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Old May 21, 2008, 7:20pm   #1
Hoss Man
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Default Probability of a Paired Board in PLO (Turn or River)

Does anyone know the probability of the board pairing on the turn or river.

EX:

Flop: As Kd Tc

What are the odds of the board pairing in some way on the turn or river?

I'm still learning PLO and would like to know how to handle pot sized bets if I have a set vs someone betting an obvious straight; or I have a straight and someone is raising with a boat draw.
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Old May 22, 2008, 3:03am   #2
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Well, let's assume you have a set.
You alredy see 7 cards. You also have 7 outs (3 of one card, 3 of another, and 1 for quads).
7/(52-7)=15.55555% chance of hitting a boat or quads on the turn.
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Old May 22, 2008, 3:42am   #3
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It's the same odds as in hold'em, only you know more cards, and you *should* be capable of estimating what kind of hand approximately your opponent has. The odds don't change per se, neither does the logic of counting outs and figuring out what cards are out (you do that in holdem too, right?), only the number of cards you can potentially know changes. Then you just do the math.

The hard part is figuring out likely blocked cards. For instance, if you had aaxx (assume the xx are both cards under 9) and bet out pot on the flop after having raised pot preflop, and its a HU pot let's assume. Your opponent, a tight player, re-raises full pot, and there are no draws on the AKT board. You put him on QJxx pretty much 100%. It's then just a question of figuring out how often his xx will have either a k, t, or a in it, then doing the math. Of course, you factor in the 3 outs you will get from any non-pairing turn card (except qj, obv)

In this instance, you can probably give your opponent 1 of your outs (on average) because they have QJ and probably have at least 1 card that in some way connects with it if they are tight and called a preflop raise. Of course, they won't always have one (QJ98 is a super legit hand, QJ78 is legit too, and sometimes people will show up with hands like qj65 b/c they're double suited or something, etc.), and they'll also sometimes show up with two of the outs (e.g. kqjt). Very rarely, but sometimes, they will show up with 3 (kkqj/qjtt). Just discount the likely blocked outs, and then figure it out by dividing it against the unknown deck. If you want to get *really* technical, in omaha it is easier to figure out the relative content of the unknown deck based on how many saw the flop - ie. if the flop went HU in a FR game, the deck is likely rich in high cards because, ceteris paribus, people prefer to play higher cards. But let's not go there now.


Anyway, so you decide you have 1 ace, 3 kings, 3 tens on the turn (less 1 block) for 6 outs on the turn, plus an additional 3 outs coming on the river, out of a deck of 41 unknown cards. The math at that point is the same for holdem (figure out the odds of you missing an out, and subtract that from 1). Ignore the differences between the odds when he has an A versus a K versus a T obv.


In this example:

1-(35/41*31/40) = 33.8% (the actual odds are slightly less b/c of the things we assumed away, such as the QJ turn). --> hand simulator says 32.8%


I suppose one could make an odds chart with this in it, that might actually be kinda useful - just estimate # of dead cards in a HU situation. I don't have one off hand - if someone wants to try the google on this one, please post what you find?

I just usually estimate in my head based on the holdem odds then, when possible, think about the # of cards I can discount versus the # of cards I can take as known for the deck. Usually the odds don't make a huge change for these HU spots - for instance, a dry aa versus qj on a akt board is a 34.44/65.1 proposition instead of 33.8% (or 32.8%).

Best idea is to have a hand simulator around in case you need it, but usually I think in this game the odds will clearly favour one play over another when the hands are face up, and there will be fewer post-flop marginal spots where you'd ideally like an equity calculator.


Cliffs notes on odds: there is no special formula for omaha hands, just calculate it the same way you do for hold'em, and use a simulator if needs be.



As for your question about how to handle pot sized bets with top set, that is *far* more complicated than an odds question. In fact, I'm sure that entire book chapters could be devoted to that situation. Why don't you post some hands so we can give you direct answers, and then you'll see the factors we think about (like pot to stack ratio, player tendencies, prevalence of other draws - which can hurt or help - position, etc.)
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Oh, and obviously, TWLLM, we'd all rather you just ruled with an iron fist of nittiness and made all decisions without consultation, but that goes without saying, right?
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Old May 22, 2008, 3:59am   #4
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Originally Posted by TWLLM View Post
It's the same odds as in hold'em, only you know more cards, and you *should* be capable of estimating what kind of hand approximately your opponent has. The odds don't change per se, neither does the logic of counting outs and figuring out what cards are out (you do that in holdem too, right?), only the number of cards you can potentially know changes. Then you just do the math.

The hard part is figuring out likely blocked cards. For instance, if you had aaxx (assume the xx are both cards under 9) and bet out pot on the flop after having raised pot preflop, and its a HU pot let's assume. Your opponent, a tight player, re-raises full pot, and there are no draws on the AKT board. You put him on QJxx pretty much 100%. It's then just a question of figuring out how often his xx will have either a k, t, or a in it, then doing the math. Of course, you factor in the 3 outs you will get from any non-pairing turn card (except qj, obv)

In this instance, you can probably give your opponent 1 of your outs (on average) because they have QJ and probably have at least 1 card that in some way connects with it if they are tight and called a preflop raise. Of course, they won't always have one (QJ98 is a super legit hand, QJ78 is legit too, and sometimes people will show up with hands like qj65 b/c they're double suited or something, etc.), and they'll also sometimes show up with two of the outs (e.g. kqjt). Very rarely, but sometimes, they will show up with 3 (kkqj/qjtt). Just discount the likely blocked outs, and then figure it out by dividing it against the unknown deck. If you want to get *really* technical, in omaha it is easier to figure out the relative content of the unknown deck based on how many saw the flop - ie. if the flop went HU in a FR game, the deck is likely rich in high cards because, ceteris paribus, people prefer to play higher cards. But let's not go there now.


Anyway, so you decide you have 1 ace, 3 kings, 3 tens on the turn (less 1 block) for 6 outs on the turn, plus an additional 3 outs coming on the river, out of a deck of 41 unknown cards. The math at that point is the same for holdem (figure out the odds of you missing an out, and subtract that from 1). Ignore the differences between the odds when he has an A versus a K versus a T obv.


In this example:

1-(35/41*31/40) = 33.8% (the actual odds are slightly less b/c of the things we assumed away, such as the QJ turn). --> hand simulator says 32.8%


I suppose one could make an odds chart with this in it, that might actually be kinda useful - just estimate # of dead cards in a HU situation. I don't have one off hand - if someone wants to try the google on this one, please post what you find?

I just usually estimate in my head based on the holdem odds then, when possible, think about the # of cards I can discount versus the # of cards I can take as known for the deck. Usually the odds don't make a huge change for these HU spots - for instance, a dry aa versus qj on a akt board is a 34.44/65.1 proposition instead of 33.8% (or 32.8%).

Best idea is to have a hand simulator around in case you need it, but usually I think in this game the odds will clearly favour one play over another when the hands are face up, and there will be fewer post-flop marginal spots where you'd ideally like an equity calculator.


Cliffs notes on odds: there is no special formula for omaha hands, just calculate it the same way you do for hold'em, and use a simulator if needs be.



As for your question about how to handle pot sized bets with top set, that is *far* more complicated than an odds question. In fact, I'm sure that entire book chapters could be devoted to that situation. Why don't you post some hands so we can give you direct answers, and then you'll see the factors we think about (like pot to stack ratio, player tendencies, prevalence of other draws - which can hurt or help - position, etc.)
I don't understand the joke in your sig at all. Explain? A bidet is a thing you wash your junk in, correct?
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Old May 22, 2008, 4:24am   #5
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I don't understand the joke in your sig at all. Explain? A bidet is a thing you wash your junk in, correct?
Afaik, it is used for washing anywhere in the 'Nether regions' (I swear that's not a joke about the low countries... ok... maybe it is ). The implication of the joke was that they were so lucky they had horseshoes up their ass... hence the bidet to keep the horseshoes clean.

BTW, good job quoting my entire post to ask that.
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Quote:
Originally Posted by DoubleU
Oh, and obviously, TWLLM, we'd all rather you just ruled with an iron fist of nittiness and made all decisions without consultation, but that goes without saying, right?
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Old May 22, 2008, 4:32am   #6
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Quote:
Originally Posted by TWLLM View Post
Afaik, it is used for washing anywhere in the 'Nether regions' (I swear that's not a joke about the low countries... ok... maybe it is ). The implication of the joke was that they were so lucky they had horseshoes up their ass... hence the bidet to keep the horseshoes clean.

BTW, good job quoting my entire post to ask that.
I thought it might build the suspense to what I'd be responding, maybe expecting a thorough analysis of your argument without counterpoints etc.

Where are you from, btw? I've honestly never heard of horseshoes being lucky. Maybe I am just sheltered.
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Old May 22, 2008, 9:10pm   #7
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Quote:
Originally Posted by kmay06 View Post
Where are you from, btw? I've honestly never heard of horseshoes being lucky. Maybe I am just sheltered.
I'm from Canada, but I would assume that most people from north america, anyway, were familiar with the concept of horseshoes being 'lucky'. Look at the symbolism of Binions, for instance - they don't just think horse shoes are pretty, they're meant to symbolize good luck.
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Quote:
Originally Posted by DoubleU
Oh, and obviously, TWLLM, we'd all rather you just ruled with an iron fist of nittiness and made all decisions without consultation, but that goes without saying, right?
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Old May 23, 2008, 12:56am   #8
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Quote:
Originally Posted by TWLLM View Post
I'm from Canada, but I would assume that most people from north america, anyway, were familiar with the concept of horseshoes being 'lucky'. Look at the symbolism of Binions, for instance - they don't just think horse shoes are pretty, they're meant to symbolize good luck.
Hmm, maybe I need to immerse myself in culture more. I've heard of all kinds of things supposed to be lucky, just never horseshoes.
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Old May 23, 2008, 1:47am   #9
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Quote:
Originally Posted by kmay06 View Post
Hmm, maybe I need to immerse myself in culture more. I've heard of all kinds of things supposed to be lucky, just never horseshoes.
Wow really? Are you American?
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Old May 23, 2008, 3:12am   #10
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Assuming your hole cards are AA24, you have 7 outs out of 45 cards that the board pairs on the turn plus 10 outs out of 44 cards that the board pairs on the river. That's 7/45 plus 10/44 = 15.6% on the turn plus + 22.7% on the river = 38.3%.

Last edited by rpark; May 23, 2008 at 3:21am.
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