Pot limit Omaha, a drawing game.
Michiel likes this game a lot, I know. Me, myself, I’m not particularly fond of it. My tendency to pick up early pots is a bit redundant in PLO since there are all of a sudden 6 combination of hands you have to fight off per player. That makes for a lot of turns and rivers on the board where I generally like to end all action on the flop.
The Mad Man hint of this week therefore is acting carefully when dealing with PLO.
How to act careful on a game where the nuts on the flop could actually be the hand with least potential?
The best way is probably knowing the numbers well enough to play them in your advantage.
Last time we played PLO however, if numbers were on my side I should have left the table with a mountain of chips, all to the courtesy of Michiel “Mickey C” Clippeleyr, his call however turned out awesome for him and instead of loosing to my top set on the turn he caught a highly needed diamond on the river for the nut flush. Numbers were against his call, he did it anyway, based on my loose image, and caught hard on the last card.
This moment, however did make me think some things over.
First of all that I have no reputation for playing PLO, but also that up until the point where the lost pot with Mickey got me on tilt, I was actually managing quite well. I had gone up a substantial amount of chips and was able to keep stabbing with my regular 30% to 35% of the hands I was dealt. Some people will tell you this is far too much, I on the other hand like to kick it up a notch against these types of players. They’ll leave me with a lot of uncontested chips I can pick up with a rather harmless raise pre-flop.
But most of all, I realised that if I won this particular hand, I would have had another notch to my bedpost of aggressive hands.
I like to make people run into my monsters, mostly off course, because that’s the most straightforward thing you can do with my style, but also because everybody who has ever called me on ace high, seeing my nut flush hit the board will never forget that moment and will be more careful next time they encounter me in a big pot.
The problem with PLO is that about 75% of that basic idea of bullying off the pre-flop phase is out the window.
In Omaha, you have to use 3 of the 5 cards on the board, meaning that your basic idea for your hand already has to be made up pre-flop, since you will always need to use at least one of the cards on the flop in your hand.
That makes for a surprisingly high amount of missed flops, unfortunately. Even more a pity since the other guys do each have 4 cards to connect to a board. When playing a pot in Omaha, the chances of someone hitting at least a pair on the flop is a whopping 53% of the time when not holding a pair in his hand already, realising this together with the fact that getting dealt a hand that contains at least one pair happens to you in about 30% of the cases, makes for a lot of possibilities.
Even more numbers: in comparison: When the flop hits in Texas Hold’Em, those cards, together with the 2 you’re holding are your current hand. 1 chance, since there simply are no other combinations. In Omaha, you’re already dealing with 6 different possibilities, each with their specific values and eventual chances to improve. Skipping the 24 possible combos on the turn (against 6 in Texas Hold’Em) we go straight to the river where the 2 cards in Texas give you 21 combinations. Omaha grants you 60!
Why these numbers?
Plain and simply to make clear that if the number of possible hands is 3 times as high, your minimal expectations for your hand should also go up by a factor 3.
| Poker hand | After the flop | After the turn | After the river | ||||||
| Combos | Probability | Odds | Combos | Probability | Odds | Combos | Probability | Odds | |
| Straight flush | 256 | 0.0116 | 85.33 : 1 | 11,712 | 0.0433 | 22.12 : 1 | 261,920 | 0.1008 | 8.923 : 1 |
| Four of a kind | 3,796 | 0.1718 | 4.822 : 1 | 85,368 | 0.3153 | 2.171 : 1 | 1,173,696 | 0.4516 | 1.214 : 1 |
| Full house | 0 | 0 | ∞ | 13 | < 0.0001 | 20,824 : 1 | 624 | 0.0002 | 4164 : 1 |
| Flush | 888 | 0.0402 | 23.89 : 1 | 27,772 | 0.1026 | 8.748 : 1 | 390,520 | 0.1503 | 5.655 : 1 |
| Straight | 3,840 | 0.1738 | 4.755 : 1 | 88,128 | 0.3255 | 2.072 : 1 | 724,800 | 0.2789 | 2.586 : 1 |
| Three of a kind | 13,320 | 0.6027 | 0.6592 : 1 | 57,732 | 0.2132 | 3.689 : 1 | 47,400 | 0.0182 | 53.83 : 1 |
| TOTAL | 22,100 | 1 | 0 : 1 | 270,725 | 1 | 0 : 1 | 2,598,960 | 1 | 0 : 1 |
Notice that while three of a kind is a 60% favorite to be the nuts after the flop, it’s less than 2% to still be on top at the river-although the three of a kind has a good chance of improving to a full house or four of a kind, if it doesn’t improve, chances are the nut hand at the river is a straight, flush or straight flush. At the river, having the nuts be four of a kind is more likely (45.2%) than all of the hands ranked below four of a kind combined (44.8%). Also, despite the rarity of straight flushes at showdown, 10% of the boards will have one as the nut hand by the river.
This of course doesn’t mean that these nut hands will always come out. If anything I put up this chart to show you how unrealistic it is to “always play for the nuts or fold”, like some people would like you to do.
Do you really have four-of-a-kind in 45% of the cases when getting to the river? I’m sure you don’t, simply because this is a chart about the absolute nuts.
Actually holding 1 pair in your hand already gives you about 34% chance that you still have 1 pair as best hand on the river and about 40% that you advanced to 2 pair, together making for 74% chance that you can’t get over that 2 pair at the showdown.
Even more, when already holding 2 pair in your hand, your chances of getting over 2 pair is a measly 39%, and yes, that does count the three of a kind.
But wait, what about a flush then?
Well, when calculating odds for flush draws you off course hope you have not 1 but 2 suits to choose from. And remember, never trust a low flush in Omaha, someone else could easily have a higher top card. So there you are, 2 suited aces, ready to see your suits fall.
In reality by the river only about 14% of your winning hands will be flushes, when holding only 1 suited combination in your hand, the outcome is even more devastating: 7% of your hands will make it to a flush.
Just to complete the story: with 3 of the same suit in your hand, you’ll get there about 5% of the time and when your entire hand is suited less than 4% of your boards will bring you a flush.
Less tactical mumbo-jumbo, more numbers, I know, but I’m sure some people will have something to think about.
If you have no idea what I’m saying here, come see dr. Mad Man, I’ll explain with your chipstack.
The Mad Man
