The Maximum Outs in hold \'em vs. a made hand
 

Here is a hypothetical sitation that I believe gives the most possible outs for one hand against another hand that is currently better ie)if the hand ended on the flop, the other hand would win.

Here it is:

Heads up

Player 1 holds : K [img]/images/graemlins/heart.gif[/img] 10 [img]/images/graemlins/heart.gif[/img]
Player 2 holds : 6 [img]/images/graemlins/diamond.gif[/img] 6 [img]/images/graemlins/spade.gif[/img]

Flop is : 2 [img]/images/graemlins/diamond.gif[/img] J [img]/images/graemlins/heart.gif[/img] Q [img]/images/graemlins/heart.gif[/img]

Now, Player 1 has 9 flush draw outs, plus 6 open-ended straight draw outs(A,9 of hearts are already counted) plus 6 kings and tens to give an over pair. This gives 21 outs in total, and player 1 has a 71% chance of winning. I deem 21 to be the maximum number of outs possible against a hand that currently beats us on the flop.

Is it possible to have more outs than 21?

Re: The Maximum Outs in hold \'em vs. a made hand
 

I tried counterfeiting, by replacing the 2 [img]/images/graemlins/diamond.gif[/img] with a jack or queen, so that if another jack or queen hits then it will counterfeit the sixes, but this decreases the chances of winning by giving the sixes more full house outs.

Re: The Maximum Outs in hold \'em vs. a made hand
 

The most outs you can have is 24.

Opponent has black 22.

Flop 9 [img]/images/graemlins/diamond.gif[/img]9 [img]/images/graemlins/heart.gif[/img]T [img]/images/graemlins/heart.gif[/img]

You hold J [img]/images/graemlins/heart.gif[/img]Q [img]/images/graemlins/heart.gif[/img]

3 J's
3 Q's
9 Hearts
8 Open-end strait minus 2 for the hearts = 6 Straits
3 T's

3+3+9+6+3 = 24

Re: The Maximum Outs in hold \'em vs. a made hand
 

No, you're wrong. Your outs seem right, but your situation reduces our chance of winning to 70%.

Re: The Maximum Outs in hold \'em vs. a made hand
 

Your situation does apply to the turn though. By adding the 3 [img]/images/graemlins/diamond.gif[/img] to your example and hence putting us on the turn, then you are now 57 % to win with no hand yet. So yes you now have 24 outs as you suggested, but this only works on the turn. Because the situation that you described reduces our chance of winning on the flop.

Re: The Maximum Outs in hold \'em vs. a made hand
 

Well, add a blank to both hands (say, 5c) and do it from the turn - you can still have 24 outs, and now a better chance to win than the 21 out hand (for obvious reasons).

Re: The Maximum Outs in hold \'em vs. a made hand
 

[ QUOTE ]
The most outs you can have is 24.

Opponent has black 22.

Flop 9 [img]/images/graemlins/diamond.gif[/img]9 [img]/images/graemlins/heart.gif[/img]T [img]/images/graemlins/heart.gif[/img]

You hold J [img]/images/graemlins/heart.gif[/img]Q [img]/images/graemlins/heart.gif[/img]

3 J's
3 Q's
9 Hearts
8 Open-end strait minus 2 for the hearts = 6 Straits
3 T's

3+3+9+6+3 = 24

[/ QUOTE ]

2 of hearts isn't an out here so you only have 8 heart outs.
By pairing the board, you've given redraws against all of your hands with any 2 which is why odds are lower for a win than the other hand.

Re: The Maximum Outs in hold \'em vs. a made hand
 

Here's my new board on the turn:

You hold Q [img]/images/graemlins/heart.gif[/img] J [img]/images/graemlins/heart.gif[/img]
Villain holds 2 [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/club.gif[/img]

Turn cards are:
T [img]/images/graemlins/heart.gif[/img] K [img]/images/graemlins/heart.gif[/img] K [img]/images/graemlins/diamond.gif[/img] 4 [img]/images/graemlins/diamond.gif[/img]

Now you have
9 flush draw outs, minus the 2 [img]/images/graemlins/heart.gif[/img]
6 open ended straight draw outs (no 9,A of [img]/images/graemlins/heart.gif[/img])
3 tens that counterfeit the deuces
3 fours that counterfeit the deuces minus the 4 of [img]/images/graemlins/heart.gif[/img]
6 Queens and Jacks to make a better two pair
Total of 25 outs

pokenum -h jh qh - 2s 2c -- kd kh th 4d
Holdem Hi: 44 enumerated boards containing Kd 4d Kh Th
cards win %win lose %lose tie %tie EV
Qh Jh 25 56.82 19 43.18 0 0.00 0.568
2s 2c 19 43.18 25 56.82 0 0.00 0.432

Now if we change the board slightly then it goes down.
For example
Player 1 : Q [img]/images/graemlins/heart.gif[/img] J [img]/images/graemlins/heart.gif[/img]
Player 2 : 2 [img]/images/graemlins/spade.gif[/img] 2 [img]/images/graemlins/club.gif[/img]

Board on turn:
T [img]/images/graemlins/heart.gif[/img] T [img]/images/graemlins/diamond.gif[/img] K [img]/images/graemlins/heart.gif[/img] 4 [img]/images/graemlins/diamond.gif[/img]

Now I see it as:
9 flush draw outs minus the 2 [img]/images/graemlins/heart.gif[/img]
6 open ended straight outs (no A,9 of [img]/images/graemlins/heart.gif[/img])
3 kings to counterfeit the 2s
3 fours to counterfeit the 2s minus the four of [img]/images/graemlins/heart.gif[/img]
6 queens and Jacks to make a better two pair
total outs of 25

But the results change

pokenum -h jh qh - 2s 2c -- td kh th 4d
Holdem Hi: 44 enumerated boards containing Td 4d Kh Th
cards win %win lose %lose tie %tie EV
Qh Jh 23 52.27 19 43.18 2 4.55 0.545
2s 2c 19 43.18 23 52.27 2 4.55 0.455

Man, it's late. I've gotta get to sleep. I'm messing something up, but I'll figure it out in the morning. Any suggestions for why these two boards aren't the same results would be appreciated. I've gotta sleep, this is insane to be up this late worrying about maximum out count.

Re: The Maximum Outs in hold \'em vs. a made hand
 

Aha, I figured it out.

When the board has tens paired and a 4 hits to counterfeit the deuces, then the king on the board is the high card and hence our Queen and Jack are meaningless and this then creates a split pot. With the kings being the pair on the board, then if the four hits to counterfeit the deuces, then suddenly our queen high is relevant and wins us the hand. So there, I have explained the discrepancy between the two different boards with the tens paired and the one with the kings paired. Now I may rest and fall asleep like a normal person would have done many hours ago.

Alas, I define the maximum number of possible outs to be 25.

Re: The Maximum Outs in hold \'em vs. a made hand
 

try this

Re: The Maximum Outs in hold \'em vs. a made hand
 

I did forget about the 2 of hearts and the other thing, but you asked how many outs you can have on the flop, not what gives you the best chance of winning.

Not sure if these "have" to correspond because of different kinds of redraws. For example, my hand posted gives more outs than your hand to make a winning hand on the turn, but it also gives more outs to the other hand because another 9 gives the 22 a full house. So the percentage to win the hand might be less, but outs are more.

BTW, if you search, we have done this before and the answer I believe is 26 or 24.

Re: The Maximum Outs in hold \'em vs. a made hand
 

This reminds me of Doyles example in SS. Whereas someone can hold 4 [img]/images/graemlins/diamond.gif[/img]5 [img]/images/graemlins/club.gif[/img] and flop 3 [img]/images/graemlins/spade.gif[/img]6 [img]/images/graemlins/heart.gif[/img]7 [img]/images/graemlins/heart.gif[/img]. They flopped the nuts...however they are a statistical underdog to someone holding 8 [img]/images/graemlins/heart.gif[/img]9 [img]/images/graemlins/heart.gif[/img].

MDoranD

Re: The Maximum Outs in hold \'em vs. a made hand
 

50 OUTS!

Re: The Maximum Outs in hold \'em vs. a made hand
 

[ QUOTE ]
The most outs you can have is 24.

Opponent has black 22.

Flop 9 [img]/images/graemlins/diamond.gif[/img]9 [img]/images/graemlins/heart.gif[/img]T [img]/images/graemlins/heart.gif[/img]

You hold J [img]/images/graemlins/heart.gif[/img]Q [img]/images/graemlins/heart.gif[/img]

3 J's
3 Q's
9 Hearts
8 Open-end strait minus 2 for the hearts = 6 Straits
3 T's

3+3+9+6+3 = 24

[/ QUOTE ]

you count the two of hearts but that would give your oppenent a full

Re: The Maximum Outs in hold \'em vs. a made hand
 

[ QUOTE ]
This reminds me of Doyles example in SS. Whereas someone can hold 4 [img]/images/graemlins/diamond.gif[/img]5 [img]/images/graemlins/club.gif[/img] and flop 3 [img]/images/graemlins/spade.gif[/img]6 [img]/images/graemlins/heart.gif[/img]7 [img]/images/graemlins/heart.gif[/img]. They flopped the nuts...however they are a statistical underdog to someone holding 8 [img]/images/graemlins/heart.gif[/img]9 [img]/images/graemlins/heart.gif[/img].


[/ QUOTE ]
That's not a good definition of the nuts. On that flop, the nuts is 4[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img], which is not a dog to any hand heads up.

Re: The Maximum Outs in hold \'em vs. a made hand
 

[ QUOTE ]
[ QUOTE ]
This reminds me of Doyles example in SS. Whereas someone can hold 4 [img]/images/graemlins/diamond.gif[/img]5 [img]/images/graemlins/club.gif[/img] and flop 3 [img]/images/graemlins/spade.gif[/img]6 [img]/images/graemlins/heart.gif[/img]7 [img]/images/graemlins/heart.gif[/img]. They flopped the nuts...however they are a statistical underdog to someone holding 8 [img]/images/graemlins/heart.gif[/img]9 [img]/images/graemlins/heart.gif[/img].


[/ QUOTE ]
That's not a good definition of the nuts. On that flop, the nuts is 4[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img], which is not a dog to any hand heads up.

[/ QUOTE ]

The nuts on that flop is any 45. It does not have to be of hearts.

Re: The Maximum Outs in hold \'em vs. a made hand
 

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Whereas someone can hold 4 [img]/images/graemlins/diamond.gif[/img]5 [img]/images/graemlins/club.gif[/img] and flop 3 [img]/images/graemlins/spade.gif[/img]6 [img]/images/graemlins/heart.gif[/img]7 [img]/images/graemlins/heart.gif[/img]. They flopped the nuts...however they are a statistical underdog to someone holding 8 [img]/images/graemlins/heart.gif[/img]9 [img]/images/graemlins/heart.gif[/img].


[/ QUOTE ]
That's not a good definition of the nuts. On that flop, the nuts is 4[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img], which is not a dog to any hand heads up.

[/ QUOTE ]

The nuts on that flop is any 45. It does not have to be of hearts.

[/ QUOTE ]
If you read the above carefully, you'll see that I suggested that there are multiple definitions of the nuts. So, what did your post add?

If Hold'em were a 5-card game, it would make sense to say that any 45 is the nuts, and if Hold'em were a 2-card game, 22 would be the 13th best hand. However, there are two more cards to come, and 4[img]/images/graemlins/diamond.gif[/img] 5[img]/images/graemlins/club.gif[/img] is a significant underdog 4[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img].

http://twodimes.net/h/?z=1281397
5[img]/images/graemlins/club.gif[/img] 4[img]/images/graemlins/diamond.gif[/img] 0.318
5[img]/images/graemlins/heart.gif[/img] 4[img]/images/graemlins/heart.gif[/img] 0.682

Given that it has 31.8% equity against 4[img]/images/graemlins/heart.gif[/img] 5[img]/images/graemlins/heart.gif[/img], would you call 4[img]/images/graemlins/diamond.gif[/img] 5[img]/images/graemlins/club.gif[/img] "an unbeatable hand?" Would you call it the best possible? I hope not. You can say that it makes an unbeatable 5-card hand if the game were stopped at this point, but again, that's a lousy definition.

Re: The Maximum Outs in hold \'em vs. a made hand
 

Whenever you are defining the nuts, you have to stop at the given stage in the hand. It is called the stone cold nuts if it is impossible that it will be beat throughout the rest of the hand. 45 and 45 of hearts are both the nuts at the given time and neither of them are the stone cold nuts. Yes, I would rather have 45 of hearts, but it does not make the hand any better at the given moment in time. This is all I was talking about.

AA is the nuts preflop. On a rainbow flop of AA7, it is the stone cold nuts on the flop. On a flop of AT7, it is the nuts, but far from stone cold.

Are you trying to say that on a flop of A [img]/images/graemlins/spade.gif[/img]T [img]/images/graemlins/heart.gif[/img]7 [img]/images/graemlins/heart.gif[/img]

A [img]/images/graemlins/diamond.gif[/img]A [img]/images/graemlins/club.gif[/img] isn't the nuts because A [img]/images/graemlins/heart.gif[/img]A [img]/images/graemlins/diamond.gif[/img] or
A [img]/images/graemlins/heart.gif[/img]A [img]/images/graemlins/club.gif[/img] is a better hand?

Re: The Maximum Outs in hold \'em vs. a made hand
 

[ QUOTE ]
Whenever you are defining the nuts, you have to stop at the given stage in the hand.

[/ QUOTE ]
Wrong. Did you overlook my definition, which does not rely on stopping in the middle of the hand?

[ QUOTE ]
AA is the nuts preflop. On a rainbow flop of AA7, it is the stone cold nuts on the flop.

[/ QUOTE ]
If you are going to post, please take the time to think about this more clearly. Quads on the flop can be beaten. Someone can always catch a runner-runner straight flush. So, that definition is just about useless.

[ QUOTE ]
Are you trying to say that on a flop of A [img]/images/graemlins/spade.gif[/img]T [img]/images/graemlins/heart.gif[/img]7 [img]/images/graemlins/heart.gif[/img], A [img]/images/graemlins/diamond.gif[/img]A [img]/images/graemlins/club.gif[/img] isn't the nuts because A [img]/images/graemlins/heart.gif[/img]A [img]/images/graemlins/diamond.gif[/img] or A [img]/images/graemlins/heart.gif[/img]A [img]/images/graemlins/club.gif[/img] is a better hand?

[/ QUOTE ]
No, that's not what I said at all.

Any AA is a favorite over any other hand heads-up on that flop. If I have A[img]/images/graemlins/diamond.gif[/img] A[img]/images/graemlins/club.gif[/img], you can't have A[img]/images/graemlins/heart.gif[/img] A[img]/images/graemlins/club.gif[/img].

Re: The Maximum Outs in hold \'em vs. a made hand
 

"If you are going to post, please take the time to think about this more clearly. Quads on the flop can be beaten. Someone can always catch a runner-runner straight flush. So, that definition is just about useless."

Yeah, that is the second time I said something stupid without thinking it over in this post. Oh well. I'll try to think before I post in the future.


BTW, most of this stuff is stupid semantics and I agree with what you are saying for the most part and I think you agree with what I'm saying, it's just semantics seperating the views.