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I don't really have one but was more hoping that exploring how various strong hands hold up might allow us to get there.
One might define "best" the following way:
1) A hand that is ALWAYS favorite regardless of what your opponent has
2) If there is more than one hand fitting criterion 1, then the hand that is the biggest favorite over its closest rival.
You're right that on criterion 2, it would probably be better to have a hand that has the biggest equity over the entire range of possible 54 hands on this board, but that gets really tedious to carry out.
My intention, really, was simply, first, to explore just which redraws are the very strongest and, secondly, to figure out where the boundaries lie on redraws where you still need to call.
I think it's pretty clear that against a tight opponent who raises your nuts, you have to have SOME redraw. But the question that Rhound's hand brought up for me is: Just how much redraw to you need to have? By making it HU here, I wanted to simplify it a bit but still get some idea of the "hierarchy" among various kinds of redraws.
I'll have to double-check your data (which I'm sure is correct since everything else you had corresponds exactly to what I got on the cardplayer calculator), but it's looking like 3456ds is the very best one...
And I don't really see why. True, the 3 takes away boating chances for the AA, but so does 3457. Ok, I think I may see where it's coming from: On 3457, one of the straight improvements also is a flush improvement. So there are only 3 independent straight outs.
With 3456, you still have a 4 or a 5 to make a better straight (hence 4 outs), but the spades are completely independent of that, so that gives you 1 extra out against the AA hand, plus your defensive 3.
Hmmmm... I think that may mean that either 3456 is the best possible hand, or else there really isn't one, because you get 3456 as favorite against certain boats, but certain boats as favorite against 4567, which is in turn a favorite over 3456 (I'll have to check into this one further).
Statistics: Posted by Aisthesis — Wed Mar 15, 2006 11:26 am
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I had noticed that 4c5c6s7s does better than 7s3s4c5c, but your 6s3s5c4c really surprizes me. I'll have to think about that one. It's impossible to have against AcAd4c5s, which I'm currently claiming to be the best. But 6c3s5c4s should amount to the same thing since the straight flush is impossible in either case.
I just don't see why it does so well. I would think the ds high wrap would be better ???
Statistics: Posted by Aisthesis — Wed Mar 15, 2006 10:03 am
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![[3s]](https://livepokerforum.com/images/smilies/3s.gif "The Three of Spades")
![[5c]](https://livepokerforum.com/images/smilies/5c.gif "The Five of Clubs")
![[4c]](https://livepokerforum.com/images/smilies/4c.gif "The Four of Clubs")
is the second best hand pokenum -o 7s 3s 5c 4c - 4s 5s ac ad -- as 2s 3c
Omaha Hi: 820 enumerated boards containing As 2s 3c
cards win %win lose %lose tie %tie EV
7s 3s 5c 4c 238 29.02 270 32.93 312 38.05 0.480
5s 4s Ac Ad 270 32.93 238 29.02 312 38.05 0.520
pokenum -o 7s 6s 5c 4c - 4s 5s ac ad -- as 2s 3c
Omaha Hi: 820 enumerated boards containing As 2s 3c
cards win %win lose %lose tie %tie EV
7s 6s 5c 4c 294 35.85 302 36.83 224 27.32 0.495
5s 4s Ac Ad 302 36.83 294 35.85 224 27.32 0.505
pokenum -o 3s 6s 5c 4c - ac ah 4s 5s -- as 2s 3c
Omaha Hi: 820 enumerated boards containing As 2s 3c
cards win %win lose %lose tie %tie EV
6s 3s 5c 4c 314 38.29 270 32.93 236 28.78 0.527
5s 4s Ac Ah 270 32.93 314 38.29 236 28.78 0.473
Statistics: Posted by GooperMC — Wed Mar 15, 2006 8:56 am
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I figured that was fairly obviously AcAd(h)4s5s, but it's not!!
That hand gives the following numbers against 7s3s5c4c, which I consider a pretty obvious second best (both runner-runners plus any 6 and not taking away any of your own outs):
Tie: 38.05%
Win: 32.93%
Loss: 29.02%
What actually seems to do the very best against the second best hand is trip aces with nut straight, runner-runner clubs (!!) and one exclusionary spade. AcAh4c5s (the heart is irrelevant and one can reverse the suits of the 4 and 5, but one needs to be a spade and one a club) vs. 7s5c4s3s gives the following percentages, which are clearly better:
Tie: 35.85%
Win: 35.61%
Loss: 28.54%
Statistics: Posted by Aisthesis — Tue Mar 14, 2006 10:01 pm
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