Poker thread

I'm sure some lg fellows are also poker players.
I've started seriously to learn about two years ago, I'm quite successful (due mostly to chance), but I'd like to exchange ideas, strategies...

I'm particularly interested now to try to quantify the value of position which I think is generally a bit over valued.
What are the hands you will play in position when you are deep (from 100bb to 200bb)?
Will you just call or 3bet?

I know most poker answers are "it depends", but I'm also interested by GTO (Game Theoretical Optimum) play as well as exploitive play in low limits.

Other topic could be on the best poker books people have read.

There has been a lot of advance in computer poker in the recent years and the equivalent of GTO is coined exploitability. I am no expert, but I did include some references in an (unpublished) work describing advances in MCTS.

< --- Quoting myself --- >

• Poker: MCTS is currently state of the art in Poker [178]. The Monte-Carlo playout models the opponents' strategies implemented using Expectimax tree search. Computer poker has also experienced a revolution in recent years. In 2006 a group of researchers including Michael Bowling stated in a conference (see slide 16 in [179]) "Expectimax cannot be used for Poker". Nowadays, the team from University of Alberta Computer Poker Research Group, of which Michael Bowling is part, is currently top level. According to "The annual AAAI Computer Poker Competition": Their program, Hyperborean, was gold and bronze in the two categories of Heads-up Limit Texas Hold'em, in 2011, and silver in 2012. Difficulties have been "ironed out" [180] and extremely large trees are stored in the form of LUTs stored in clusters of computers. Furthermore, Monte Carlo Counter Factual Regret (MCCFR) has been able to approximate Nash equilibria and the notion of exploitability has been coined and is measurable [181]. In [182] it is stated that exploitability has been reducing in computer Poker over the recent years. If, in the near future, exploitability (measured in milliblinds per game) reached near zero values for some program, it would mean that no long term strategy exists consistently winning any money against it. This is arguably the closest possible situation to Poker being "solved" (as randomized hidden information games can obviously not be minimax-solved) and that could happen in the next three years.

178. Rubin, J. and I. Watson, Computer poker: A review. Artificial intelligence, 2011. 175(5): p. 958-987.
179. Billings, D., et al., Game-tree search with adaptation in stochastic imperfect-information games. Computers and Games, 2006: p. 21-34.
180. Lanctot, M., et al., Monte Carlo sampling for regret minimization in extensive games. Advances in neural information processing systems, 2009. 22: p. 1078-1086.
181. Johanson, M. and M. Bowling. Data biased robust counter strategies. in Twelfth International Conference on Articial Intelligence and Statistics, p. 264-271. 2009.
182. Johanson, M. Calculating the Exploitability of Heads-Up Limit Agents. in 2012 ACPC Symposium. 2012.

Hope this helps.

> LUTs

Look-up tables?

> randomized hidden information games can obviously not be minimax-solved

No, but there should be at least one optimal mixed strategy. Or am I hopelessly out of date?

> 179 Billings, D.

is registered on Little Golem as darse, although AFAIK he's no longer active.

Look-up tables?

Yes. Look-up tables. I had the opportunity to talk to Michael Bowling at CIG and he told us they had to hire computers for the tournaments because they require extremely large memory sizes. During a tournament the program is mostly looking up evaluations that have been learned previously. What I find fascinating is that exploitability can be measured and that they are approaching "exploitability zero".

No, but there should be at least one optimal mixed strategy. Or am I hopelessly out of date?

But how can you prove that in a real game, in few games there is such thing as a mathematically sound winning strategy (in Nim there is for instance). And you cannot "brute force" the game evaluating all positions backwards as in checkers or awari. So "exploitability zero" looks to me like the closest thing that can be to "solving" the game, but of course someone may prove that wrong.

Regarding position, referred to in the original question, I feel that one of the main advantages is that it allows you to control the pot size more effectively. If you have a good but vulnerable hand, you can just check if your opponent tries to trap you. If they bet, it's out of position and 'looks' stronger, this should be a clue that you either play a small pot or fold.

Out of position though, if you check and your opponent bets, it's much harder to fold. Because you checked and showed weakness, it's much harder to fold a decent hand.

Similarly if you have a strong hand that you're happy to play for all your chips, it's much easier in position. If your opponent shows weakness, you get to see this before you act and can slow down accordingly. Alternatively they may bet first, which is even better of course.

I personally play any pair and some connecting cards in late position, though I need more than one opponent for some of the weaker connectors. I'm not too bothered about suited cards, but it helps of course. You'll usually either lose a small pot or win a big pot, but position makes the wins a bit bigger and the losses a bit smaller.

Regarding the optimal mixed strategy, my opinion is that there isn't one. If you knew what your opponent's strategy was, I think it would always be possible to devise a strategy to beat it. Of course by this logic, there would be other strategies available that would beat the one you are using.

I'm no computer expert, but I assume their optimal play would involve observing the opposition, selecting the optimal strategy for that situation and repeatedly checking that the opponents haven't switched style to counter this strategy. Interesting stuff, and I'd love to know more!

@Martyn:

I'm pretty sure what Nash proved was there's always at least a weakly optimal mixed strategy. By "weakly optimal" I mean that it can't be beat; not necessarily that it beats anyone else.

Rock-paper-scissors is a good example of both ideas. If you know what your opponent is going to play, you can always win, right? But what if your opponent's strategy is to pick at random (probability 1/3 for each)? They can't be exploited.

OTOH, neither will they beat you. That's what's I mean by "weakly optimal".

A long time ago, I analyzed some over-simplified poker games and find that they had optima which were stronger than that, but not much. The unexploitable strategy wins against stupid strategies, and ties against a wide range of non-stupid strategies. Also interesting: in the limit of an infinite number of possible hands, you don't need randomness. You can allow the hidden information to work for you.

The real best poker players do what you say. But there is a "fixed" strategy out there that doesn't care what its opponents are doing, and that would beat or tie the best poker players in head-to-head competition, if somebody could find it. This optimal strategy, though, would not be as good at exploiting weak players as your strategy could be.

Actually, I've been assuming head-to-head competition all along! For multi-player everything is more complicated, and you have to ask questions like: do we have 9 fixed algorithms and one adaptive expert? Or 9 adaptive experts and 1 fixed algorith? Or some fish?

Position is fairly big, especially in draw games, and especially in live games, where fewer of your opponents know as much about poker. But poker enthusiasts often tend to seek out other poker enthusiasts to play, since for them it's about challenging their game theory, rather than picking up easy money. :)

Not only is position about pot control, but it's information. There are only four or five streets of betting. If you're out of position, you're one street behind the information war, which can be 25% of the hand. It becomes even more important with a regular opponent, as you have more information about his betting patterns, and can reference that information before acting.

Relative position is also important. Usually position means being to the left of your opponent, but if you're at a table with a hyper-aggressive player to your left, you have relative position. Usually that player will make a move, so you get to see how everybody else reacts to it before you respond. On the other hand, you absolutely want the "calling station" to your right, as he almost never bets unless he has it. He also rarely folds, so any bluffing advantage from sitting to his right also vanishes. Against that player, you win the least and lose the most by being out of position.

As to hand ranges... well, that's based entirely on the players, the game type, the game format, the number of people at the table, the table history, and the player history.

tl;dr: It depends. :)

To give an example... in 2-7 Triple Draw OOP, I'm probably not playing any hand that's not a draw to the nuts. At the very least, I'm folding anything with a 6 in it. But OTB in a short-handed game against a known opponent who likes to make the big laydown, I might play absolute garbage and stand pat on the second draw.

But then again, in the right situation, I might do that OOP and lead out every street. So much depends on the table dynamic, especially in a live game.

Thank you all for the very interesting answers.

I would like to characterize the situations where being out of position is an advantage. The example Pfafulous gave about being on the right of an hyper-aggresive player being a good example.

I have in mind a situation on Hold'em No Limit where you have a stack of 60bb, suppose you bet 3bb under the gun with KQo, and a player on the button decides to just call you with AQs with 15bb, because he wants to trap or he thinks it is a drawing hand in position. You are a 3:1 underdog here as he caught one of your cards, the Q, which is the drawback to play this type of hand for opening.
Now on a lot of flops, aggression with your big stack will be an advantage for you:
suppose the flop comes JT8 rainbow, this flop did not really help you, you are still 3:1, but as it matches well with the middle pairs you are representing on a significant part of your range, you cbet to the pot or 4bb. this is about the third of the stack of villain and even if he calls the first barrel, it will be a lot harder for him to call a second barrel of 7 or 8bb or 2/3 of his stack (only about 1/7th of yours) if he missed the turn which is 88% of the time with his 6 outs, meaning a possible tournament elimination against any hand that paired with the board or a pocket pair.

About Nash equilibrium and GTO compared to exploitive play, there are Nash equilibrium for head's up play, but it is difficult to define it for multi-players because of collusion (even implicit one) destroying the equilibrium. Some studies has computed them for 3-players where you play jam or fold and argue it is not prone to collusion.

There is another situation where being out of position against a hyper-aggressive player can be good, it can help to trap other players. Suppose you limp with aces under the gun and the aggressive player raises.

Other players may call the raise with deep stacks, hoping to outplay the aggressive player. However you can then put a large re-raise in and pick up loads of dead money. And if somebody calls, even better.

Having said that, I still prefer to be in position more often than not.

I have read that poker is a game of information and the out of position (OPP) player gives one street more information than the in position (IP) player.
I'm not sure I agree with this if you don't play to standard:

In head's up OOP, you get AT, villain on the button will bet or min-raise your blind as he does 90% of the time. You just call his bet.
Now the flop comes A85.
If you now check, what information do you give him?
The way I see it, you can flip a coin to decide to bet on the flop, or you can check from A6 to AJ and bet any other Ax. There checking with a middle Ace which is surely the best hand (only 3% of hands have a better Ace) is an aggressive play, which will prevent villain from betting each time you will check a flop.
So at my level, doing the opposite of most 1-level players, betting when you did not hit the flop in first example, and checking when you hit in second one, I get the impression that the information given out of position is at least blurred, especially if you mix your play.

The other factor in favour of OOP play is that you will mostly play big hands where most players following you IP will play a lot of poor hands like small suited connectors. So if you don't give up too easily and manage to go to show down or raise the to aggressive players, you should get your share of pots won.

In that scenario the player on the button has the advantage that if they check, they know they get to see the next card for free. If they have something like A6 or even a drawing hand like 76 they can probably ensure that one of the betting rounds is checked and save a bet. That's assuming you're not betting your AT every time.

This isn't the case for the OOP player, they may get a free card or they may face bet. It's harder to generate the right pot size for your hand. Mixing up your play like you suggest certainly reduces the advantage of position though.

A strictly HU game has its own set of rules. Not only can game theory really be analyzed, but the psychological game is also ramped up. HU is not one hand at a time, it's an entire session (or more).

In a full ring, I probably don't open with KQo UTG, especially not with a short 60bb stack. JT8 is a disgusting flop for me. It's a hand where I win the least and lose the most. Am I stacking JT or T8 when a 9 peels? Probably not. KJ, KT, QJ, QT destroy my hopes of winning with pair outs. Q9 is already there.

The pot is 7.5bb with 57bb behind, or a stack-to-pot ratio of around 8. How do I play this? Do I lead out 6bb? What do I do if I'm raised to 15bb? Can I re-raise to 25bb and then fold to a shove? If so, I've put in almost half my stack and folding, which is not profitable long-term. Do I just call a raise and fold if I don't improve? If I get a call to my initial bet, what can I bet on the next street? How many cards scare my opponent off the hand? What hands that I beat does he keep playing? When I make my straight, does he pay me off? Do I check? Now my opponent can decide what to do, and a lot of cards either scare him off entirely, or give me an expensive second-best hand.

OTOH, if I have position, it's probably against the big blind, who will probably lead out with a probe if he likes the flop. I can fold for cheap, or make the 15bb raise. If he checks, I might win with a 6bb bet. He's already given me a lot of information, and I can apply more pressure with smaller bets.

Of corse, this is all just my thoughts. The thing about poker is that the thinking about it goes back and forth on levels. You need to be one level above your opponent and no more, otherwise you out-think yourself and lose money.