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.
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