Monday, August 06, 2007

PLO Strategy vs NL Holdem Strategy - Guest Article!

Very happy to announce a guest article today. This is written by a gentleman by the name of David Kent who got in touch after reading my eBook (yep, still available 7 months on... somewhere in the right hand column!). This excellent piece covers some of the differences between Pot Limit Omaha Strategy and No Limit Holdem Strategy.

Promise to consolidate my Omaha Strategy posts into a single 'jump off page' some time this week... in the meantime enjoy!


I have a confession to make. I sometimes get bored with No limit Hold’em. Yes, dear reader (if there is one out there), it’s the ultimate blasphemy. The so-called ‘Cadillac of poker’ occasionally just doesn’t appeal to me. Yes. I know that it’s a game of great subtlety and that situations which look the same are often completely different. It’s just that you can see so many damn hands on this here interweb thingy that, after a while, they all start to look the same. After all, there are only 169 variations on the starting hands

The serious point is that when No Limit poker Hold’em becomes formulaic and when the player becomes blasé about seeing 10 8o or even K Ko for the umpteenth time in the last few days / hours / minutes (delete as appropriate) it’s time for a change. If you don’t make a change, or take a rest, (and, after all a change is as good as…), then your own play is going to start impacting your short term results just as much as our old pal, variance. Bad habits are hard to break, however, and if they are developed through simply seeing too many cards in the same game they may have a much longer term effect than the fact that A Ao is going to lose about 20% of the time. In a team sport which I used to play to a reasonable standard, we used to have a saying: ‘Form is temporary. Class is permanent’. The saying in poker might be: ‘Variance is temporary. Incompetence caused by boredom can be pretty darn close to permanent.’

So what do I do when this type of ennui starts to pervade? Well, I usually turn first to PLO. Now, let me preface this by saying that I’m by no means an expert PLO player (Insert boast – even though my biggest ever poker pot was won in a three handed PLO game and to which pot a very young Andy Black made a substantial contribution. It’s hard, however, not to win with the mortal nut flush against the second nut flush and a top set which fails to fill up. It’s still, probably however, one of my most abiding poker memories because I really did know, even at that time over twenty years ago, that Andy would end up as a big name player. - End of boast). The good news is that, at least at the low limits which I frequent, you don’t have to be particularly skilled in order to keep your head above water. Basically, you just have to know that it isn’t four-card Hold’em and that it is a game of the nuts. To trot out another of the clichés, Hold’em is largely a game of some sort of made, usually less than nut, hand against either another made hand or a drawing hand. Omaha, on the other hand, is a game of drawing hands. Even if you hold the current nuts post flop, it’s almost the norm that you’ll need to improve again to win the pot at showdown. It’s also a fact that a very high proportion of Omaha pots go to showdown.

It’s for these reasons (and others) that it’s not always a good idea to play high pairs which are unsupported by other options. QQ72 unsuited for instance, is, I would consider, a pretty horrible PLO hand. As Plan3t Gong has pointed out before, each opponent in PLO potentially has six Hold’em hands working for them. Because of the fact that there really isn’t that much between lots of the hands in Omaha, you’ll find a much higher number of players seeing each flop. Even pre – flop raises tend not to thin the field too much because, after the raise is called once, the other players tend to be ‘priced in’ to the call.

If you find yourself accompanied to the flop by four others (which is not at all out of the ordinary), you could be competing against twenty four other Hold’em hands. As my rule of thumb, I’m looking to have at least three and preferably four different hands working for me in order to limp, raise or call a raise pre - flop. On the assumption that you’re playing against four ‘me’s’, you’re probably up against about fourteen decent Hold’em hands. You, however, have just one. We all know that high pairs in Hold’em play well against one opponent, preferably in a raised pot where the opportunity is likely to exist in many cases to make that opponent fold post flop. I’m not sure that anyone has ever run the numbers to show how QQ fares against fourteen opponents! Nonetheless, I suspect that the answer may be along the lines of (euphemistically): ‘Not too well, really’.

Even when you do hit your 7.5 to one shot at top set on an unpaired flop, there is a high probability of the existence of straight and flush draws. In all likelihood, some of your opponents are going to have at least one, if not more, of these. Excluding the extremely rare Q + pair and ‘miracle’ 7 7 2 and 2 2 7 types of flop, 88 times out of a hundred you’ll miss completely and have to fold. Of the other twelve times, you’ll still have work to do post flop in a significant number of them. That’s not to say that you should never play these types of hands – they’re fine for a bit of variation provided you can see a cheap flop, preferably with position. Profitable, you ask me, though to play them hard every time? I have my doubts (actually, I don’t).

Government Health Warning: - Sweeping generalisation follows – do not take as being 100% true without any exceptions whatsoever. All decisions in poker are ‘situation dependent’ and there will always be exceptions to the next statement which in my opinion, however, remains true in general terms.

What you may take from the analysis above is that No Limit Hold’em is essentially a pre-flop game with post – flop elements while PLO is essentially a post – flop game with limited pre –flop elements. That’s why it works for me as a change of pace. The texture and ‘feel’ of the game is different and, probably more importantly for those who are looking to eke out a few shekels from the game, the decisions are different.

To expand a little on the ‘texture and feel’ theme, it’s normally correct for every street in Omaha to be bet by someone. In practice, virtually every street in low limit games is actually bet by someone, sometimes, however, by the person who ‘should’ be betting and sometimes by someone else. Conversely, however, it’s often incorrect, usually on the basis of odds, to call bets. Situations are therefore often presented in PLO where it can be extremely profitable to be a ‘calling station’ (or at least extremely passive) because the person (incorrectly or over aggressively) making the bets wouldn’t actually call a bet if you (correctly) made it. Let this person do the betting for you! This type of situation rarely if ever arises in Hold’em, where a ‘calling station’ is probably the worst thing you can be. Generally, you’re putting money in on someone else’s terms instead of on your own, not getting enough money into pots where you have the advantage and putting far too much money into pots where the situation for you is marginal at best.

I inferred earlier that many people who are new to the game think of it as four card Hold’em and that it’s a huge mistake to have that mindset. It happens because all of the publicity and much of the writing about poker is about Hold’em and virtually everybody who plays the game plays Hold’em, often exclusively. It’s rare, however, for a player to think of Hold’em as two card Omaha. I did; however, come across a recent piece on a very well known blog written by an obviously extremely skilled poker player who used this thinking to arrive at what I think was a dreadful decision in a 6 max NL Hold’em game. Fortunately for him, he got away with it in this particular instance because someone else did his betting for him and because he won the hand. Unfortunately for him perhaps, I have the feeling that he still thinks that he played the hand correctly. Before I sign off here, I’m going to do a little analysis of this particular situation because to me it sums up perfectly the general difference .between the thinking in the two games. In the hand, our hero flops top set in a raised against three opponents on an all small spade flop. Because of his Omaha experience, he feels that he can’t drive out the draws and he may already be up against a ‘made’ flush. Not betting will allow him to get away from the hand cheaply if a fourth spade flops. He therefore checks, not to check / raise or as a slowplay, but in order to avoid putting money in the pot and to allow himself to check / fold on the turn or river if a fourth spade falls. Because there was betting not initiated by hero, the pot was heads up on the turn.

Firstly, let’s take the intuitive thinking. In Hold’em, most players would be asking themselves if they should fold. I believe that most would think that they are ahead the vast majority of the time and that, even if they aren’t, they have the redraws to the boat or quads. (In fact, they are mathematically correct but let’s leave that aside just for one moment). Folding is not an option in virtually all foreseeable situations. If you’re not folding (because you believe you’re ahead most of the time) you must bet so that the money goes in while you have the best of it and also to ensure that you give your opponents the wrong odds to draw. You’re not far enough ahead (again intuitively) to allow your opponent an opportunity to catch up and therefore a slowplay is not justifiable. If I were playing the hand and if it were possible, I’d like all of the money in now.

In Omaha, the intuition for me would be that I’m behind most of the time to a made flush (again mathematically correct) and my only decision is whether I feel like gambling on my redraw. The problem with redraws in Omaha is that they generally don’t attract any implied odds. If the board pairs, my opponent is quite likely to shut down completely and may well fold to any decent sized bet. In this case, I’d like a free turn card, if possible, and I will seriously consider folding to a pot sized bet.

Now let’s turn to the maths (that’s the English for math, for the benefit of my American friends). In 6 max Hold’em, only 20% of the cards which aren’t in your hand are in play pre – flop (10/50), as compared to 75% in a full ring PLO game (36/48). Each opponent has only 2 cards in Hold’em, against 4 cards in Omaha. These two factors result in a massive difference. Given the 3 known spades on the flop and the two known non – spades in your hand, the odds of any opponent holding two spades in the six max scenario are about 23 or 24 / 1 against (10/47 times 9/46). Given that there are three opponents, the combined odds are about 8 / 1 against you being up against a made flush. Eight times, you’re in front and once you’re behind. In the case where you’re behind, you have about a 30% chance of winning with a boat or quads (7 outs on the turn and 10 on the river if you don’t hit on the turn). 0.7 times, the opponent wins and 0.3 times you win.

Even if it is assumed (and this is an extremely conservative assumption) that every time you’re in front, the opponent has a spade, he’s still 2 / 1 against hitting the flush by the river. If we ignore runner runner something for any player (including you), opponent hits the flush 2.7 times but doesn’t hit (and you win) 5.3 times. Of the 2.7 times villain does hit, you still have the 30% redraw. Villain wins 1.9 and you win 0.8. Overall, therefore, you win 6.4 (0.3 + 5.3 + 0.8) or 71% and you lose 2.6 (0.7 + 1.9) or 29%. Check with the intention of check / folding if a scare card comes on the turn or river? I don’t think so. I’d be giving away an absolute ton of positive EV.

The calculations are much more complex in Omaha but I hope that the approximations will give you some idea. The odds of any opponent having at least two spades in his / her hand are less than 3 / 1 against (long calculation involving 6 combinations of 2 spades, four combinations of 3 spades and one combination of four spades). The fact that there are three known spades on the flop increases the odds at that point to closer to 4 / 1. If we assume that 60% of the opponents play to the flop (in order to be consistent with the 3 of 5 playing in the Hold’em hand), we have about 5 opponents. I’m afraid that my brain is a little atrophied and I can’t do the exact calculation but I believe that it’s close to 80% that one of the opponents has at least two spades. Given the normal Omaha game texture, it follows that it is highly unlikely that anyone (except perhaps the button after an ‘all check’ in front) would bet without it. Let’s, however take 80%, just to be conservative. This time, 4 times you’re behind on the flop and once you’re ahead. You lose 2.8 times of the four and win 1.2. Because we’re not allowing runner runners (which are actually much more common in Omaha), you win the other one. At best, therefore, we lose 2.8 (56%) and win 2.2 (44%). This, therefore, is a marginal call at best unless there are other callers. In reality it’s probably –EV as compared to the hugely +EV situation in NL Hold’em. Check with the intention of check / folding? Quite possibly.

Now for the real confession. I’ve never written a poker piece of any sort in my life before. Kudos, therefore, to Mark for risking his readership by letting me loose on his unsuspecting audience. He has achieved his stated mission for this blog, however, because writing this has made me think. I hope it’s given you, the reader, at least a little food for thought. Outside of playing the game, thinking about it may be the best way of improving, perhaps better even than reading the theory books. This particular piece started as something else entirely but I’m glad I did what it turned out to be. Thanks again to Mark and, for the rest of you out there, keep reading this fine blog!

Good luck at the tables.

1 comment:

Andrew said...

I thought it was pretty well written. Thanks.