Lomaha
From LowballWiki
Lomaha (or lowmaha) is a lowball variant of Omaha. Players receive four cards face down; there are four betting rounds and a flop, turn, and river as in normal Omaha. However, the winning hand is the one whose best Omaha High hand has the lowest rank. That is, each player uses the two cards from their hand, and the three from the board, that give them the highest-ranked Omaha hand. The lowest such hand wins.
An alternative description is that the game is played as regular omaha high, but with the loser scooping the pot at showdown.
Contents |
[edit] Examples
Player A holds A
A
24
, player B holds 234
9, and player C holds K743.
On a board of 58TJQ, player A has a pair of aces (not T852A), player B has a flush, and player C has KQJT7 and takes the pot.
On a board of K7562, players B and C each have a straight (76543), and player A wins with a pair of aces.
The worst possible Lomaha hand is not 23457, since there is no combination of hand and board cards that can achieve this. Instead the nuts is a JT754. (23457 on board, 69TJ in hand.) If you hold 2345, the best possible hand you can make is JT954 (on a 789TJ board.)
[edit] Starting Hands
Good starting hands will be low and uncoordinated. Rainbow hands are preferable to suited ones. Anecdotally, the worst starting hand for Omaha Hi is 2378, which suggests it should be a strong starting hand for lowmaha. But, note that its best possible hand is QT987 (on a board of 459TQ.)
The hand that is probably best over all is 2345 because it has the best "kickers" (54) when the board is high and/or paired, despite having more straight possibilities than 2378. (Note that if there is a low straight out, 2345 is likely to have paired a card anyway.) On balance it appears that being low is more important than being uncoordinated, though a hand such as 279T may do OK.
Pairs should generally be avoided, although quad low cards are quite strong. A single opponent playing four unmatched cards against your quads will have the board pair one of his cards 1 - (32C5)/(44C5) = 81% of the time, so 2222 is a 4:1 favorite to win! Higher quads suffer because of the possibility that your opponent will pair only a deuce but are probably still a favorite to win. Trip deuces should also be profitable to play.
[edit] Which Hands Make the Nuts Most Often?
Here are the results of a simulation which dealt all 2,598,960 possible boards and calculated the nut lomaha hand for each board. As noted above, 2345 is the nut hand far more often than any other holding. When multiple hands are listed they are all equally likely to be the nuts (for example, both 2456 and 3456 have 6.5% chance, not 6.5% combined.)
| Hand(s) | Percentage of boards for which this hand is the nuts |
|---|---|
| 2345 | 13.54% |
| 2456, 3456 | 6.50% |
| 2346, 2356 | 5.79% |
| 2457, 3457 | 2.53% |
| 2349, 2678, 2789, 3789 | 2.14% |
| 2347, 2357 | 1.82% |
| 2467, 3467 | 1.60% |
| 2359, 3678, 4789 | 1.42% |
| 279T | 1.15% |
| 2367 | 1.11% |
| 2389, 2489 | 0.95% |
The top 11 hands are the nuts on more than 50% of the boards.
There are a total of 150 hands that can make the nuts. (2378 is not one of them.) The complete list is:
- 2345 2346 2347 2349 234T 234J 2356 2357 2359 235T 235J 2367 2369 236T 236J 2389 238T 238J 238Q 239T 239J 239Q 23TQ
- 2456 2457 245T 245J 2467 246T 246J 2489 248T 248J 248Q 249T 249J 249Q 24TQ
- 2567 256J 2589 258T 258Q 259T 259Q 25TQ
- 2678 2679 267T 2689 268T 269T 269J 26TJ
- 2789 278T 278J 279T 279J 279Q 27TJ 27TQ 27JQ
- 289T 289J 28JQ 28TJ 28TQ 29JQ 29TJ
- 3456 3457 3458 345J 345T 3467 3468 346J 346T 349J 349Q 349T 34TQ
- 3567 3568 356J 359Q 359T 35TQ
- 3678 3679 367T 3689 368T 369T 36TJ
- 3789 378T 378J 379J 379T 37JQ 37TJ 37TQ
- 389J 389T 38JQ 38TJ 38TQ 39JQ 39TJ
- 4567 4568 4569 456J 45TQ
- 4678 4679 467T 4689 468T 469T
- 4789 478J 478T 479T 479J 47JQ 47TJ
- 489J 489T 48JQ 48TJ
- 49TJ 49JQ
- 5789 578J 578T 579T 579J 57TJ
- 589J 589T 58TJ
- 59TJ
- 689T 689J 68TJ
- 69TJ
- 79TJ
There are many hands that are the nuts less than 1% of the time. The 31 italicized hands in this list make the nuts the minimal number of times, on only 0.0394% of boards. A further 20 hands make the nuts twice as often, 0.0788% of boards.
[edit] Counting Outs
Counting outs in Lomaha is nontrivial. Generally you can only count "negative outs": cards that you are sure will lose the hand for you. However, when you currently have a small pair you may also be able to estimate how many "hidden outs" you have: cards that will hurt your opponent and give you a winning hand.
Suppose you hold 2345 and the board shows 788T on the turn. You hold the best hand at the moment. On the river, a 6 gives you a straight, while 2, 3, 4, or 5 give you one pair (which may still win.) Any other card ensures that you have the best possible hand. So in this case you have 27 outs to the nuts in 43 unknown cards; you will win at least 63% of the time no matter how many players are in the pot. (Even one of 2345 can win for you if your opponent also holds one of these cards.)
Now, say you have 2345 but the board is 289J. If your opponent has 3456 then you have seven outs to win: four 7's giving him a straight and three 6's giving him two higher pair. If your opponent instead holds 367Q then you have twenty-one outs in forty cards to win (52.5% chance): two 5's or three T's (not including the 5 and T) giving him a straight, two 7's, three 6's or three Q's giving him a higher pair (not counting the 7), or one of the eight remaining clubs for a flush.
For heads-up situations, the twodimes odds calculator (pokenum) can be used in Omaha High mode since the winner in Omaha High is the loser in Lomaha, so you need only swap the hand equities. The examples from the previous paragraph are shown here:
pokenum -o 2c 3d 4s 5h - 3c 4d 5s 6h -- 2h 8c 9d jc Omaha Hi: 40 enumerated boards containing Jc 8c 9d 2h cards win %win lose %lose tie %tie EV 4s 2c 3d 5h 33 82.50 7 17.50 0 0.00 0.825 5s 3c 4d 6h 7 17.50 33 82.50 0 0.00 0.175
pokenum -o 2c 3d 4s 5h - 3h 6c 7d qc -- 2h 8c 9d jc Omaha Hi: 40 enumerated boards containing Jc 8c 9d 2h cards win %win lose %lose tie %tie EV 4s 2c 3d 5h 19 47.50 21 52.50 0 0.00 0.475 Qc 6c 7d 3h 21 52.50 19 47.50 0 0.00 0.525
Unfortunately this cannot be extended to three players, although we can get information about preflop and flop matchups as well. This shows that 2345 is a nearly 2:1 favorite over 2378 preflop:
pokenum -mc 500000 -o 2c 3d 4s 5h - 2d 3c 7h 8s Omaha Hi: 500000 sampled boards cards win %win lose %lose tie %tie EV 4s 2c 3d 5h 165686 33.14 324351 64.87 9963 1.99 0.341 8s 3c 2d 7h 324351 64.87 165686 33.14 9963 1.99 0.659
[edit] Where to Play
This variant is probably only seen in drunken home games.
