Heads Up limit vs Ten Handed

Heads-up limit hold'em is available at most of the online cardrooms, and I

was wondering how it compared with ten-handed limit hold'em, particularly

against that played in a bricks-and-mortar cardroom.


1) Firstly, how many times 'bigger' is an online heads-up game than the

same limit ten-handed? In terms of money staked, how much more (per hand)

would one expect a typical player to put in heads-up than ten-handed?


2) What is the variance comparison, in absolute terms, between heads-up and

ten-handed? Over x hands, which game would one expect to yield larger

swings?


3) What is the profitability comparison? Is it best to be a good player up

against nine average players ten-handed; or to be a good player against one

average player heads-up?

Good questions! I hope you get answers for 1) and 2). Regarding 3), it should be clear that it's much more profitable to be up against only one player. However, the variance will be much higher. Also note that heads-up is a very different game than a ring game, so "good player" should mean "good heads-up player" and not "good ring player".

Explaing why heads-up should be more profitable. Against 9 opponents you will be playing far, far fewer hands than against 1 opponent.

My theory is heads up and short-handed games are more profitable than ten-handed full games against the same inferior players. In a full ring game, you hold a 1-plus -in-10 advantage and in a heads up game you hold a 1-plus -in-2 edge. If the game is scalable, that is 5 times in difference. But I don't believe that to be the case from a staking point of view. Poker is a game of mistakes. When an inferior player makes mistakes in a full ring game, the result is not as drastic as making the same mistake in a short-handed game.

This is not wholly true. If you take a ring game with a decent amount of loose players, it is very beatable. However, if those same loose players are in your 5max game they may actually not play any MORE hands than they were in ring, and thus actually be playing better in relation preflop. Also, when they chase in shorthanded their odds are much better, so they are not making much of a mistake if any. On the contrary, if they constantly chase hands in ring games they will lose all of their money.

Two thing stick out like sore thumbs that have either gotten burnt or hammered on or both.


First, your reference to the number of hands played is not necessarily correct. You are trying to infer that they are playing better if they continue to play the same hands as they would in a full game. That is like flipping a coin. On one hand, you may be correct but on the other you may be way off. To play well short-handed, you need to play more hands because the distribution of hands is the same in either game. Playing 10% of the hands dealt instead of 20% or more is setting up for less than optimal results.


Second, please explain how the chasing improves the odds in a short-game. It seems to me if I play a small pair, the odds of making a set by the river are still the same in either game. However, my small pair may be a hand and not a draw in short-handed game. The odds are going to be the same for any draw regardless of the number of players in the game. Actually, in a short-handed game, drawing to a straight is a more severe mistake than in a full game because the odds are hardly ever consistent with the draw after the flop. So, please explain how their odds improve with chasing given they have the same probability of making their hand.

Regarding the first point, most poor players play too many hands in a ring game, so they are likely to be playing more nearly correctly in a short-handed game. That is, in the 10%-20% scenario you pictured, they are much more likely to be in the 20% part than the 10%.


Regarding the second point, those "chasing" are more likely to be ahead in a short-handed game, so are more correct to stay in and "chase" than in a full-ring game because, in addition to the chance of catching (which is the same as in a ring game), their chance of winning without improving is greater.


The original poster asked about heads-up vs. ten-handed. I think there can be no doubt a good player would do better heads-up just due to the fact that he would be in many, many more contests with the inferior player. A 5-handed would be seem better than a ten-handed game for the same reason, because, even though weak opponents are more likely to be playing in some sense more correctly (such as playing a more correct % of hands), they are still going to be making mistakes (playing poorly after the flop, not adjusting to position, not noting how their opponents play, etc.) In a 5-handed game the good player will be involved in many more contests than in a 10-handed game, so should show more of a profit.

I agree with your point that poor players tend to play more hands. But I think you got the gist of my post in that there are more mistakes than just playing too many hands.


Let me clarify what you meant regards to "chasing". You inferred that a "chasing" player is ahead during a particular hand. You were not inferring that the same player was ahead in chips.


You mentioned not adjusting to position. I hold that position is much less important in a short-handed game than in a full game. But let me clarify that as well. Position with regards to starting hands is less important. Position with regards to starting hands in a short-handed hold'em game is as relevant to position in Omaha hi-lo. On the other hand, position with regards to betting may actually be more important. For instance, you are playing heads up and flop a straight draw with one overcard. The flop is a rainbow with no pairs. I cannot count the times that I have bet this hand from the big blind when I should have checked. Remember, the big blind is the first to act ATF in a heads up game. However, it is an excellent bet from the small blind (the button) in the same game.


And, yes, you do play more hands heads up. In fact, from the small blind you can play anything and everything if you know your opponent will not punish you for limping with hands as even as bad as 72 offsuit. You have to adjust your starting hands based on the raise potential from the big blind in a heads up game.

Let me clarify what you meant regards to "chasing". You inferred that a "chasing" player is ahead during a particular hand. You were not inferring that the same player was ahead in chips.


Yes, that's what I meant.


I hold that position is much less important in a short-handed game than in a full game. But let me clarify that as well. Position with regards to starting hands is less important.


I understand your clarification about betting be more important, but didn't understand this part. Why do you say "position with regards to starting hands is less important"?

You are playing more hands. Their relative strength increases in a short-handed game. Hands like AJos or KJos are stronger than in a full game and can be played from any position. One flush draw is as good as another flush draw. It is the flop, and sometimes the turn, that determine whether to play or muck. And in that sense, the game is more like Omaha Hi-Lo. To me, that game is not nearly as dependent upon position as is hold'em and it usually requires taking the flop.


In heads up, your starting hands are determined more so by the skill of your opponent. Against some opponents, any and all hands are playable. With others, one has to selective.

This is an interesting theory. If I understand you correctly, you're saying that position, at least as it relates to starting hands, decreases in importance as the number of players goes down.


I'm not sure that's true. I'll have to think about it. It's certainly an interesting thought.


You wrote, "In heads up, your starting hands are determined more so by the skill of your opponent. Against some opponents, any and all hands are playable. With others, one has to selective."


On the button, any hand should be playable, regardless of the skill of the opposition (unless the opposition is better than you are, in which case you might play fewer hands just to cut down your losses). I'm not sure that's true off the button. Any hand has enough pot equity theoretically to play based how often they will win no-fold'em show downs, but I'm not sure how playing out of position affects this. In HEFAP21, they recommend playing 40% of hands out of position, but make no recommendation on the button. If one can play 100% of hands in position but only 40% out of position, that is certainly a huge difference and it would be hard to imagine a bigger difference than that, in which case position would be more important heads-up than in other games. In this case position would be relatively more important as the number of players goes down, the exact opposite of what you're proposing.


I'm not saying this is the case, as I really don't know. I think it's an interesting question and worth thinking about.

Let's take the easy example in heads up. You are dealt 72os in the small blind on the button. In the first case, the opponent is a true calling station, a passive player who rarely raises. The course of action is to see the flop. In the second, case, the opponent is an aggressive player who is strong at heads up and who uses game theory to bluff-raise. Do you commit a half-bet in spite of the threat of having to call or fold to a raise or do you cut your losses and muck?


Against an aggressive player, I prefer to limit my engagements and avoid any raising contests unless I have the best of it. Against a passive player, a check will usually hold up and I can take the worst of it because of the number of free cards coming my way.


I agree with poster above "How good is this advice?". Heads up is about controlling the betting. Against a die-hard maniac who is not a strong heads up player, it is still better to let him go. He only thinks he is in control with his aggression. I have had more than one player mock at my fold, fold, fold, wham! style of play and then wonder where their chips went.


The question I ask myself in a heads up contest is "How much am I giving up?" if I fold the small blind. I base the answer on the play of my opponent. With the 72, 83, 94, and others, I am giving up too much against a passive opponent if I fold the small blind. With the same hands, I am not giving up very much if I fold the small blind against a strong heads up, aggressive player. The style of play of my opponents also dictates the amount game theory I use to attempt a steal.


Anyway, those are my thoughts on position wrt starting hands. I am relatively new to heads up but I know too well what happens to solid, tight-aggressive players in heads up competition. I used to be one.

There's two issues being discussed here. One is strategy (controling the betting), and the other is the effect of position regarding starting hands.


You'll recall, the original post suggests playing every hand heads-up. If you have 72 on the button, you are getting 3-1 odds on your bet, and your hand has odds to play. (play, not necessarily raise -- that would depend on the opponent). Against certain player-types, I agree that it would be better to fold, although not necessarily for the same reason you're suggesting. The reason is that by folding you may give the impression that you are playing "tight", and take advantage of that to manipulate your opponent. 72 is a good enough hand to play on the button. How well your opponent plays has no bearing on that. But if he plays poorly, you may be able to make more of a profit by not playing it than playing it.


Your point about starting hands being heavily dependent on your opponents, and more so as the number of opponents goes down, is clearly true. However, that doesn't necessarily mean that position becomes less important. That is, the two concepts are not necessarily related in a way that if one becomes more important the other becomes less so. At least, it's not obvious to me that that is the case. Maybe it is.


One way of thinking of the problem, which seems to support your statement is to consider the difference in how you would play 5-handed vs. a ring game in which the first 5 players fold. In the latter case, you should play somewhat more tightly than in the former because you're likely to be against better hands as opposed to random hands. So you play more hands when there are fewer players.


Another way to approach this question is to extrapolate. For example, in a 20 person game in early position you would have to play extremely tight, more so than in a 10 person game. So I think your contention that position has less bearing on starting hand selection as the number of players goes down may be right.


What puts doubt in my mind is that with fewer players the difference from one position to the other is drastic, whereas the more players there are the less difference it makes to shift one position. I guess the difficulty I'm having is what it means in a mathematical sense to say that starting position is less important as the number of players descreases. If it means that other factors (such as how your opponents play) become more important, that's certainly true. If it means you change your starting hand requirements less as your position changes, I'm not sure that's true.