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

#1 10-13-2005, 04:58 AM

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?

#2 10-13-2005, 07:17 AM

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.

Xelent · #3 10-13-2005, 07:18 AM

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

#4 10-13-2005, 07:21 AM

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

#5 10-13-2005, 07:29 AM

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.

OrangeKing · #6 10-13-2005, 07:33 AM

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).

benkahuna · #7 10-13-2005, 07:40 AM

[ 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.

#8 10-13-2005, 08:52 AM

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.

#9 10-13-2005, 09:16 AM

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.

bugstud · #10 10-13-2005, 09:50 AM

try this