Saturday, March 07, 2009

An Omaha Conundrum - Flop the Nuts, a Set of Aces, and Have 31% Equity!

Ferret and I were just talking Pot Limit Omaha post-flop and I was musing about the sort of trouble you can get into with top set on a semi-connected board. One situation we considered was flopping top pair with second set, making it unlikely your opponent has top set. Another is flopping top set against two opponents - its good on the flop, and yet you have less than 33% equity in the hand.

Both situations are employed in this example.

Ferret is in the big blind, Gramps is in middle position, Scotty is on the button.

Gramps is well behaved today, and just limps in with his 5h 7s 8h 9s.

Scotty wakes up on the button with Aces, and another Broadway card which is suited. Ah Ac Qd 2d. He raises pot.

Wil folds the small blind and Ferret finds 6s Ad Td 6d. He has a suited Ace, two Broadway cards, and a small pair. He knows Gramps will call, so he figures he’ll take a flop.

Gramps calls.

The flop is 4s 6h As. Ferret flopped second set. He also believes Scotty will continuation bet, representing Aces, but thinks it is unlikely he has them, since Ferret holds an Ace himself. He checks.

Gramps checks his disgusting wrap with 9-high flush draw and backdoor 8-high flush draw.

Scotty bets full pot, protecting his flopped top set. Ferret believes he has trapped his opponent, and re-raises the full amount of the pot.

Gramps is now getting sickening pot odds, and has a full pot-sized bet remaining. He believes the numbers support getting it all in and he does. Scotty has the nuts, and calls off his remaining chips. Ferret feels he’s committed, and believes he may be wrong about Scotty’s holdings, but knows he’s capable of having a wrap here as well. He calls off the remainder of his chips.

Who is in good shape? Scotty doesn't know... says the players have the following pot equity:
pokenum -o ah ac qd 2d - 5h 7s 8h 9s - ad 6d 6s td -- 4s 6h as

Omaha Hi: 666 enumerated boards containing As 4s 6h

cards win %win lose %lose tie %tie EV
Scotty Ac Qd 2d Ah 213 31.98 453 68.02 0 0.00 0.320
Gramps 9s 7s 8h 5h 417 62.61 249 37.39 0 0.00 0.626
Ferret 6s Ad Td 6d 36 5.41 630 94.59 0 0.00 0.054

Interestingly, the set of Aces, currently the nuts, have only 31%, while the wrap and two live flush draws have nearly 63% equity! The small mammal is in mammal jail, drawing to the case 6 for quads.


The Ferret said...

The next questions are (1) can Scotty get away from this hand, and (2) should he? Let's put some numbers to this scenario: The game $1/$2 PLO. The preflop pot, with Gramps' raise and Ferret's and Scotty's calls, is $25. Scotty's pot-sized bet is $25 (making the pot $50). Ferret's re-pot is $100 (pot $150). And Gramps' re-re-pot is $250, putting him all-in. The pot is now $400, and Scotty has to call $225 into a pot of $400 giving him slightly worse than 2 to 1 odds, which is not good for Scotty. Note, that if Scotty calls, Ferret now has to call $150 into a $625 pot, giving Ferret great odds to call (since he doesn't know he's in little mammal jail) and further justifying Scotty's call.

Regardless of Ferret's move, however, since it's very difficult to put Gramps on such a strong holding, I don't think Scotty can fold here. In the long run, Gramps' hand won't be so nasty, making Scotty's call more +EV.

Even if Scotty knows Gramps' exact holding, however, should Scotty fold? Maybe that depends on Ferret's move. But be careful, he's feisty.

ChicagoJason said...

Scotty potted pre-flop, not Gramps.

In a 1-2 PLO game, after one limper, Scotty can raise to $10. With two callers and a dead SB, the pot is $31, not $25.

The flop checks to Scotty who pots, $31. If Ferret re-pots, the bet is $124. If Gramps re-pops it, the bet is $434. If we assume Scotty started the hand with 200 BB, this puts him all in. There's $520 in the pot and he must call his last $359, being offered slightly less than 3-to-2 (1.4-to-1). If he can see all of the cards (and do math very quickly), then he sees that he's only got 31% equity and he needs 42-ish... Since he cannot see the cards, he might assume that Gramps and Ferret are sharing a number of cards (some straight, some flush), which is very logical, and most of the time he is correct to call here with the current nuts.

As it stands, it is Ferret's awful spot which hurts Scotty as well. With two 6s and an Ace in his hand, Scotty is missing 3 of his 7 turn draws (and 3 of his 10 river draws) to the winning full house/quads.