Rock, Paper, Scissors

[Oblivious]

In April's 2+2 internet mag, there's an artical that begins:
[ QUOTE ]
Suppose Hero, at a nine handed table, voluntarily plays only the best fifth of Omaha-8 hands dealt to him.

[/ QUOTE ]
This reminded me of an old question I filed away in the back of my head from several years ago, but never got a solid solution.

Can we rank all the hands in Omaha Hi (or O/8) in value by comparing each hand heads up to everyother hand? If we tried this, would we run into any rock, paper, scissors paradoxes when we considered 3 unique hands on our ladder of ranking? In other words, say you had two unique hands: A and B. A is ranked slightly higher than B when compared heads up to eachother. A>B. If we added a 3rd hand to the comparison C, could it rank higher to A and lower to B? C>A>B>C? I imagine this could be possible if C containted blocking cards for A which demoted A's value below B's. C would also have to rank above A heads up and at the same time below B heads up.

I see why the only reason this problem is tricky is because we are taking heads up comparisons and applying them to multiway situations. Now that I think about it we could do the same thing in holdem and probably come up with the same paradox. Can anyone shed any light on this subject for me?

[spino1i]

True but a certain class of hands stands out above others.
I think hands could be ranked:
AA2x
AAxx
A23x/A24x
A2xx
A345
etc

[Fiasco]

well, in HE 2c 2s > Ad Ts > Jh Th > 2c 2s

in omaha high 6789DS > AA23 > JJTT > 6789 DS

in omaha 8 ... hell, i dont know, you can probably make one.

Its not that important. Here I go shedding some light on the topic: Its not that important how well one hand stacks up against another hand hot/cold when it comes to evaluating that hand. The only time this should even come up is when youre short stacked in a PLO8 tourney.

In almost all other situations hands should be evaluated for their potential to be played postflop.

[bbartlog]

Easy enough to find some:
A299r > A234ss (60/40)
A234ss > KKQJds (55/45) (assumes one of KKQJ flushes is dominated)
KKQJds > A299r (54/46)

As Fiasco says, it's not important. Much more critical to understand which hands suffer or benefit from having more players in the pot.

Related thing that came up in the poker theory forum was to find the set of most intransitive HE hands. This is defined as the set of three hands meeting the rock-paper-scissors criterion, where the advantage to the second player to choose a hand is the greatest (in other words, set things up so that the smallest edge in these three matchups is still as large as possible). I found Ah2h vs 2d2c vs JhTh, which seems to be the best solution for HE.

Based on how quickly I found the first set of O8 hands that work, I'd say the most intransitive set of O8 hands would be significantly *more* intransitive than those HE hands.

[Colonel Ingus]

[ QUOTE ]
True but a certain class of hands stands out above others.
I think hands could be ranked:
AA2x
AAxx
A23x/A24x
A2xx
A345
etc

[/ QUOTE ]

don't forget 2345ss. i love this hand.

[Mendacious]

I don't think Cappeletti's book is great overall, but it does cover some of these ideas dealing with "Push" vs "Pull" hands.

[Oblivious]

Wow. Great replies. I realize this idea essentially has no practical application when it comes to playing in a real world situation. It's just something Ive been curious about for a while. I remember the idea first entered my head when having a discussion with a dealer. He claimed AAKKds was the best hand in O/8, because "theres not always a low." I of course knew at the time this was nonsense, and expected something like AA23ds would be the best hand. Then I got to wondering if there was no single best hand in omaha. If I could show that there were transitive hands, I would know that it could be possible that there would be no single best hand. The hypothesis of "no single best hand" could obviously be easily disproven, but I was still curious about the rock, paper, scissors idea.

[EffenDolts]

If four opponents all hold A234r, 5555 is a mortal lock for high. This despite A234 being a damn good hand and 5555 being the 4th worst of all possible starters.

[Oblivious]

[ QUOTE ]
If four opponents all hold A234r, 5555 is a mortal lock for high. This despite A234 being a damn good hand and 5555 being the 4th worst of all possible starters.

[/ QUOTE ]

Heads up comparisons arent worth much in a multiway arena.

[TxRedMan]

the thing you need to know about comparing LO8 hands is that HU isn't good enough to determine true value.

i.e., you can add a hand in the mix to the two hands that you are comparing HU and it drastically changes the value of the hands.