Unexploitable Heads Up play

[GaF]

I decided to take the plunge and bought a copy of SnG Power Tools - it seems expensive compared to other tools like Poker Tracker, however on twoplustwo seems to get rave reviews, and Harrington supposedly praises it in HOH III - if it's good for Harrington ........ ;) Anyway, first thing that really took my eye was not the program itself, but an article in the help files on "Unexploitable Heads Up play". I don't feel it's right to reproduce the whole article, but will summarise and maybe give one table example of the data - so it may be that only others with the program can answer my query..... I make no secret that I think my HU play is quite weak - so this, a "robotic" way to play HU reasonably well hits the right spots with me. In brief, the argument is that if you follow this mathmatical approach - to either shove or fold every hand, you can play the "Nash Equilibrium" (apparently thats a "game theory" term) and it is impossible for your opponent to have an edge on you. And if he doesn't play the NE, then you will have an edge on him. The hands you shove (or fold) depend not on M or Q, but on R!!! Effectively the same - it is the multiplier of your stack over the Big Blind. However having read it, and tried it (only over 2 games - so no statistical significance at all) I am extremely dubious over the possibility that this has any chance at all of working - specifically at high M (or High R) moments (I haven't formed an opinion yet for low R moments - I haven't lasted long enough to find out). However, the guy who wrote the article is clearly very talented and his mathmatical and studious approach is one that I like and would want to "follow" - maybe I need to do some research on how Howard Lederer plays........ Here is an example of the criteria for when R=25 ...... HU, all-in/fold, Blinds 100/200, Min Stack 5000 (R=25)

	A	K	Q	J	T	9	8	7	6	5	4	3	2
A	AA	AKs	AQs	AJs	ATs	A9s	A8s	A7s	A6s	A5s	A4s	A3s	A2s
K	AKo	KK	KQs	KJs	KTs	K9s	K8s	K7s	K6s	K5s	K4s	K3s	K2s
Q	AQo	KQo	QQ	QJs	QTs	Q9s	Q8s	Q7s	Q6s	Q5s	Q4s	Q3s	Q2s
J	AJo	KJo	QJo	JJ	JTs	J9s	J8s	J7s	J6s	J5s	J4s	J3s	J2s
T	ATo	KTo	QTo	JTo	TT	T9s	T8s	T7s	T6s	T5s	T4s	T3s	T2s
9	A9o	K9o	Q9o	J9o	T9o	99	98s	97s	96s	95s	94s	93s	92s
8	A8o	K8o	Q8o	J8o	T8o	98o	88	87s	86s	85s	84s	83s	82s
7	A7o	K7o	Q7o	J7o	T7o	97o	87o	77	76s	75s	74s	73s	72s
6	A6o	K6o	Q6o	J6o	T6o	96o	86o	76o	66	65s	64s	63s	62s
5	A5o	K5o	Q5o	J5o	T5o	95o	85o	75o	65o	55	54s	53s	52s
4	A4o	K4o	Q4o	J4o	T4o	94o	84o	74o	64o	54o	44	43s	42s
3	A3o	K3o	Q3o	J3o	T3o	93o	83o	73o	63o	53o	43o	33	32s
2	A2o	K2o	Q2o	J2o	T2o	92o	82o	72o	62o	52o	42o	32o	22

Basically Red is fold, green is all in and yellow is all in for SB but fold for BB. First thing is - if you are all in, what difference does the SB/BB make? ESPECIALLY at high R? The odds will be virtually identical. Secondly - there seems little distinction between going all in and calling all in - which must be utter crap mustn't it? (ok confession time - I've skim read it 3 or 4 times - but not read it properly yet - so I MAY have missed a point somewhere......) So you have a relatively huge stack and stand to win pretty small blinds - can it really be right to go all in pre flop with the likes of J9o, 96s - sounds like high risk for little reward to me........ I just cannot see it...... So my question - anyone else who has this - have you tried it and does it work for you? Is it my application that is wrong or the system? As I said - I'm talking specifically at high R moments - have formed no opinion yet on the lower R proposals, but can imagine that it may work - at that stage aggression is key ..... and this certainly advocates aggression!!!!! Also worth adding - this "all in" approach doesn't claim to be the best ("Maximal") solution, but it does claim to be a solution in which your oppoenent cannot get an edge on you - i.e. you will win 50% if your opponent plays the same, increasing if your opponent deviates from this..... or am I REALLY missing the point somewhere? :unsure

[slick mick]

Re: Unexploitable Heads Up play Being of a mathematical background (degree in statistics) i've done a little research on game theory and can see you're missing a few points but you're asking so many questions and I've had so many stella's that I'm going to have to reply tomorrow with a fuller explanation. Basically there is a basic theory of heads up and lots of more and more complex theories. I tend to do really well in heads up due to a mixture of maths backgound knowledge and poker instinct but it is such a complex area it's difficult to know where to start.

[Galronix]

Re: Unexploitable Heads Up play Surely it would also depend on how the other person is playing. :unsure Maybe you could print the table out and play a few HU games to see how it goes. :unsure

[GaF]

Re: Unexploitable Heads Up play

and can see you're missing a few points but you're asking so many questions and I've had so many stella's that I'm going to have to reply tomorrow with a fuller explanation.

Brilliant - looking forward to it :ok

Surely it would also depend on how the other person is playing. :unsure

No - the argument is that if you play like this, it is unexploitable by any tactic!!!! But as I said - it sounds too good to be true and pretty unbelievable to be honest. I have tried a couple - was going all in frequently with small blinds ..... my opponents waited me out ..... then called when they were ahead and had the better of it........ I lost both........

[Masterplan]

Re: Unexploitable Heads Up play playing mathematically HU is surely easily exploitable by your opponent, no matter how much R you have

[viggosen]

Re: Unexploitable Heads Up play Well I use a system close to it, when R is 10 or below. Answer to the first question, The difference in what hands you should go all-in with in SB and which you should call a hand with has nothing to do with the different seize of BB versus SB, its because of the GAP concept. If you raise you have to chances of winning A) you have the best hand and your opponent call B) you have the worst hand but you opponent fold. While if you call an all-in you only have 1 chance of winning, you have to have the best hand. Thats why you can go all-in with much weaker hands, than you need to call an all-in. This only apply when R is high, when R is very low the effect of potodds will be more importent. To answer your question of going all-in with J9 , 96s etc in the SB. It works becuse there is only very few hands they are big dogs to, and alot they are marginal to. And the point is your opponent don´t know your are sitting with J9, 96s etc he can figure out from the amount of times you go all-in thet you could have such a hand but you could also have somthing better. And it will only makes sence for him to call your all-in with a hand that can beat the average hand you go all-in with, it doesnt make sence to call with something that can only beats the worst hand he knows you could go all-in with. Imagine you was playing with a robot, and the very first hand in a tournament it goes all-in. You know for a fact that it has been programmed to go all-in with AA and KK only, and you have KK yourself, even though it is as good a hand, than the one the robot could be going all-in with, it would be right to lay KK down, because you either have the same hand or a worse hand, as the robot.

[GaF]

Re: Unexploitable Heads Up play

The difference in what hands you should go all-in with in SB and which you should call a hand with has nothing to do with the different seize of BB versus SB, its because of the GAP concept. If you raise you have to chances of winning A) you have the best hand and your opponent call B) you have the worst hand but you opponent fold.

My assumption is that because R is so large, opponent is unlikely to have gone all in (or anything near it) - but your answer is basically where I'm coming from with the second question......... I can understand aggression (and all in aggression) when R is low. I think that I have a good grasp (and application) of the gap too ....... but where I'm struggling is when R is high!!! There is too much play to keep going all in.......

[slick mick]

Re: Unexploitable Heads Up play As I said above it's a simple system so when R is high a better play is to raise rather than go all in.

[GaF]

Re: Unexploitable Heads Up play

As I said above it's a simple system so when R is high a better play is to raise rather than go all in.

Yep, the article acknowledges that there may be better/more profitable plays ...... BUT it says this strategy cannot be exploited and noone can get an edge on you if you play this way......

[chelskired]

Re: Unexploitable Heads Up play

Surely it would also depend on how the other person is playing. :unsure Maybe you could print the table out and play a few HU games to see how it goes. :unsure

Or just ask Morls :unsure ....................................;) C.R.

[AJ]

Re: Unexploitable Heads Up play with a HU win rate of under 40% I'm willing to give anything a go

[AJ]

Re: Unexploitable Heads Up play trying it now

[AJ]

Re: Unexploitable Heads Up play won

[slapdash]

Re: Unexploitable Heads Up play If this is the same thing I've seen, it doesn't quite claim to be unexploitable. It claims to be unexploitable by any other strategy that only involves shoving and folding (and actually only to be a good approximation to the optimal strategy even in that case). So it will be a good strategy if the stacks are small in comparison to the blinds (and so you probably would either shove or fold anyway), but not so good if you have large stacks. Even among shove/fold strategies, the optimal strategy will almost certainly be a "mixed strategy", which means that you don't always do the same thing in a given situation, but (say) randomly shove 10% of the time and fold 90% of the time. And if you stick to shove/fold strategies, it is a manageable computer calculation to figure out exactly what the optimal such strategy is. But I think it turns out that the deterministic strategy described, which approximates the optimal strategy, is only very slightly inferior. If you look at all possible strategies (not just shove/fold ones), then the calculation of the optimal strategy just gets unmanageably complicated. That's my understanding, anyway.

[GaF]

Re: Unexploitable Heads Up play This claims to be unexploitable by any strategy that your opponent can play - not just shove/fold strategies........

[GaF]

Re: Unexploitable Heads Up play Ooops - this will teach me to post, having only skim read ..... he does go on to say,

Let me emphasize now that these charts are describing the NE all-in strategy, which isn't necessarily the NE strategy given full strategic options. However, my educated guess having done a significant amount of research in this area and related game theory is that the all-in NE strategies are quite close to the fully general NE strategy, especially for R around 12 or lower.

Think I'll give it a bash later, playing "normally" where R > 12, then switch to this for situations where the small stack has a R

[slick mick]

Re: Unexploitable Heads Up play okay point one the Nash Equilibrium is NOT a winning play, it is designed to minimise losses WHEN certain conditions are met. For example in Horse Racing always backing the favourite is a NE, it minimises losses but does not stop them. Here's an interesting quote from Wikipedia; Where the conditions are not met Examples of game theory problems in which these conditions are not met:

1. In “Chicken” or an arms race, a major consideration is the possibility that the opponent is irrational. This criterion may not be met even where the fifth criterion actually is true (so that players wrongly distrusting each other's rationality adopt counter-strategies to expected irrational play on their opponents’ behalf).
2. The prisoner’s dilemma is not a dilemma if either player is happy to be jailed indefinitely.
3. Pong has a NE which can be played perfectly by a computer, but to make human vs. computer games interesting the programmers add small errors in execution.
4. If playing tic-tac-toe with a small child who desperately wants to win (meeting the other criteria) the NE strategy is often not optimal because your young opponent will not themselves adopt an optimal strategy. When playing Chinese chess most people are uncertain of the NE strategy since they haven’t the deductive ability to produce it.^[1]
5. Even if every player believes that all the others are rational one of them may subvert this assumption and opt for an irrational (and possibly self-destructive) strategy. This occasionally happens in top-level >poker, when an expert player surprisingly goes "on tilt".

Discuss? For more on NE try http://en.wikipedia.org/wiki/Nash_equilibrium

[Dave Mardell]

Re: Unexploitable Heads Up play

No - the argument is that if you play like this, it is unexploitable by any tactic!!!! But as I said - it sounds too good to be true and pretty unbelievable to be honest.

OK a lot of this goes way over my head, but i think the "theory" is based around the fact that a GOOD heads up player should beat a BAD heads up player the mjority of the time because of the ability to exploit weakness in the bad player to take them off the best hand.... This theory could never work in heads up cash because your man just has to wait for aces, and I dont think it would work in a heads up STT because there is too much time for your opponent to wait for the good to take you on with. I think the tinking is aimed at the heads up stage of a tournament where the blinds are high. The thinking being that if you attemt to play the guy then baring some fluke hand like a beaten boat you probably have no shot to win, but being that you are now "freerolling" with 2nd place money you can adopt a super aggressive strategy that gives you maybe a 1 in 3, 1 in 4 shot at the top spot. It looks to me that the hands he has you moving in with from the small blind figure to be a better than evens chance again a random holding. Win the large BB or be a favourite...Its also figured to get you called if you have a Top 10 hand because you will be pushing all the time. I think the important thing is not to get "unexploitable" confused with "unbeatable". What hes saying is that by getting your money all in you give a superior player no opportunity to outplay you, and so basically cards talk. In the late stages of a tournament he might not pick up enough cards fast enough to take you on until he is crippled.

[Tweetypie05]

Re: Unexploitable Heads Up play Cheers Dave... at last some-one who speaks plain English... I thought I must be going mad... or am just stupid :\, which may still be true! What I understand from this then is that the basic strategy would be ALL-in at the end of Torunament HU when you have a half decent hand (KJo 55 QJs) with an M of around 9... lower requirements as your M decreases? It's probably more complicated than that but surely this is not so far different from what Harrington advocates? Is this not just basic strategy for HU play at the end of a STT or MTT anyway? Or is this strategy even more aggressive suggetsing that you go ALL-IN with an above average hand when your M is 12+ on the basis that your opponent won't know what you're doing? Have I totally missed the point????? :unsure

[slapdash]

Re: Unexploitable Heads Up play Here's a simple example to illustrate what's meant by "Nash equilibrium" and "unexploitable". Think about playing Scissors, Paper, Rock. Here the Nash equilibrium strategy is to randomly choose which to play, giving each of them a one in three chance. If you do this, then whatever strategy your opponent chooses, he can't do better than win as often as he loses on average. But if you use any other strategy, then if your opponent knows what strategy you're using, then he can adjust his strategy to win on average. For example, if you play scissors one time in six, paper two times in six and rock three times in six, then if he played paper every time, he'd win three out of six games and lose only one out of six. (In this example, if you use the Nash equilibrium strategy, then it doesn't actually matter what strategy your opponent uses: he'll break even anyway. But that's not generally going to be the case in other games.) In general, the Nash equilibrium strategy has the property that, assuming your opponent knows your strategy and adjusts for it, you can't do better than use the Nash equilibrium. In the case of a symmetrical game like Scissors, Paper and Rock, where both players are in exactly the same situation, this means that if you use the Nash equilibrium, then you will win at least 50% of the time, and maybe more if your opponent doesn't play correctly. Heads-up poker, even with both players starting with equal chip stacks, is not quite symmetrical, because it makes a difference who is first to be big blind. But in the Scissors, Paper, Rock example, you can "exploit" your opponent's strategy if he deviates from the Nash equilibrium, by deviating intelligently from it yourself. If he becomes too predictable, then if you persist with the Nash equilibrium, you'll still just break even, but if you exploit his predictability, then you can do better. Of course, if he then realizes that you're no longer using the Nash equilibrium, he can in turn adjust his strategy to exploit that. So if you're better at "mind games" than your opponent, the Nash equilibrium may not be the optimal strategy. But your opponent can nullify your superiority at mind games by adopting the Nash equilibrium strategy himself.

[Tweetypie05]

Re: Unexploitable Heads Up play Cheers Slapdash... basically it's a technique then to keep your opponent off balance! Or at least to keep them guessing. Sounds a bit like Hungarian poker to me... ALL-in with anything! Not sure if it's for me but need to get heads up first to find out... so I will probably have forgotten it by the time this occurs :loon . Thanks... trying to learn more as I don't have a plan! Damn this game is tricky! :\

[viggosen]

Re: Unexploitable Heads Up play

This theory could never work in heads up cash because your man just has to wait for aces, and I dont think it would work in a heads up STT because there is too much time for your opponent to wait for the good to take you on with.

Well I dont disagree that it would probably not work when R gets very high, But I think your argument is wrong, if someone played this strategy against you in a cash game then you couldn´t wait for Aces, in cash games buyin is typical 100 BB, and you get AA 1 out of 221 hands, so even if you rebuyed every time you folded a blind so you continues to have 100 BB, and we asumed that your AA would hold up every time (which they don`t) you would still on average pay 221 BB to win 100 BB.

[slapdash]

Re: Unexploitable Heads Up play

Cheers Slapdash... basically it's a technique then to keep your opponent off balance! Or at least to keep them guessing.

Not really. It's more a technique that you can follow rigidly to stop your opponent from keeping you off balance. Assuming they've calculated the strategy correctly (and I don't have any reason to think they haven't), and ignoring the fact that it's only the Nash equilibrium strategy among those that only involve folding and going all-in (which is not going to be such a bad approximation if the blinds are high compared to the stacks), and ignoring the slight asymmetry because of one player being big blind first, then if you start the heads up with equal stacks, and you follow this strategy, you will win at least half the time, however your opponent plays. If your opponent plays "badly" (i.e., he doesn't follow this strategy), then there may well be a strategy you can follow that will win even more often than if you follow this strategy. Like in Scissors, Paper, Rock, you might think you can get inside your opponent's head and guess what he's going to do. If you can, then that's great, but maybe he's even better at getting inside your head, in which case he'll beat you. But if he is better than you, then you can use the Nash equilibrium strategy of playing randomly, and his mental hold over you becomes worthless: you don't take maximum advantage of the deficiencies in his strategy, but at least you don't give him any opportunity to take advantage of the deficiencies in yours (assuming you don't give any tells). Even in heads up poker with very large stacks, there is a Nash equilibrium strategy (which won't involve only folding and going all-in), but it's just far too complicated to work out what it is.

[GaF]

Re: Unexploitable Heads Up play

Well I dont disagree that it would probably not work when R gets very high' date=' But I think your argument is wrong, if someone played this strategy against you in a cash game then you couldn´t wait for Aces, in cash games buyin is typical 100 BB, and you get AA 1 out of 221 hands, so even if you rebuyed every time you folded a blind so you continues to have 100 BB, and we asumed that your AA would hold up every time (which they don`t) you would still on average pay 221 BB to win 100 BB.[/quote'] Exactly what I was going to say :ok I suspect Dave means witing for premium hands, rather than Aces - so AA, KK, QQ, JJ, AKo, AKs, AQs ...... which my gut feel says would be profitable (and even a lot looser - in a cash game where you don't have a "tournament life" to protect).....

[viggosen]

Re: Unexploitable Heads Up play just realized I made a small mistake, on average you would only lose 3/4 of a BB because you would only pay SB half the time, but that still a losing about 165 BB to win 100 still assuming that you AA hold up every time (which they don´t).

[GaF]

Re: Unexploitable Heads Up play Slapdash/Mick - would you broadly agree with this hypothesis (from the article)?

the all-in NE strategies are quite close to the fully general NE strategy, especially for R around 12 or lower

The key factor seems to be that the lower your R is, the truer this statement is......... As someone who struggles with Heads Up and would take 50% win rate without hesitation (and 50% + x where x is my opponents weakness from deviating from the NE is fantasy stuff!!!) - do you think that an automated approach to HU (with R below 12) along the lines of this article could bear fruits?

[slick mick]

Re: Unexploitable Heads Up play As I said before it is NOT a winning strategy but one that minimises losses and assumes your opponent is also aware of the strategy. Point 2. The key to making money is to play the player not the cards. If you have got to heads up then you should have a good idea of what your opponent is like and how to play. The main thing to take from the article is the wide range of hands you can be aggressive with when heads up or even short handed. People are often puzzled by Gus Hansen's choice of cards to play but try watching him with these tables to refer to.

[GaF]

Re: Unexploitable Heads Up play

As I said before it is NOT a winning strategy but one that minimises losses and assumes your opponent is also aware of the strategy.

I cannot quite get my head around this - specifically in this example, not NE generally ....... If there is NOTHING your oppoenent can do, and no strategy your opponent can follow to beat you more than 50% of the time, then it is a break even strategy (well 50% success rate) at worst ........ if your opponent isn't aware of this strategy then he will deviate from it by a large margin and your success HU will be over 50% ..... not the maximal solution, but a success rate over 50% nonetheless ..... or am I missing something? :unsure

[slapdash]

Re: Unexploitable Heads Up play

Slapdash/Mick - would you broadly agree with this hypothesis (from the article)? Quote:

the all-in NE strategies are quite close to the fully general NE strategy, especially for R around 12 or lower

I can't really say I have much insight into what the NE is with large stacks, but I'd be quite surprised if an "all-in" strategy was that close to the NE if you had very large stacks (e.g., at the beginning of a heads-up match with 1500 stacks and 10/20 blinds). But the article seems to be talking mainly about the heads up at the end of a MTT, when the blinds will be large, and then I can believe it. Take a look at this http://www.daimi.au.dk/~bromille/Papers/poker.pdf that I found earler today. It may even be what your article was based on. They look at a heads up with stacks of 8000 and fixed blinds of 300/600 and describe an "all-in" strategy that will be beat any other strategy (not just an "all-in" one) at least 48.6% of the time.

The key factor seems to be that the lower your R is, the truer this statement is.........

Yes, that's almost certainly the case.

[slapdash]

Re: Unexploitable Heads Up play

Take a look at this http://www.daimi.au.dk/~bromille/Papers/poker.pdf that I found earler today. It may even be what your article was based on. They look at a heads up with stacks of 8000 and fixed blinds of 300/600 and describe an "all-in" strategy that will be beat any other strategy (not just an "all-in" one) at least 48.6% of the time.

And maybe even more surprisingly, they remark that, with the same sized stacks and blinds, I think, the even simpler strategy of going all-in every hand (and never folding), will beat any other strategy nearly 45% of the time.