happening too frequently and wonder what the actual odds are of boards pairing.
Especially the chances of a flop containing a pair which is the most common flop I see when I've been trying to play.

vectorspace · Posted: Thu Aug 13, 2009 2:59 am Post subject:

As a general rule, you don't want to chase straights/flushes on paired boards. This is generally true in holdem, but very very true in omaha. It usually takes the nuts or close to it on the river in omaha to win the pot. If the board is paired, the nuts will be quads or a full house, not straights or flushes.

vectorspace · Posted: Thu Aug 13, 2009 3:04 am Post subject:

The probability of getting a pair on the flop is not hard to calculate. Disregarding anyone's hole cards it is

(13C1)(4C2)(48C1)/(52C3), which is about 17% or 1/6 as a fraction.

HuJwang · Posted: Thu Aug 13, 2009 3:15 am Post subject:

the chance of any 5 cards containing a pair is about 49.3%.

the chance of any 3 cards containing a pair is aobut 17.2%

if a flop is unpaired, the chance of the board pairing on the turn or river is about 38.8%.

if you have a set on an unpaired flop, the chances of you improving to a full house or better by the river is 33.4%

hope that helped

vectorspace · Posted: Thu Aug 13, 2009 11:25 am Post subject:

francois8 · Posted: Thu Aug 13, 2009 3:44 pm Post subject:

If they're not completely accurate numbers, they're really close. I'll take a crack at approximating the math for the last one, the rest of the math should be similar.

Turn card can do one of three things, pair the board (then river doesn't matter), pair one of your hole cards, or do neither.

Turn card pairing board = 7/45 * 100% of time river doesn't matter cotnributes 15.556% to total
Turn card pairs a hole card of yours = 6/45 * 9/44 (9 outs on river) contributes 2.727% to total
Turn card does not pair board or one of your hole cards = 32/45 *10/45 contributes 15.802% to total

Adding these together I get 34.085% which is very close to 33.4% considering I left out some details.

Most likely, that 33.4% would account for instances where one of your other hole cards paired something on the flop which obviously would lower your chances of improving (KKJT on KJ4 flop)... also times when it paired both the other cards in your hand, which would also lower the chances (KKJT on KJT flop). The math to incorporate all of these situations is more detailed than I care to think about so late in the afternoon. Obviously it would lower the chances of improving, but its impact would be lessened as it would only happen a small percentage of the time you flopped a set.

But including these would clearly bring down the 34% value I calculated, and I'm happy to assume that it would end up either very near or exactly on the 33.4%. In terms of figuring out how to play my hand, these differences don't matter, I'll call it one time in three.

vectorspace · Posted: Thu Aug 13, 2009 6:36 pm Post subject:

I was just kidding francois8. Good job on this though!

adam27x · Posted: Thu Aug 13, 2009 6:51 pm Post subject:

pokerstove is kinda useful afaik

francois8 · Posted: Thu Aug 13, 2009 9:31 pm Post subject:

DforDissent · Posted: Tue Sep 15, 2009 5:11 pm Post subject:

junkbutton · Posted: Tue Sep 15, 2009 5:24 pm Post subject:

anytime I flop the naked nut straight or flush, the chances of the board pairing is pretty much 100%...

DforDissent · Posted: Tue Sep 15, 2009 5:26 pm Post subject:

I want to try again, briefer this time... see how close my results are this time... From personal experience (there is a juicy LIMIT omaha-high game here in town, there's usually 7 seeing a Turn, and 4 or 5 seeing a river, so you KNOW the river fills somebody up when it finally pairs!) it's about 25% of the time. I remember doing the math a while ago. You can also check ProPokerTools.com ** and give yourself the nut flush on the turn and see how often the bottom set beats you.

OP has [AKQJ] and the rest are unknown. To miss being paired, Flop's 1st card is T..2 (36outs), 2nd card is one of 32outs, and 3rd card is one of 28outs = 36*32*28 / 48*47*46 = 31.08% of the time the flop didn't pair OP's hand, but also didn't pair up thus a fullhouse/quads ain't out there yet (completely different % chance from the other replies, because I mentioned that the flop didn't pair OP either -- you know what, forget it, there's too many variables, I guess what OP is really asking is, you've got the straight or flush nuts on the turn, how often does that river pair up, forgetting your own three-of-a-kind benefit of that pairing up? In that case I guess there's 4 cards, 3 suits each means 12outs to pair up, with 8 cards seen that's 12/44 = 27.27% chance that the river pairs up... OR LESS, if the OP has some of those outs in his hand. So yeah, like 1 time in *4* you will HATE the river. That's why you raise preflop with strong starters, and why you rarely try for a CHECK-raise on a strong flop since once you've got a huge group seeing a turn card there's gonna be at least 1 guy seeing the river with 2 pair, if not a hidden set.)

Brief enough? Sorry, I'm done with my math-rambling. Hope it helped somebody Wink

**Exactly 25.0%, wow:
http://www.propokertools.com/simulator/simulate.jsp?g=oh&b=AcKdQh2s&d=&h1=JcTd6h9s&h2=2d2c3d3c&h3=&h4=&h5=

but keep in mind, since we gave an exact hand for the villain, your straight-holding-up % chance might be as low as 73% or as high as 77% depending on if villain's 3d3c is instead a couple of paint cards that are already on the board, so let's just do the 5-handed lottery that I'm used to in that crazy Limit Omaha game I mentioned...

http://www.propokertools.com/simulator/simulate.jsp?g=oh&b=AcKdQh2s&d=&h1=JcTd6h9s&h2=****&h3=****&h4=****&h5=****

74.47% your straight is the "winner" thus 25.53% chance you lose (by the board pairing, virtually guaranteeing a fullhouse to one of the villains)

you're good 3 out of 4 times. Kinda like in Holdem when you shove your winning pair on the turn against an unpaired-undercard flush draw. Get used to being rivered a non-trivial percent of the time. But be happy for them chasing, since you win an inflated pot a vast majority of the time. That's Poker!

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