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Variance & Randomness in Omaha and Holdem
> Badger wrote:
> > However... while Omaha plays slower, there are more pot pieces per
> > round available than on Holdem. In nine hands dealt in Holdem, nine pots
> > are won (meaning a pot is only split about 1 out 100 times). In Omaha, in
> > nine hands there will be about four low portions of pots available (after
> > 100 hands about 140 pot pieces are available -- not counting when pots
> > are quartered). These additional pot pieces reduce variance. Additionally,
> > these extra pot pieces make Omaha much closer to Holdem in terms of
> > pot (pieces) per hour. If a Holdem game has 30 hands an hour, and an
> > Omaha game has 22, about the same amount of pot pieces are being
> > awarded an hour (30).

Iceman wrote...
> What does that matter? The return on the bets you put in is more variable
> in Omaha-8, so the fact that you win 1/2 or 1/4 of a pot more often is
> outweighed by the fact that more money goes in while hands are less
> defined, and that made hands at any point in the hand are more vulnerable.

I think this is wrong for a bunch of reasons...

HiLo split has more opportunities to save one's butt than scoop pot games. Iceman says it doesn't matter that a player has more ways to win in any individual hand. Of course it does. If three people are in a pot in Holdem, almost always one wins and two lose. If three are in in Omaha, often two win and one loses. Sometimes all three get a piece of the pot. There are more winners each hand! The game is less volatile, less variance, almost by definition.

> The return on the bets you put in is more variable in Omaha-8,

This is a a non-statement of your contention to prove your contention, or it's just flat out wrong by definition. Omaha bets return money more often than Holdem bets. Period. Again, that's just the nature of HiLo split.

> so the fact that you win 1/2 or 1/4 of a pot more often is outweighed by the
> fact that more money goes in while hands are less defined, and that made
> hands at any point in the hand are more vulnerable

Hands are always more defined in Omaha. More cards, more definition. Weak "made" hands are more vulnerable but so what? It's irrelevant to variance.

> Starting hands retain their values more in holdem, and flopped hands hold up
> better, that's why the variance is lower. And you don't get raising wars on
> the flop and turn in situations when many hands each have a small equity
> like in Omaha.

These concepts have almost nothing to do with variance. What difference does it make if a starting hand "retains" it's value? Whether flopped hands hold up better doesn't matter a microbe in terms of variance!

> If you're a good player, in a loose game you play mostly low draws.

Not the point. In a loose game you play scoop hands. Suckers play for half the pot.

> There is very little to proper pre- and on-the-flop play in Omaha, especially
> in loose games.

If you are a novice Omaha player, read this line, and know it is about the worst possible philosophy about Omaha. Omaha is 75% about starting hands. That's part of preflop play. Secondly, most of the rest of Omaha is about pot manipulation. In a loose game, with most everybody playing a random hand, the way to win is to get as many bets in before the flop as possible. Same goes for on the flop when it is mathematically favorable to you. Loose game Omaha is mostly math. Good starting values, then maximizing advantages (and minimizing disadvantageous flops).

> All you need to know is to draw only to a lock, and to not make obvious
> errors with quartered lows or the one-way nuts.

Minor concepts, especially quartered pots. In a loose game you should hardly ever even think about being quartered. It's almost never costly (in limit). Again, this is just evidence of the low variance of Omaha.

Badger wrote..
> > A decent but not spectacular hand like AK42 offsuit has more than double
> > the showdown value of a random hand. This is an extremely important
> > concept that so many players misunderstand. Just because when most
> > any two Omaha8 hands are *played head-up* there isn't a huge difference
> > between them does not mean there isn't an enormous variation in value
> > when played multiway! Understanding this one thing will go a long way to
> > make a player a winner at Omaha.

Iceman wrote...
> Hands like A23x, AA2x, A24x or A2KK are extremely rare. Most of the hands
> you play are of the A2xy and A3xy families, and those do not have
> exceptional value preflop. Neither do most high hands when many players
> are in, and by raising them you would make them more vulnerable post-flop.

We dealt with your non-appreciation of powerful high hands previously, but what about the above. So good hands are rare. That's just another reason variance is lower in Omaha!

Badger wrote...
> > The beauty of Omaha is that there are more hands, like the AK42, that are
> > more than double the expectation of a random hand, than in Holdem,
> > where even a hand like KQs isn't as strong against a full field as AK42 is.

Iceman wrote...
> The problem with your showdown simulations is that people won't keep
> calling with a lot of the trash hands that miss the flop. Also, they don't
> account for how much a hand wins when it wins and loses when it loses.

First, in the real world, people do call with shit all the time in Omaha. Second, because people fold doesn't effect the *minimum* of how often a hand will win! It'll just win more. Let them fold, our winning percentage goes up and our variance goes down even further!

Badger wrote...
> > It's (partly) exactly because good hands in Omaha are *not close at all*
> > to the value of random hands that Omaha is lower variance. A few
> > simulations can easily show this.

Iceman wrote...
> Simulations are worthless. Lets see the results of actual professionals.

Simulations are not worthless. They have limited value. How much is open for discussion. Feel free to ask professionals. You will find how rare your opinion is.

Iceman wrote...
> when compared to holdem, you have a game where (1) there is more
> multiway action on post-flop, and raising and reraising are more frequent on
> later streets,

Huh? I assume in a discussion like this that we are talking about parallel games -- a loose Omaha vs. a loose Holdem, or a tight Omaha vs. a tight Holdem. Obviously a super-loose Omaha has more variance than a super-tight Holdem, and vice versa.

> (2) flopped hands are less likely to hold up,

Again, utterly irrelevant to variance. What matters is the probability of winning on the flop, not who is at the moment in the lead. Even thinking in terms of "flopped hands" is an incorrect concept in Omaha. The idea, usually, is about having a hand on the river, and the probability of making that hand. Whether you flop a made hand or a draw or a backdoor draw is irrelevant, what matters is your prospects, your probabilities, of having the winning hand on the river.

> (3) the turn card and river card do more to change outcomes,

Again, not a variance issue. It's all a matter of how likely a hand is to win. So it loses sometimes. Big deal. In Omaha it is common to get situations where you are an 80% or better favorite against a full field of opponents. Sometimes you'll lose, but you just have to make this very low variance play hand after hand and you'll turn a huge profit.

> and (4) hands are more equal in value and less defined preflop.

The key error. There are only 4 Holdem hands with really well above average winning percentage value preflop in a loose game. Being real generous you can include a couple more hands. That's it. And only AA is hugely ahead of the field. On the other hand, Omaha has a very large group of hands that have winning rate percentage of double random hands. Except for the best four, Holdem hands are far more close to each other in value multiway than Omaha hands! If you don't know and appreciate this basic concept, you are going to be in trouble in Omaha.

> On an individual bet, you are less sure of the outcome of the hand at that point.

I can't figure out what you mean by this because the one thing that should be clear about Omaha is the mathematically likely outcome is far more known in Omaha than Holdem. A player with 20, or 12, or 4, outs has *that* many outs.

> That's what I'm saying. As compared to holdem, it's true preflop, it's true on
> the flop, and it's true on the turn.

You seem to think because the identity of the highest value hand (that is, the hand that will win the pot) changes more easily in Omaha that this somehow relates to making the game higher variance. That's just missing the point. If you have a hand that will win 80% of the time on the turn, and the river card kills it, so what? If you commonly play that 80% situation, you will have an awfully low variance! Omaha provides these opportunities time and again (with 90% opportunities regularly available).

To use the most obvious example, if you have top set *and* the nut flush draw, you don't care which way you win (assuming no low is possible either way)! The changeability of your winner is irrelevant. What matters is what game you can get the best of it better!

> [Hands aren't defined as much in Omaha] on the flop since even the flopped
> nuts is usually a very vulnerable hand. There can be few safe cards in the
> deck for the current best hand, and the status of low is uncertain.

Again you focus on the trivial. What matters is the expectation and probabilities.

> KKQQ or A234 preflop are not well defined at all. In holdem and more so
> in stud, your starting hand bears much closer relation to your finishing hand.

KKQQ and A234 not well defined "at all"? Strange way to define "define"!

> The difference is that you're putting a lot of money in on hands that might
> not be good - that's where variance comes from. In holdem, the variance is
> lower since made hands hold up better.

Okay readers, here it is again. Iceman simply focuses on a minor issue at the expense of the key to winning Omaha. "Hold up better" should not be your focus at all. It's neither the way to play the game or think about the game. Making the winner, having the best hand on the river, those count, not who is in the lead! There is no "leader money" in poker! In Omaha, you should play hands before the flop, on the flop, and on the turn that have a high probability to be the winner on the river.

Ideally, it should always be your hand that has this highest probability. That's impossible, but that's the direction you should aim for, and this is extremely easy to do in loose game Omaha, which leads to small variance relative to the bets in play and profit potential.

Who flops the leading hand doesn't count for squat. The "best" hand is the one with the highest winning potential (including the understanding that some hands will win more bets than others).

> In a game where hands hold up better, there will tend to be less variance.

Again. Not at all true or sensible to think in these terms. There is less variance when it is easier to know the exact math of a pot situation. That's what you get in Omaha. Clear math. If you got clear math, and you only play when the math is in your favor, you have less variance. "Holds up better" isn't involved.

> In games where it's close to a crapshoot from the flop on, there will tend to
> be higher variance. What don't you understand here?

You are saying Omaha is "close to a crapshoot" after the flop? That's nuts. The math is there. The math is (usually) very apparent and easy to do. There is no crapshoot. If you have x% chance of making a hand on the turn, you better be getting x% pot odds. You're just conceptually not playing the right game.

> Omaha is 95% hand selection. A robot could play well after the flop.

You say this and then say there is high variance! How can you possibly reconcile these statements?

Of course it's just wrong too. There is plenty of pot manipulation to do after the flop, especially when it comes to winning 3/4s of some pots.

Badger wrote...
> > That's part of preflop play. Secondly, most of the rest of Omaha is about
> > pot manipulation. In a loose game, with most people playing a random
> > hand, the way to win is to get as many bets in before the flop as possible.

Iceman wrote...
> In many cases, this isn't true. The reason is pot manipulation. It also isn't
> true in loose holdem games for the same reason.

Again, you gotta learn some math on this. Getting garbage hands with a low winning expectation to pay before the flop when they are enormous dogs is a big part of winning Omaha. If one of your opponents has 9992 and is willing to put three bets in before the flop, this is good. Perhaps you are trying to apply Morton's Theorem here, but it just doesn't work that way in Omaha. Schooling benefits the favorites, not the dogs.

> Variance is lower in holdem or stud, precisely because hands differ
> more in value.

Just saying it don't make it so. You think KQ in Holdem is relatively more valuable versus a field than AK35 is in Omaha? Since you don't accept simulations, you just are gonna have to play the necessary number of hands to figure this out for yourself.

> You can play a hand strongly with much more confidence in the outcome in those
> games, while in Omaha the outcome is less certain, which makes for a higher variance.

Just bizarre. Omaha is a game of information. Holdem is a game of uncertainty. That's how they were *designed*. Loose game Omaha is generally about ending up with the nuts. Loose game Holdem is far more shadowy and difficult.

> The expectation is certainly higher in loose Omaha-8 games than in holdem
> or stud. If the variance was also lower, the bad players would quickly go
> broke and lose interest.

Iceman. Hello. This is reality. This is what does happen.

> That's why Stud8 games don't tend to last - the expectation against bad
> players is high, while the variance is low. Fish lose at a slower rate in
> holdem or stud. The high variance in Omaha8 keeps the bad players in action.

Boy... bad players have a short-run shot in Holdem. They are just flat out dead in Omaha (just like Stud8). The low variance allows mediocre players to survive in Omaha. Horrible players, ones who don't care about the math of their hands, go broke fast. This is why Omaha remains an unpopular game, especially if there are several good players around.
---

Iceman wrote...
> That you should play in terms of probability of winning on the river is true.
> But the fact that the current leader is more vulnerable will increase variance.

So you say this. Why? How do you come to this? One thing doesn't logically lead to another, and they are otherwise unrelated things. Why do you assert this? As I tried to show, and you seemed even to agree, who the leader is is irrelevant. What matters is the probability. But you still link the "flopped nuts" with variance. Why? Why are you even thinking in terms of the "current leader"?

> It has nothing to do with correct strategy, it's just an aspect of the game,
> and it means that the outcome of a specific hand is usually less
> certain at any given point in that hand.

Well, your focus on the "current leader" just leads you astray from focusing on the real point, but at least you mentioned here about the outcome. I think you just don't appreciate the nature of Omaha. The outcome of a seven way Omaha hand is virtually always more knowable to a thoughtful player than a seven way Holdem pot. A good player will know exactly how many outs they have, or how many outs the field has against them. You very seldom have this knowledge in Holdem.

Good players make money in Omaha because the outcome is more certain. That's a primary reason good players take up the game. It sure not because of it's speed! You have a uniquely opposite view of the game. I don't know how you can come to that after playing the game, but I guess you do. At least though I think this area should be your focus, and not the pure distraction of a wholly irrelevant concept like "current leader".

> It could be that the fact that Omaha-8 is a split pot game outweighs the
> other factors that I mention, and that Omaha-8 is indeed lower variance.
> It's generally considered that Omaha-8 hands run closer in value than
> holdem hands, but this may not be true in the loosest games.

No, that isn't generally held! Only head up is this true. It's generally held, by good players anyway, that some Omaha hands are much stronger than the large mass of hands.

> My own results show higher variance in Omaha-8, and my own
> suspicions confirm this, but I'd like to hear other players' figures
> for which game is higher variance.

I don't want to personalize this, but I suggest you examine your game. You dramatically undervalue high hands. You don't focus on scooping pots. It's not my business, but I think your variance is higher because your game has serious flaws.

> It could also be that loose Omaha-8 games are low variance for a tight
> expert, while being high variance for the many fish (who are constantly in
> hands against each other with equally crappy hands).

An entirely different issue. Omaha is high variance for a bad player. It's low variance for a winning player, and just lower than other games for a breakeven player. Variance goes up in Omaha the poorer you play.
###

Luck in Holdem and Omaha
Krmin wrote...
> Obviously my Stud and Omaha talents are not carrying over to Holdem, but I
> can't figure out why. Does anyone have any advice as to what I should be
> looking at?

This is interesting, partly because IMO the worst Omaha players come from Stud backgrounds (and just don't get the problem of the commonality of the cards). But you do well in Stud and Omaha, and now are having trouble in Holdem.

Ashley makes a good point about the difference in information available, in Omaha and in Stud up till 7th street, you can always know the nut hand your opponent has, and have a strategy around that. In Holdem, you can also know the nuts, but usually at bigger limits people have far less than the nuts, and aren't even drawing for much when they draw. It's a very different kettle of fish. You have to learn to read your opponents not based on the cards showing, but on their betting action, established playing reputation, tells, etc... Very different skills.

Also, Holdem has far far far far more short-term luck than Omaha or Stud. That's why it's the most popular game most places. The poor players can do better, longer. Holdem, somewhat bizarrely, also has the most *longterm* skill. You may just need to learn to accept the luck in Holdem, while you work on those skills that don't come into play in Omaha and stud nearly as much.
---

Lee Munzer wrote...
> Badger wrote...
> > should be easier to "know" how many outs your opponent has, or conversely
> > how many outs you have. It is *very* common for one player to have two or
> > three other players literally drawing for literally one or two or three
> > cards in the deck. This is much more easily "knowable" than in Holdem.
> > Omaha is a game of complete hands (flushes, straights, full houses).
> > Holdem is much more of a game of pairs.

> While I agree with both concepts, I read into Jim's question (and, if wrong,
> I'll make it my position) that I can eliminate possible holdings for
> opponents in HE and by the turn or river have a pretty good idea of what I'm
> up against. In Omaha that "oh, by the way, I'm your fourth card" is
> basically unreadable. For example, a middle position, aggressive player calls
> my A3QT big blind lead bets with a board of QQ4J then raises when a 6 hits on
> the river (no flush possible). He shows Q6 along with his reason for playing (AA).

Lousy bet. But where is the "luck" in this? The player played a logical hand, and had the winner (though a tie) all the way through. The player calls your bet on the turn, you should figure he has a queen, meaning, even if he doesn't have an ace to tie you, he has plenty of kickers to hit. In this case he had four outs to your ten. Sure he got "lucky" to hit his kicker as opposed to you hitting yours, but his hand is straightforward.

> The next hand his A229 knocks off a solid player when 99 hits on
> the turn and river.

Again, this shouldn't be thought of as "luck". People get four cards. If your four cards don't "gin" the flop, somebody else's likely will. This is not the question I was talking about -- if only because Jim was talking about when he was in the lead. If you have the nuts on the turn in Omaha, you can usually know every single "bad" card in the deck. In Holdem, if your holding is one pair, as it usually will be, every card can hurt you.

> In HE the possibilities seem much more limited. I suppose you could argue the
> more variables, the more skill required thus, I'm making your point.

Whoa! I didn't say there was more skill in Omaha! Jesus, no. I said there was more random luck in Holdem, by far. There also happens to be more skill. The two are not mutually exclusive. Omaha is a simpler game. Holdem has more moving parts than Omaha.

> Players seem to agree (do you) that Omaha is more a river game
> -- if so, more luck, right?

Omaha is more than anything else a pre-flop game. Then there is a huge amount of defining on the flop, so flop play is the second most important thing. The turn is comparatively unimportant. The river ends the hand, and because Omaha as so many variables, this additional card can change everything. However, there is usually only a tiny percentage of money action on the river in Omaha. Poker is about money. Omaha is not about the river. That's naive. Omaha is about getting money in the pot in a mathematically advantageous way before the river. And obviously luck has little to do with that.

> I don't classify redraw made hands and use of pot odds as bad beats,
> but it seems when I have the lead in Holdem I can play defense better.

Maybe you can, but I would think you should be able to play defense better in any split pot game. More options, more fallback positions.