heads up omaha high question

[Sly_Grin]

can someone tell me the odds of these 2 hands vs each other?

JQKK, one K suited
AA96 rainbow

guy who went all-in against me with the AA hand was bitching that he was a big favorite to which I replied he's nuts.Like to know the true %.

[Bozeman]

63%, which is a pretty big favorite for omaha preflop.

[Wake up CALL]

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63%, which is a pretty big favorite for omaha preflop.

[/ QUOTE ]+

64% if one of the aces is the same suit as the suited king.

[Bozeman]

Can someone explain this to me?

As Ac 9h 6d vs.

Kc Ks Qs Jd 62.73%
Kc Kh Qs Jh 62.88%
Kd Kh Qd Jc 63.13%

These are using enumeration (poker calculator), not Monte Carlo simulation, so random errors are non-existent.

I bet you got your 64% by simulation, Wake up CALL,
Craig

[Wake up CALL]

I was mistaken Craig, your computations were correct. Sorry

[Copernicus]

Explain what? The increasing favorite status of the AA96 is primarily because it is challenged by hands with 3, then 2, then 1 of the A cards' suits duplicated, making A high flushes slightly more likely as you go down the list.

That is a more powerful effect than 2, 1, 0 of the suits of the Ks being duplicated by the As (which would imply that those hands are getting stronger not weaker as you go down the list), because the improving probability of making the flush at all dominates the improving probability of K being high vs A being high when you do make it.

[Bozeman]

But a pure rainbow can't make a flush in Omaha!

[AJo Go All In]

he's right. you're nuts.

[crockpot]

i believe the difference has to do with straight flushes. between hands 1 and 2, hand 2 is more likely to hit a straight flush against a full house (or better) than in hand 1, because the ace of hearts makes it easy for the aces to hit a full. the ace of spades, meanwhile, cannot do the same in hand 1 because it is in the aces' hand.

in hand 3, the fact that the nine of diamonds is live doubles the number of straight flushes you can hit. this still seems like a pretty big difference just due to that, but it's better than anything else i can think of. try running the simulation again but swapping the suits of the 6h and 9d for hand 3, and see if you get the same result.

of course, it is naturally better to have your suited cards be in a suit where the ace is still in the deck, so that if that ace comes on board, you have a better chance to make a flush and draw out on the trips. so hand 1 is the worst here for a reason.

[Copernicus]

Where is there a pure rainbow?

[Bozeman]

As Ac 9h 6d

[ramjam]

I think straight flushes are only a very minor part of the differences (too small to account for 0.4% equity).

I believe the main factor that makes 1 the best hand is that if the A high flush comes for 2 or 3 (and the A would be there 30%+ of the time there's a flush), AA96 has made at least a set and could therefore have improved to a full house. Conversely, if hand 1 flushes (at least three non-A cards on the board) there's less chance than normal that AA96 has filled up.

I think what mainly makes 2 better than 3 is how hand 2 benefits from both the 9d (possible str8) or the 6h (possible flush) arriving whereas hand 3 is only helped by the former (although in two ways). Make these two cards "dead" and you should get nearly identical equity figures for 2 and 3.

[Bozeman]

Thanks, I could only think of str8 flushes and that seemed to be too small a probability.

Craig