Hold'em Poker Puzzle (hand with most outs)

[chapstick]

Here's a puzzle (you might only find interetsing if you're bored). I haven't though too much about it, and this might be completely trivial, but work is not so interesting right now...

Which pocket cards and set of community cards to 4th street (i.e. only the river to come) give you the most outs to the absolute nuts? The only condition, to make this non-trivial, is that on 4th street you can't have a hand better than three-of-a-kind.

For example, if you have A/images/graemlins/spade.gif A/images/graemlins/heart.gif in the pocket with A/images/graemlins/club.gif 5/images/graemlins/heart.gif 9/images/graemlins/spade.gif K/images/graemlins/diamond.gif on the board, the remaining fives in the deck are not strictly outs to the absolute nuts since villain may be holding pocket fives, and will make a four-of-a-kind. But the Queens are outs since they cant make anyone a better hand.

[LetYouDown]

I gotta vote for OESFD.

[SossMan]

[ QUOTE ]
For example, if you have A A in the pocket with A 5 9 K on the board, the remaining fives in the deck are not strictly outs to the absolute nuts since villain may be holding pocket fives, and will make a four-of-a-kind. But the Queens are outs since they cant make anyone a better hand.



[/ QUOTE ]

really? so does JT beat AA on that board?

[chapstick]

[ QUOTE ]

really? so does JT beat AA on that board?

[/ QUOTE ]

Woops! Apologies. I just grabbed Q out of thin air without really thinking (obviously). Actually, with that board I don't see any outs to the absolute nuts except the other A.

[LetYouDown]

Actually...wouldn't ANY open ended, nut straight draw on a rainbow board at the turn have the most entirely clean, "can't lose" outs, with 8? Nut flush draws only have 7 if I'm correct.

[Paul2432]

Does "absolute nuts" mean no ties possible?

Paul

[Paul2432]

[ QUOTE ]
Does "absolute nuts" mean no ties possible?

Paul

[/ QUOTE ]

Actually, it doesn't matter. 20 is my answer.

You: Kc Kd
Board: Ks Qd 7c 2h

Outs: any 3,4,5,6,8

Paul

[LetYouDown]

Woops. Didn't notice the "street you can't have a hand BETTER than three-of-a-kind." Question is still oddly worded. Assuming I'm not missing anything, I can't see any more than 20.

[CieloAzor]

[ QUOTE ]
[ QUOTE ]
Does "absolute nuts" mean no ties possible?

Paul

[/ QUOTE ]

Actually, it doesn't matter. 21 is my answer.

You: Kc Kd
Board: Ks Qd 7c 2h

Outs: any 3,4,5,6,8,K

Paul

[/ QUOTE ]

FYP.

[motorholdem]

Doesn't the concept of "outs" infer that you are behind.

Don't we need to know what hand you are behind to, in order to know what outs are tainted?

[Rasputin]

[ QUOTE ]
Doesn't the concept of "outs" infer that you are behind.

Don't we need to know what hand you are behind to, in order to know what outs are tainted?

[/ QUOTE ]

Concepts can't infer. Only people can infer.

That said, yes.

[Little Fishy]

A /images/graemlins/heart.gif K /images/graemlins/heart.gif

A /images/graemlins/club.gif Q /images/graemlins/heart.gif J /images/graemlins/heart.gif 6 /images/graemlins/spade.gif


T-4 ways
/images/graemlins/heart.gif-8 ways

so 12 ways to the nuts and 2 ways to 3 of a kind

[Paul2432]

[ QUOTE ]
Doesn't the concept of "outs" infer that you are behind.

Don't we need to know what hand you are behind to, in order to know what outs are tainted?

[/ QUOTE ]

[ QUOTE ]
For example, if you have A A in the pocket with A 5 9 K on the board

[/ QUOTE ]

In the example given by the OP, this does not seem to be a requirement.

If it is, then my answer is 10.

Paul

[Little Fishy]

Nut flush draws have 9 and if you combine a nut flush draw with a high strait draw than i think you get 12 outs

[Little Fishy]

Bravo

[chapstick]

[ QUOTE ]
Woops. Didn't notice the "street you can't have a hand BETTER than three-of-a-kind." Question is still oddly worded. Assuming I'm not missing anything, I can't see any more than 20.

[/ QUOTE ]

I don't know the answer. I was just making up possible hands (while at work... programming can drive me nuts),
and started counting outs and stuff to keep me entertained.
The "better than three-of-a-kind" clause, was to keep out the trivial cases of having a royal-flush before the river (in which case I would say every river card is an out, i.e. is a card giving you a win).

Anyway, I just wanted to see the types of hands people would throw out. The example with the kings and 20 outs is a nice one. Quite creative.

[motorholdem]

[ QUOTE ]
[ QUOTE ]
Doesn't the concept of "outs" infer that you are behind.

Don't we need to know what hand you are behind to, in order to know what outs are tainted?

[/ QUOTE ]

Concepts can't infer. Only people can infer.

That said, yes.

[/ QUOTE ]

Sooooorrrryyyy

In the future I'll try suggest, posit, affirm or imply. Is that the worst violation you found while lurking the threads?

[FishAndChips]

[ QUOTE ]
A /images/graemlins/heart.gif K /images/graemlins/heart.gif

A /images/graemlins/club.gif Q /images/graemlins/heart.gif J /images/graemlins/heart.gif 6 /images/graemlins/spade.gif


T-4 ways
/images/graemlins/heart.gif-8 ways

so 12 ways to the nuts and 2 ways to 3 of a kind

[/ QUOTE ]


Actually a 9/images/graemlins/heart.gif or 8 /images/graemlins/heart.gif could make someone with T /images/graemlins/heart.gif 8 /images/graemlins/heart.gif or T /images/graemlins/heart.gif 9 /images/graemlins/heart.gif a straight flush.

Therefore you can't count those two cards as nut outs /images/graemlins/smile.gif

[FishAndChips]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Doesn't the concept of "outs" infer that you are behind.

Don't we need to know what hand you are behind to, in order to know what outs are tainted?

[/ QUOTE ]

Concepts can't infer. Only people can infer.

That said, yes.

[/ QUOTE ]

Sooooorrrryyyy

In the future I'll try suggest, posit, affirm or imply. Is that the worst violation you found while lurking the threads?

[/ QUOTE ]

People don't infer. Minds of people infer. They do so using concepts. Thus concepts within a mind DO infer. Thus Motor wasn't out of line in what he wrote there, Rasputin good buddy.

/images/graemlins/smile.gif

[Paul2432]

[ QUOTE ]
[ QUOTE ]
A /images/graemlins/heart.gif K /images/graemlins/heart.gif

A /images/graemlins/club.gif Q /images/graemlins/heart.gif J /images/graemlins/heart.gif 6 /images/graemlins/spade.gif


T-4 ways
/images/graemlins/heart.gif-8 ways

so 12 ways to the nuts and 2 ways to 3 of a kind

[/ QUOTE ]


Actually a 9/images/graemlins/heart.gif or 8 /images/graemlins/heart.gif could make someone with T /images/graemlins/heart.gif 8 /images/graemlins/heart.gif or T /images/graemlins/heart.gif 9 /images/graemlins/heart.gif a straight flush.

Therefore you can't count those two cards as nut outs /images/graemlins/smile.gif

[/ QUOTE ]

Don't forget that the 6h could make someone quads. This example only has 9 nut outs.

If your hand must improve, ten is the most nut outs possible. For example, you hold As Ts, board is Ks Js 3c 2d. Nut outs are the four queens plus six non-pairing spades.

Technically, I suppose you could argue the answer is still 21. You hold Kd Kc, board is Ks 7h 3c 2s. Any K,Q,J,T,9,8 leaves you with the nuts and improves your hand from KKK73 to KKK with a higher kicker.

Paul

[Paul2432]

[ QUOTE ]
If your hand must improve, ten is the most nut outs possible. For example, you hold As Ts, board is Ks Js 3c 2d. Nut outs are the four queens plus six non-pairing spades.
Paul

[/ QUOTE ]

Man, this problem is tricky. If outs that tie for the nuts count, and your hand must improve to a new category (not just kicker improvement), then my answer is 14.

You hold As Ts, Board Ah Qs Js Td. Your nut outs are Ad Ac Ks Kd Kc Kh 9s 8s 7s 6s 5s 4s 3s 2s. You could argue that Ad Ac should not count, because quad aces would be the nuts on those boards (I count them as nut outs because the ace in your hand blocks quads, I suppose you could say 9s, 8s are not nut outs by the same argument), and that the Kh Kd Kc should not count because the board plays.

Paul