# The most "outs" possible to win in Hold 'Em on the river

**URL:** <https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581>\
**Category:** Factual Questions\
**Created:** [November 24, 2005, 1:29pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581 "2005-11-24T13:29:29Z")\
**Posts on this page:** 16\
**Page:** 2

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**Author:** ![Otto](https://avatars.discourse-cdn.com/v4/letter/o/bbe5ce/32.png) [@Otto](https://boards.straightdope.com/u/Otto)\
**Post date:** [November 29, 2005, 10:06pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/21 "2005-11-29T22:06:47Z")

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> [@Usram](#):
>
> If the board is 87543 unsuited, the nuts is 56789.

But it’s not the lowest possible card combination with those cards that wins the hand, which is what I thought was the question.

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**Author:** ![Ximenean](https://avatars.discourse-cdn.com/v4/letter/x/aca169/32.png) [@Ximenean](https://boards.straightdope.com/u/Ximenean)\
**Post date:** [November 29, 2005, 11:30pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/22 "2005-11-29T23:30:03Z")

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Let’s just agree that the puzzle could have been stated more clearly. How about “what is the lowest-ranked hand that can be the nuts after the communal cards have been revealed?”

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**Author:** ![JSexton](https://avatars.discourse-cdn.com/v4/letter/j/96bed5/32.png) [@JSexton](https://boards.straightdope.com/u/JSexton)\
**Post date:** [November 29, 2005, 11:47pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/23 "2005-11-29T23:47:34Z")

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> [@Otto](#):
>
> But it’s not the lowest possible card combination with those cards that wins the hand, which is what I thought was the question.

Otto, do you understand what “nuts” means? It means the best possible hand, not just something that happens to beat to other player.

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**Author:** ![Otto](https://avatars.discourse-cdn.com/v4/letter/o/bbe5ce/32.png) [@Otto](https://boards.straightdope.com/u/Otto)\
**Post date:** [November 30, 2005, 1:12am UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/24 "2005-11-30T01:12:44Z")

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Look, you’re the one who closed out your post by admitting that you wrote the question poorly. I misunderstood it, I gave an answer to the question as I did understand it, and am now moving on with my life in hopes of one day dealing with the shame of, you know, misunderstanding a meaningless trivia question on a message board. Sorry to have distressed you with my error.

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**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\
**Post date:** [November 30, 2005, 8:12pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/25 "2005-11-30T20:12:44Z")

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Can’t you see this poker guessing game is tearing us apart?!?!

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**Author:** ![Gangster\_Octopus](https://avatars.discourse-cdn.com/v4/letter/g/a8b319/32.png) [@Gangster\_Octopus](https://boards.straightdope.com/u/Gangster_Octopus)\
**Post date:** [November 30, 2005, 8:50pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/26 "2005-11-30T20:50:09Z")

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What is the highest hand that can be the lowest nuts of with the longest odds before the flop but still ahead before the flop, while at the same time the turn is revealed to reverse the odds and then the river trumps the fourth street with a lowball hi/lo hand that would still win in Omaha but would only win half the time in razz?

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**Author:** ![Yeticus\_Rex](https://avatars.discourse-cdn.com/v4/letter/y/a698b9/32.png) [@Yeticus\_Rex](https://boards.straightdope.com/u/Yeticus_Rex)\
**Post date:** [November 30, 2005, 8:50pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/27 "2005-11-30T20:50:11Z")

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> [@Usram](#):
>
> Let’s just agree that the puzzle could have been stated more clearly. How about “what is the lowest-ranked hand that can be the nuts after the communal cards have been revealed?”

Ten high.

Player A: T8o  
Player B: 98o

Communal: 2 3 4 5 7, rainbowed

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**Author:** ![Gangster\_Octopus](https://avatars.discourse-cdn.com/v4/letter/g/a8b319/32.png) [@Gangster\_Octopus](https://boards.straightdope.com/u/Gangster_Octopus)\
**Post date:** [November 30, 2005, 8:52pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/28 "2005-11-30T20:52:02Z")

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Yeti, Yeti, Yeti…the nuts in that case would be hole cards of 68 with a straight.

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**Author:** ![Yeticus\_Rex](https://avatars.discourse-cdn.com/v4/letter/y/a698b9/32.png) [@Yeticus\_Rex](https://boards.straightdope.com/u/Yeticus_Rex)\
**Post date:** [November 30, 2005, 8:53pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/29 "2005-11-30T20:53:21Z")

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Oops, I misunderstood THAT question!

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**Author:** ![Gangster\_Octopus](https://avatars.discourse-cdn.com/v4/letter/g/a8b319/32.png) [@Gangster\_Octopus](https://boards.straightdope.com/u/Gangster_Octopus)\
**Post date:** [November 30, 2005, 9:13pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/30 "2005-11-30T21:13:25Z")

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Certainly if I write this out the wuestion in Math it will clear everything up:

Let **C** = set of all five card combinations (i.e. all the possible community card combos)

Define **K(_c_)** as the function which defines all the possible seven card combinations from the given five card cobination _c_ in **C**

Let _k[sub]c,max[/sub]_ be defined as the maximjum valued hand in the set **K(_c_)**. If not unique pick any one of them (we are assuming that higher ranked hands are given higher values). Let **K[sub]C[/sub]** be the set of all these _k[sub]c,max[/sub]_ values over all the _c_ in **C**.

Then the question asks what _c_ solves Max **K[sub]C[/sub]**.

I apologize but it has been solong since I have done this stuff I fear my definitions are a bit…crude.

But that should really clear everything up. 😃

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**Author:** ![Yeticus\_Rex](https://avatars.discourse-cdn.com/v4/letter/y/a698b9/32.png) [@Yeticus\_Rex](https://boards.straightdope.com/u/Yeticus_Rex)\
**Post date:** [November 30, 2005, 9:32pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/31 "2005-11-30T21:32:52Z")

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> [@](#):
>
> But that should really clear everything up.

As clear as “wuestion”, “maximjum”, and “solong”.

_Snort_

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**Author:** ![Gangster\_Octopus](https://avatars.discourse-cdn.com/v4/letter/g/a8b319/32.png) [@Gangster\_Octopus](https://boards.straightdope.com/u/Gangster_Octopus)\
**Post date:** [November 30, 2005, 9:37pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/32 "2005-11-30T21:37:59Z")

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Those are perfectly cromulent words.

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**Author:** ![Duke\_of\_Rat](https://avatars.discourse-cdn.com/v4/letter/d/ad7895/32.png) [@Duke\_of\_Rat](https://boards.straightdope.com/u/Duke_of_Rat)\
**Post date:** [November 30, 2005, 9:45pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/33 "2005-11-30T21:45:32Z")

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> [@Yeticus Rex](#):
>
> As clear as “wuestion”, “maximjum”, and “solong”.
> 
> _Snort_

You forgaught “cobination”.

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**Author:** ![Gangster\_Octopus](https://avatars.discourse-cdn.com/v4/letter/g/a8b319/32.png) [@Gangster\_Octopus](https://boards.straightdope.com/u/Gangster_Octopus)\
**Post date:** [November 30, 2005, 9:48pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/34 "2005-11-30T21:48:19Z")

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Guilty. I was concentrating much more on the coding.

I can take it…out on you guys on Thursday. Much as I have done the last couple of times.

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**Author:** ![Duke\_of\_Rat](https://avatars.discourse-cdn.com/v4/letter/d/ad7895/32.png) [@Duke\_of\_Rat](https://boards.straightdope.com/u/Duke_of_Rat)\
**Post date:** [November 30, 2005, 9:50pm UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/35 "2005-11-30T21:50:39Z")

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Oh, like me and **Yeti** have anything left to lose…

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**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\
**Post date:** [December 1, 2005, 7:06am UTC](https://boards.straightdope.com/t/the-most-outs-possible-to-win-in-hold-em-on-the-river/332581/36 "2005-12-01T07:06:45Z")

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> [@Gangster Octopus](#):
>
> What is the highest hand that can be the lowest nuts of with the longest odds before the flop but still ahead before the flop, while at the same time the turn is revealed to reverse the odds and then the river trumps the fourth street with a lowball hi/lo hand that would still win in Omaha but would only win half the time in razz?

AJo. Trust me.

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