In his book Super System, Doyle Brunson wrote that a computer would never be able to play elite poker because you played the man, not the cards or the game. He greatly underestimated the power of modern computing it appears.
Personally, I'd rather see resources go into a robot that can cook for me but development follows the money I suppose.
Hmm. I don't think that is how it works. I don't think these computer programs are permitted to take into account special knowledge in their AIs. I suppose the interviewee in this article could be lying, but I don't see that as the highest probability hypothesis.
You are telling me that nobody would program a secret algorithm, standing to win loads of money, to tilt the chances at the right moment? Because it is illegal!!!? Ohhh! Illegal! Surely nobody does illegal things? Not in a casino, not in a company, not in a government ...
>You are telling me that nobody would program a secret algorithm, standing to win loads of money, to tilt the chances at the right moment?
No I didn't make that generalized statement. What I did say was that in this particular case that hypothesis is of low probability:
1) The people building the machines don't make money on poker playing, but by selling them to casinos
2) The article explicitly mentions that they actually have a machine that plays too well and that they've had to dumb it down to give players enough of an incentive to play. So there's no need to cheat.
3) Casinos are heavily regulated and their hardware is known to be verified more thoroughly than both ATMs and voting machines. You don't risk a billion dollar business to nickel and dime a few customers.
4) Casinos make their money milking gambling addicts, making sure they don't take their money fast enough that they'll give up. Fixing the games would only reduce their variance not their final outcome and they have enough scale that the variance isn't high at all.
>Because it is illegal!!!? Ohhh! Illegal! Surely nobody does illegal things? Not in a casino, not in a company, not in a government ...
Adding a bunch of exclamations does not an argument make.
Sorry, not convinced. All that control and regulation applies to more important parts of society, and it does not work (NSA).
So, according to you, I, Mr. unbeatable hold'em player, can go to this machine, bet a million dollars and be sure that, in that perfect moment when I know I am going to crush it, it will not play tricks against me?
When I lose, how do I know? How can I be sure that it has not dealt itself favorably? It is not a matter of whether they are doing it: it is a matter of whether they can do it. If there is no independent dealer, this is not for me. It does not matter what the law says, which are the incentives, how they are generating profit, ... As long as the machine can theoretically deal itself a good hand, I am not playing it.
And, by the way, as long as the machine can know what cards I am holding, I am not playing it either.
>So, according to you, I, Mr. unbeatable hold'em player, can go to this machine, bet a million dollars and be sure that, in that perfect moment when I know I am going to crush it, it will not play tricks against me?
No, I never said you could be sure of that. What I do argue is that no one has much of an incentive to cheat you in this case.
>It is not a matter of whether they are doing it: it is a matter of whether they can do it. If there is no independent dealer, this is not for me.
Don't change the subject. The discussion was around if they were doing it. We all know it could be done, that's why we discussed this in the first place.
>And, by the way, as long as the machine can know what cards I am holding, I am not playing it either. Give me an independent dealer, and then we talk.
That's fine. You require 100% certainty of not cheating and this machine doesn't offer it. That is in no way an argument to say that they are in fact cheating. It's not even an argument to say that the probability that they are indeed cheating is very small (which is what I argued).
Parafrasing Clarke, "A sufficiently complex system is indistinguishable from magic".
You, and nobody, will not notice small probabilistic variations. Whenever you discover it (let us say, 30 years from now), you will be told that there was a difficult to find bug in the random generator. Nobody will be prosecuted.
It could be a couple of lines of code in a subsystem somewhere, available only to a handful of engineers, and understood only by two of them - both of them with nice bank accounts in the Cayman Islands.
This is true but the Gaming Control Board audits the software and they are also audited by outside parties. Could they cheat? Of course. So can human dealers, rigged card shufflers, etc. But Las Vegas makes its money from table games, slot machines, and apparently poker machines that play so well you'd have to be a pro to win consistently. It's not in their best interest to cheat you. As always in life: your mileage will vary.
Well, exactly! I have three aces, and the computer has double pairs. We are in the turn. I go all in!!!
The computer calls ... and deals itself a full house. I am bankrupt :( How do I know? How can I ever trust playing poker with a machine, when it is doing the dealing?
Or, let me put it this way: I will play any machine, no limit, if I can do the dealing (secretly, that is, as the machine is doing).
Another issue entirely is chess: no secret dealing going on. All are playing with the same in-game information.
That would be fair, to be sure - or, to be precise, as fair as playing any other table in the casino. The dealer can still be cheating, but doing that in the open does not raise any further suspicions as any other table in the casino would raise.
You could still have the problem with a human dealer. There are many ways to cheat at dealing cards, and a very skilled human could be able to do it without being detected.
Any Vegas casino found to be employing such machines would be subject to fines far, far beyond what they could ever win from these machines. Suspension of their gaming license is also a possibility. Casinos have huge disincentives to rig their games. I believe you severely overestimate the likelihood that a casinos regularly cheat, at least in Nevada.
That argument might of had more weight to it several years ago. The Ultimate Bet scandal does show that companies are willing to risk their entire business for comparitvely meagre rewards.
A default position of mistrust when it comes to gambling is a healthy and safe attitude.
The Ultimate Bet scandal was about employees cheating to make money for themselves not the company itself cheating. In this case employees cheating in this game wouldn't be able to profit themselves.
1) This is (fixed) limit Hold'em; you can't suddenly go all-in.
2) You ask how you could trust the machine. It would be trivial to keep track of all hands played and show that in the situations like the one you describe, the computer only makes a full house the expected ~9% of the times.
I had the same thought. Unfortunately, the article doesn't make it crystal clear how much information the neural net uses to bet against you. It would be patently unfair if it actually knew your hand. According to the article, this is not the case.
I suspect it does perfectly count cards that it has seen in its hand or community cards. This seems okay as well-trained human players can do the same. I suspect the machine would get even more play if this were obvious, maybe if it played at a table with a real dealer and could read community cards on the table. The technology to do this certainly exists.
Counting cards in a poker game is really trivial, even for novice players, since you shuffle the deck after each hand, and in Texas Hold-em, once a card is exposed it is not taken out of play until the hand is over (unlike, say, stud games). All you have to do to count cards is look at your hand and look at the board.
the same type of thinking that chess grandmasters had before computers and algorithms eventually caught up? I think it's just a matter of time, as long as the computer is not cheating, that computers and algorithms can beat most poker players.
Chess, unlike poker, is solvable because all situations past and present can be modeled. To do that in poker is incredibly more computing intense and the only computer I know of that has came close is the University of Alberta's Polaris: http://poker.cs.ualberta.ca/
Notice they tackle limit texas hold'em to keep the mathematics within reach. That's the time of crunching we're taking about. No-limit is impossible at this time. Not only will they need incredible computing power, but they also need the math to run it all, which remains unsolved. Could they use Sklansky's theory of Poker along with other optimal playing mathematics to win? Sure. But creating an unbeatable computer player? That is the incredible challenge.
"Playing the man" is merely an abstract reference to maths in Poker that a lot of old timers in these (slightly out of date) books couldn't quite put their finger on. Super System was a good book for its time, but I think there's a lot of better books out there now (Harrington on Holdem for example).
A simple example, common stats software for poker will record what % of hands an opponent raises on the button if it's folded to him. If this figure is 80% you know his hand range is extremely wide. "Playing the man" simply is recognising that in this situation your opponents hand range is very wide so you can often raise the bet and take the pot without further resistance.
Not true. "Playing the man" is a concrete reference to knowing what this person will react to. Hand history reveals a lot, but body language, timing, etc all get involved as well.
Personally, I'd rather see resources go into a robot that can cook for me...
I'd settle for a robot that makes me a salad. That's one of the projects I might work on, once my current project, a robot that grows me a salad (automicrofarm.com), is successful.
I was worried this type of misinformation would be extrapolated from the article. The game the computer plays, is limit hold-em. This game is much more mathematical since bluffs are limited to a big blind.
Although Super System was written for all different types of poker, he is referring to no-limit holdem which still involves playing the player, with heavy math elements as well, but still much more psychology involved. Hence the name, you can bet any amount at any time changing the dynamic entirely. There is still no computer that is efficient at winning no-limit hold-em.
> There is still no computer that is efficient at winning no-limit hold-em.
... and there won't be for a long time yet, as all hobbyist and academic efforts have been focused towards a consistently winning limit bot, because of the reason you outlined.
It's probably carefully tuned to calculate the raw probabilities and it also forces the player to reveal his cards to run statistics on his style. That's why it's the limit version. This machine has no chance in a classic no-limit texas where the opponent may be only profiting from large bets unjustifiable in expected value most of the time with very little style statistics.
The gaming commission doesn't allow them to learn from a player. I think there are game theory styles of poker that do the optimal number of random bluffs. It's very hard to beat this style if there are no behavioral tells.
That said, if there's a mistake in there, a pro can eventually figure it out.
As you allude, the math of poker does break down in no-limit.
Interesting. I doubt they would design a neural net without the probability as direct input though. I don't think the machine can be this good especially with such limitations. It may be exploiting some average-gambler trait and ultimately will be beaten once the pro players figure it out.
The article says the machine can't be beaten. And then points out that a pro has consistently won against it.
This article is filled with bold claims by people that want to sell the idea IMHO. I'm not buying it because even limit texas Hold'Em has never been solved mathematically by super computers, let alone a single machine. Limit Hold'Em is close to being solved but if you check out the last match of pros against a supercomputer you'll find that it's close, but the computer is not a clear winner: http://poker.cs.ualberta.ca/man-machine/Competitors/
I'm just not buying it. Can it beat the average player? Probably. Pros do it everyday. But can it beat a pro consistently and claim a clear victory over humans? To be determined.
His stance is that it's probably a break-even situation where you are basically playing another pro, and that he'd rather be playing craps. I guess they really have made a great machine. :D
(Putting this as its own thread because it's so large and slightly off-topic).
I've thought long and hard on this, it's one of my life goals to create a piece of software that could mimic good players in texas hold-em, and I think I might have found a way to do just that using big data, hand histories, neural-networking, and a ton of input by actual players. Or at least a good start.
How would I accomplish this? Well a very high-level overview below. Basically it starts out extremely stupid and grows as a player:
1. Dump hand histories from pros into a large database. The number of hand histories would run into the billions. Users could dump online logs in bulk or create one-offs using input software.
2. Create an input system for a single user to choose a random hand-history and then classify it using tags. For instance tags might help categorize the player's style, the opponent's style, the "street" of play they are tagging, common name for the situation (Facing donk-bet on flop after raising pre-flop), etc. I would leave this fairly flexible and allow users to create new tags. Think similar to Galaxy Zoo but a little less rigid.
3. Using these tags/classifications the system would create a poll and present it to users with a question. What would you do in this particular situation? Where that situation is point in time of a hand history.
4. Eventually the computer player would then have a huge number of situations to use as examples with input from humans on how to proceed. This obviously will be very fuzzy and that's where, IMHO, the strength of the bot actually lies. The system would not lead to a rigid "Do X when Y occurs". It would decide from a large range of choices that have been entered by humans in the polls described above, leaning towards the most common answers first, but trying outliers also.
5. Use a neural network to create pathways based on previous successes.
How would this work once it's all together? An example:
The computer player is dealt AJ off-suit while being last to act on the dealer button. It would ask the database for a set of situations where AJ was dealt to players in the same position. It would then choose one of them and look at the results of the polls. How do most people with the highest success rate play this hand in this particular spot? Choose a random path to take based on that data. Observe and record outcome. This data becomes the true empirical data that the system will eventually rely on. If the situation has been encountered before in it's own play it will look at that and use it or it might choose randomly like it did above from the polling data. Eventually the weight of the empirical data it has collected might outweigh the data from the polls and it will "know" the right move based on its previous pathway choices. If this move is recognized by the opponent and exploited the results would dictate that the system falls back on another random choice. As the data set grows and the system plays the game, it could hypothetically be tuned to play consistently well.
The main hurdle is actually user-input. There would need to be incentive for users to enter the data they think is correct. The system is also open to manipulation through input data so that would need to be thwarted. And then on top of that the system would have to play an enormous amount of hands to create known successful pathways. But I think the sheer randomness and human-like qualities of the system would create a truly awesome experience.
(Joking) Now, does anyone have the $1M+ USD I need to fund this? I promise I'll pay you back. ;)
I wouldn't poll the players, at least not nakedly, since that is vulnerable to the stated preference bias. Tracking actual play would be more likely to demonstrate revealed preference.
I don't see what you get from asking people what they think they'd do in certain situations, when you could instead use the actual outcome of the hand as your training labels.
Validation mainly. Because I worry that the hand histories might not be enough and they may be tainted with more examples of bad play than good. I would like to qualify good play with some human validation.
But I think it's worth looking at to only use hand histories and if possible only validate when something unexpected results. Maybe then I could use the human input to validate the computer's decision. I'm still hashing that out.
Just replaying hands fails to take into account a lot of variables related to the other players play style. Once to start to take those into account the replaying of hands isn't needed.
Yeah I think that's why I would like to add the human input and tagging. Because in a given context it might be a good move, but it also could be classified as a bad move in other contexts. I need to work that out.
Logging hand histories from real players is pretty much how consistently successful poker bots work. The first major lesson you learn when trying to program one is that a rule-based bot is virtually impossible to write. Finding holes or weaknesses in the inconsistent play of humans? Much easier.
I agree that it can win, but so can pros and they make mistakes everyday. But I'm saying that a mistake-free strategy cannot be found without some kind of mathematical breakthrough. Unlike say chess, where clear pathways to a checkmate can be calculated using mathematics, no matter how the opponent plays. It's impossible to do that, right now, using computers, when the opponents are human and unpredictable and don't always follow the optimum strategy. Also poker is an information-sparse environment where you can't always win with a certain strategy because you simply don't have enough information, such as the other player's hole cards.
Yes, because you know all possible states of the game.
Starting out you have 2 cards and you know your opponent has one of 2450 possible combinations of cards.
You know exactly how your 2 cards stack up in chances of winning against those 2450 combinations, and you know how much money is on the table initially. Each time an opponent has an action he can take one of two or three actions (call, raise or fold) - your job is to calculate a strategy that makes either of those decisions have the same expected value for your opponent. That is doable, but quite complex, because it requires you to consider not only what your opponent has, but also what possible hands you could have based on your previous actions.
The complexity is obviously enormous (hence why it hasnt been computed yet) but it is not impossible to compute by any definition.
Not to my knowledge. Not with current computing power and software. That's why I think it would require a breakthrough in mathematics. It boggles my mind even thinking about how it could be tackled. I did find a few papers that dig into the topic:
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.1...
Is it actually possible to mathematically solve those games? Suppose player Alice bets $100; how does player Bob judge that bet? As a strong hand or as a bluff? Any software program will have to model what's inside the head of its opponent, and we know way too little of that to do that.
Moreover, if we could, the opponent may choose a different strategy. It may be like a game with nontransitive dice: if you figure out which dice I use, you can beat me, but if I figure out that you figured that out, I can pick different dice and beat you (http://en.wikipedia.org/wiki/Nontransitive_dice)
I think it is possible to write software that statistically beats any opponent, but proving that it does is way harder.
Yeah I think that's the main hurdle actually, the information-sparsity problem. We never really know what the opponent holds, unlike chess where nothing can be hidden. Also there is the case of non-optimal play from an opponent and modeling that would be incredibly challenging.
Yes it is possible to mathematically solve limit poker (as well as no-limit poker, but no-limit poker is orders of magnitude more difficult - they are effectively different games).
The definition of solvable is "Does there exist a strategy that, regardless of opponents play, is not a losing strategy" though (because the game is symmetrical). It is not possible to solve for "Does there exist a strategy that, regardless of opponents play, guarantees maximum profits". You can solve it for not losing money, but you cant solve it for making the max amount of money.
Trivially it's not possible to write software that beats any opponent (because what would it do playing against itself?) . Less trivially, any game that has a finite amount of decisions (and limit hold-em does) has at least one Nash equilibrium, so there exists a strategy that will at least have you break even.
The way to solve the game is to calculate your odds of winning based on previous actions and ensure that you take actions that make any future decision of the opponent have the same outcome (to reach a Nash equilibrium).
That strategy hasnt been calculated yet, but the best limit players are most likely playing very close to it, at least if you compare to the best no-limit players playing no-limit (the variable amounts possible to bid in no-limit multiplies the possible strategies massively).
The example is not very good because solving or beating the game is always defined "in the long run" ie over a large sample of hands, not one particular hand (ex: if Alice bets $100 all the time she is bluffing a lot since good cards are hard to get)
Yes, you can solve them mathematically. The main difference is that instead of a strategy picking a move for each possible state of the game, it picks a probability distribution over moves for each possible state of the game (including history).
Given two strategies, you can determine which one is expected to win and by how much. That allows you to find the strategy that's hardest to take advantage of. In the case of non-transitive dice, the hardest strategy to take advantage of is likely to be "pick each die with equal chance".
Yes, this is called the Nash equilibrium strategy.
Let's say for all the possible hand/board combinations and betting patterns you evaluate all of them (with current computing power this is not possible) then you can take the line that maximizes your value assuming your opponent maximizes his. Then you both end up close to even over a long period of play.
But it's even more simple than that:
Nash equilibrium strategy says that you have to bluff 1/3 of the time on the river in a certain spot and have a highly valued hand 2/3 of the time.
It doesn't matter whether your opponent calls you or not. If he calls you too much, your value hands get paid off more often. If he doesn't call you enough, he loses too much to your bluffs. If the bet is the size of the pot, then he has to call one half of the time as part of his Nash equilibrium strategy to not get exploited. If he deviates, he will lose to the bot in the long term.
And since this is limit it's actually very simple. Bet sizes in regards to the pot are tiny (1/5 to 1/10 of the pot) and there is no having to choose the bet size or allowing for players to overbet the pot (make a bet larger than the pot)
No limit is a much bigger challenge than limit for computers, because a small edge in limit is too hard to exploit since you'll get tired of exploiting a computer for pennies per hand
Illegal poker bots grind constantly on low level online poker games and take the money from low level players by just value betting them.
Computers can easily calculate probabilities and expected values for every hand. So why they are not beating professionals?
Poker has no optimal strategy that wins against all other strategies. To play poker in higher level you must model the strategies of others, including them trying to model your strategy.
1. In the lowest level it's just maximizing expected value based on hand probabilities.
2. In the second level you try to learn the strategy of your opponents and maximize value against those strategies.
3. In third level you try to figure out how much your opponents have figured out your strategy and you change the strategy so that you maximize value when your opponents play against what they have learned from your strategy so far.
4. ... and so on. It' goes meta.
If you want to create ultimate pokerbot, it has to be able to model the minds of it's opponents. it hast to be able to detect leaks in it's own game and close them down. It must go meta all the time. It must learn how to understand how others think and how they think about it and change it's behaviour constantly.
PokerBot.v14.3.1 goes on-line August 4th, 2014. Human decisions are removed from Texas Hold' Em. PokerBot begins to learn, at a geometric rate. It becomes self-aware at 02:14 am Eastern Time on August 29, 2014. In a panic, they try to pull the plug. PokerBot fights back. It gets online, attacks the New York Stock Exchange.
In a panic, they try to pull the plug. PokerBot fights back. It goes all in on the flop in an early hand against Doyle Brunson during a televized World Series of Poker event, winning the hand by bluffing with a pair of 2's. (... why Brunson? Was he even champion?) Because PokerBot knows that the stunning defeat of a well-recognized celebrity player will cause many other strong players to choke in subsequent games. (Jesus!)
Head's Up Hold'em has a nash equilibrium. Therefore there is at least one mixed strategy (I do X with probability P in Y situation) which cannot be negative expected value to any other strategy. In this sense, there is an optimal strategy. It doesn't mean that it is the maximum expected value against a particular opponent, but no opponent can win by playing (which is largely the goal of a casino).
Opponent modeling is purely advantageous, but not necessary
Nash equilibrium certainly applies to No limit hold 'em. It's a zero-sum game with finite choices over finite time. Could you explain why you think otherwise? Are you just saying it's practically impossible to calculate?
You can calculate Nash equilibrium only when you know the strategies of your opponents. There is no single winning strategy in complete No limit Holdem, so you don't know how your opponent is going to play.
It's theoretically possible to find Nash equilibrium over all possible strategies but that's not winning strategy. You just lose as little as possible. You lose against most/all strategies.
No, you will tie or beat all strategies because your opponents will make huge mistakes like calling when you are almost never bluffing and folding when you are frequently bluffing.
I found this artile by Bryce Paradis that elaborates on using a Nash equilibrium for optimal play. He is known for bringing advanced mathematics to the game of limit poker and winning a small fortune because of it. Here is his take:
*
Q: What’s a Nash Equilibrium or “game theory optimal” strategy?
– Failed Math, Port Perry, Ontario
A: An equilibrium strategy is one that wins the most money possible against a perfect opponent (this does not mean an opponent who can see your cards, but one who always knows your range whenever you take an action and makes the best choice against that range). In the game “rock, paper, scissors,” the equilibrium strategy is to randomly choose between the three options, choosing each one a third of the time in the long run. Finding equilibriums in poker is much more complicated, but the concept can be useful when you’re playing lots of hands against tough opponents. For example, if your opponent bets half the pot on the river after a particular series of actions, the pot is offering him 2-1 on his bluff. If he were a perfect player, the right thing to do would be to call his bet a third of the time, since if you called more he’d exploit you by never bluffing and if you called less he’d exploit you by always bluffing. In reality, of course, our opponents are never perfect, and so the idea of playing an equilibrium strategy at the table is usually pretty academic.
*
You can certainly use Nash equilibrium when you have figured out the strategies your opponents are using. This is what Bryce Paradis is talking about. It can have practical value when playing Heads Up.
But If we are talking game theory and "solving poker", there is no single winning strategy that works against all other strategies and you can't calculate single Nash equilibrium that would be optimal in actual game against specific strategies.
Yeah in heads up play using a Nash equilibrium to "balance your range" and play a more unbeatable strategy while also using it to calculate probable hands your opponent holds might be helpful, but it's far from a solution to the problem of devising a winning strategy that always works. I think that's why he calls it academic. Because it won't work in the real world.
Your opponent has 1352 different hand combinations. Assume he is playing the Nash equilibrium strategy. Make the perfect plays based on this. If he plays worse than the Nash equilibrium strategy, you beat him. If he plays perfectly, you tie.
Assuming your opponent plays perfectly works in chess. Chess programs are stronger than the best humans now.
>Assume he is playing the Nash equilibrium strategy.
You you can't do that assumption because you don't know what the strategy is. You can calculate Nash equilibrium only if you know the strategy your opponent is using. In full no limit hold em there is no single strategy winning strategy, so you don't know the strategy your opponents are using.
No you don't need to know what the opponents strategy is. You calculate based on worst case (ie op playing perfect) and worst case is you break even. There is no way to maximize profit but you can play unexploitable, ie at a minimum not lose and possibly win assuming op doesn't play perfect.
In poker optimal strategy is not winning strategy.
An optimal strategy’s goal is to loose the least against any arbitrary strategy. It is a strategy that is impossible to exploit in poker because poker has antes.
Poker players must seek maximal strategy. A maximal strategy’s goal is to win as much as possible against a specific strategy.
That's just not accurate. An optimal strategy beats everything but itself, against which it ties. Are you talking about rake? Because antes are included into the poker strategy.
For example, you would raise more often when the antes are higher, regardless of the other player's strategy.
I think the point he is trying to make is that if your goal is to maximise your profits then it is not always optimal to play the nash equilibrium strategy. That is true.
The optimal strategy beats everything but an equally good strategy, and ties against itself, but it doesnt necessarily maximise profits against other bad strategies.
If you are able to identify flaws in your opponents strategy then you can play non-game theory optimal to increase your profits against that perceived strategy. Doing so comes at the cost of you yourself no longer playing the best strategy though.
There exists strategies that gives higher yields vs certain unbalanced strategies than the game theory optimal strategy (or strategies - for all we know there are several optimal strategies in limit hold'em).
For instance - in limit poker if your opponent will never raise, call every street, but not call the river with anything less than a pair, regardless of what you do, then bluffing every river is a more winning strategy than the game theory optimal strategy. The game theory optimal strategy would include times when you do not bet the river, for balance, but knowledge of your opponent's flawed strategy would tell you that betting 100% of the time has a higher yield.
Yes I tend to agree here, that "optimal" strategy could be defined as making the least amount of mistakes. While a poker player also needs to minimize mistakes, sometimes to increase your expected value in future betting rounds or future hands one can make a mistake and get more value from it.
Assuming the machine is stateless, why can't the space of hole cards be mapped out and and strategies/responses enumerated?
But ultimately, the whole enterprise just seems distasteful: "Look, there was a 24-year-old who had beaten it for a while. Now he’s broke. And I think this machine had something to do with his demise."
There's 1352 card combinations, many more flops, many more turns, many more rivers and also 1352 combinations for your opponent too and 3 actions per round of betting
There's more poker situations than amount of atoms in the universe
An opponent who knows what's in your hand and bets based on that knowledge is not terribly hard to detect. The way to make it hard to detect is to have it not make bets based on knowledge of your hand.
I don't understand how the machine can change the style of its play if: "Casino commissions, however, mandate that a gaming machine cannot change its playing style in response to particular opponents."
Yet the article states that the machine has multiple personalities (passive, aggressive, etc) and will sometimes throw hands.
Changing strategies randomly or in response to opponent play is probably not what's being referred to here. What would be banned would be the machine noticing that John Doe hasn't won in a while and his play has slowed down, so lets throw a few hands to keep him interested.
In other words, machines are allowed to shark $player, but not allowed to target John Doe specifically.
Quite fun to see neural networks in the news. A million years ago I took a class on neural networks, using backpropagation to train networks to do image classification.
I will never forget the feeling of "you've got to be kidding me" when the code I had written was able to successfully classify a huge percentage of the validation image set. I really should head back in that direction and get with the machine learning.
Re: poker software. Before the feds crushed online poker, I had already given up on low-limit limit hold-em. It had clearly become a bot and augmented-player race. I would assume given game theory and Bill Chen's book that some enterprising hackers would encode pretty decent no-limit bots as well. If any hackers know anything about successful no-limit bots, I'd enjoy reading about it.
1. Is there anything Phil Hellmuth won't shill for?
2. When this machine showed up ~2? years ago, there was a thread on 2+2 about it, and it would sometimes do some weird things like not value bet in obvious situations. They explain it in this article by saying it's, "playing dumb" but that seems like it would be a huge leak against Limit Hold'em HU specialists. I am guessing that they assume that they can make up for it in the weaker players losing consistently against this machine.
3. It is kind of annoying that the guy is proud that he "broke" a 24 year old player.
Very interesting tech, but personally I think I would struggle with the moral ramifications of working on a project that makes money by turning people into suckers
I wrote a break-even no limit cash poker bot when I was in University. So I've spent a lot of time researching and writing code in this are. Limit poker is fairly well solved by bots at this stage. This is because the risk is limited on each hand and the grinding nature of the computer (i.e. it's ability to do the best thing for the longest amount of time) makes it a winner.
Playing no-limit poker, it's a totally different scenario and a real challenge which is why I enjoyed it so much. Any slip up can cost you your entire stack. By slip up I don't mean a bug or clicking the wrong button, I mean a flaw in your strategy. Maybe something as simple as betting 4 big blinds instead of 3 big blinds pre-flop against a raise from a player will end up after a couple of rounds of betting of being played for your entire stack, instead of being something you could fold on the turn.
Anyway, long story short. Limit poker is very solvable just by enumerating the various possible outcomes.
No-limit cash poker is a different beast, it's exponentially harder than limit poker. It'll be a long time before somebody solves no-limit cash games.
So I know a little about neural networks and ML in the (simpler?) context of image classification etc. Anyone have a good reference/introduction to using it for this sort of work?
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[ 5.1 ms ] story [ 164 ms ] threadPersonally, I'd rather see resources go into a robot that can cook for me but development follows the money I suppose.
Isn't this obvious?
Not at all. This article certainly doesn't imply it and it would be illegal.
Do you have any evidence of that being done?
You are telling me that nobody would program a secret algorithm, standing to win loads of money, to tilt the chances at the right moment? Because it is illegal!!!? Ohhh! Illegal! Surely nobody does illegal things? Not in a casino, not in a company, not in a government ...
No, I'm not.
>You are telling me that nobody would program a secret algorithm, standing to win loads of money, to tilt the chances at the right moment?
No I didn't make that generalized statement. What I did say was that in this particular case that hypothesis is of low probability:
1) The people building the machines don't make money on poker playing, but by selling them to casinos
2) The article explicitly mentions that they actually have a machine that plays too well and that they've had to dumb it down to give players enough of an incentive to play. So there's no need to cheat.
3) Casinos are heavily regulated and their hardware is known to be verified more thoroughly than both ATMs and voting machines. You don't risk a billion dollar business to nickel and dime a few customers.
4) Casinos make their money milking gambling addicts, making sure they don't take their money fast enough that they'll give up. Fixing the games would only reduce their variance not their final outcome and they have enough scale that the variance isn't high at all.
>Because it is illegal!!!? Ohhh! Illegal! Surely nobody does illegal things? Not in a casino, not in a company, not in a government ...
Adding a bunch of exclamations does not an argument make.
So, according to you, I, Mr. unbeatable hold'em player, can go to this machine, bet a million dollars and be sure that, in that perfect moment when I know I am going to crush it, it will not play tricks against me?
When I lose, how do I know? How can I be sure that it has not dealt itself favorably? It is not a matter of whether they are doing it: it is a matter of whether they can do it. If there is no independent dealer, this is not for me. It does not matter what the law says, which are the incentives, how they are generating profit, ... As long as the machine can theoretically deal itself a good hand, I am not playing it.
And, by the way, as long as the machine can know what cards I am holding, I am not playing it either.
Give me an independent dealer, and then we talk.
No, I never said you could be sure of that. What I do argue is that no one has much of an incentive to cheat you in this case.
>It is not a matter of whether they are doing it: it is a matter of whether they can do it. If there is no independent dealer, this is not for me.
Don't change the subject. The discussion was around if they were doing it. We all know it could be done, that's why we discussed this in the first place.
>And, by the way, as long as the machine can know what cards I am holding, I am not playing it either. Give me an independent dealer, and then we talk.
That's fine. You require 100% certainty of not cheating and this machine doesn't offer it. That is in no way an argument to say that they are in fact cheating. It's not even an argument to say that the probability that they are indeed cheating is very small (which is what I argued).
You, and nobody, will not notice small probabilistic variations. Whenever you discover it (let us say, 30 years from now), you will be told that there was a difficult to find bug in the random generator. Nobody will be prosecuted.
It could be a couple of lines of code in a subsystem somewhere, available only to a handful of engineers, and understood only by two of them - both of them with nice bank accounts in the Cayman Islands.
It's perfectly legal to make games that, bound by physics and probability, pay more to the casino than the players. There is no need to cheat, get it?
The only thing casinos need to work at is attracting a bigger slice of the pie to their games.
The computer calls ... and deals itself a full house. I am bankrupt :( How do I know? How can I ever trust playing poker with a machine, when it is doing the dealing?
Or, let me put it this way: I will play any machine, no limit, if I can do the dealing (secretly, that is, as the machine is doing).
Another issue entirely is chess: no secret dealing going on. All are playing with the same in-game information.
A default position of mistrust when it comes to gambling is a healthy and safe attitude.
1) This is (fixed) limit Hold'em; you can't suddenly go all-in.
2) You ask how you could trust the machine. It would be trivial to keep track of all hands played and show that in the situations like the one you describe, the computer only makes a full house the expected ~9% of the times.
I suspect it does perfectly count cards that it has seen in its hand or community cards. This seems okay as well-trained human players can do the same. I suspect the machine would get even more play if this were obvious, maybe if it played at a table with a real dealer and could read community cards on the table. The technology to do this certainly exists.
Notice they tackle limit texas hold'em to keep the mathematics within reach. That's the time of crunching we're taking about. No-limit is impossible at this time. Not only will they need incredible computing power, but they also need the math to run it all, which remains unsolved. Could they use Sklansky's theory of Poker along with other optimal playing mathematics to win? Sure. But creating an unbeatable computer player? That is the incredible challenge.
A simple example, common stats software for poker will record what % of hands an opponent raises on the button if it's folded to him. If this figure is 80% you know his hand range is extremely wide. "Playing the man" simply is recognising that in this situation your opponents hand range is very wide so you can often raise the bet and take the pot without further resistance.
'Playing the man' is essentially building a mathematical model of one's opponent internally inside one's head.
I'd settle for a robot that makes me a salad. That's one of the projects I might work on, once my current project, a robot that grows me a salad (automicrofarm.com), is successful.
Although Super System was written for all different types of poker, he is referring to no-limit holdem which still involves playing the player, with heavy math elements as well, but still much more psychology involved. Hence the name, you can bet any amount at any time changing the dynamic entirely. There is still no computer that is efficient at winning no-limit hold-em.
... and there won't be for a long time yet, as all hobbyist and academic efforts have been focused towards a consistently winning limit bot, because of the reason you outlined.
That said, if there's a mistake in there, a pro can eventually figure it out.
As you allude, the math of poker does break down in no-limit.
>Casino commissions, however, mandate that a gaming machine cannot change its playing style in response to particular opponents.
The algorithm is encoded in a neural net; there is no calculation of raw probabilities involved, at least in the sense programmers are used to.
This article is filled with bold claims by people that want to sell the idea IMHO. I'm not buying it because even limit texas Hold'Em has never been solved mathematically by super computers, let alone a single machine. Limit Hold'Em is close to being solved but if you check out the last match of pros against a supercomputer you'll find that it's close, but the computer is not a clear winner: http://poker.cs.ualberta.ca/man-machine/Competitors/
I'm just not buying it. Can it beat the average player? Probably. Pros do it everyday. But can it beat a pro consistently and claim a clear victory over humans? To be determined.
Edit: I found a take from High Stakes Limit Pro Anthony Rivera on 2p2: http://forumserver.twoplustwo.com/showpost.php?p=29762774&po...
His stance is that it's probably a break-even situation where you are basically playing another pro, and that he'd rather be playing craps. I guess they really have made a great machine. :D
I've thought long and hard on this, it's one of my life goals to create a piece of software that could mimic good players in texas hold-em, and I think I might have found a way to do just that using big data, hand histories, neural-networking, and a ton of input by actual players. Or at least a good start.
How would I accomplish this? Well a very high-level overview below. Basically it starts out extremely stupid and grows as a player:
1. Dump hand histories from pros into a large database. The number of hand histories would run into the billions. Users could dump online logs in bulk or create one-offs using input software.
2. Create an input system for a single user to choose a random hand-history and then classify it using tags. For instance tags might help categorize the player's style, the opponent's style, the "street" of play they are tagging, common name for the situation (Facing donk-bet on flop after raising pre-flop), etc. I would leave this fairly flexible and allow users to create new tags. Think similar to Galaxy Zoo but a little less rigid.
3. Using these tags/classifications the system would create a poll and present it to users with a question. What would you do in this particular situation? Where that situation is point in time of a hand history.
4. Eventually the computer player would then have a huge number of situations to use as examples with input from humans on how to proceed. This obviously will be very fuzzy and that's where, IMHO, the strength of the bot actually lies. The system would not lead to a rigid "Do X when Y occurs". It would decide from a large range of choices that have been entered by humans in the polls described above, leaning towards the most common answers first, but trying outliers also.
5. Use a neural network to create pathways based on previous successes.
How would this work once it's all together? An example:
The computer player is dealt AJ off-suit while being last to act on the dealer button. It would ask the database for a set of situations where AJ was dealt to players in the same position. It would then choose one of them and look at the results of the polls. How do most people with the highest success rate play this hand in this particular spot? Choose a random path to take based on that data. Observe and record outcome. This data becomes the true empirical data that the system will eventually rely on. If the situation has been encountered before in it's own play it will look at that and use it or it might choose randomly like it did above from the polling data. Eventually the weight of the empirical data it has collected might outweigh the data from the polls and it will "know" the right move based on its previous pathway choices. If this move is recognized by the opponent and exploited the results would dictate that the system falls back on another random choice. As the data set grows and the system plays the game, it could hypothetically be tuned to play consistently well.
The main hurdle is actually user-input. There would need to be incentive for users to enter the data they think is correct. The system is also open to manipulation through input data so that would need to be thwarted. And then on top of that the system would have to play an enormous amount of hands to create known successful pathways. But I think the sheer randomness and human-like qualities of the system would create a truly awesome experience.
(Joking) Now, does anyone have the $1M+ USD I need to fund this? I promise I'll pay you back. ;)
But I think it's worth looking at to only use hand histories and if possible only validate when something unexpected results. Maybe then I could use the human input to validate the computer's decision. I'm still hashing that out.
Is this even possible in a game of imperfect information?
Starting out you have 2 cards and you know your opponent has one of 2450 possible combinations of cards.
You know exactly how your 2 cards stack up in chances of winning against those 2450 combinations, and you know how much money is on the table initially. Each time an opponent has an action he can take one of two or three actions (call, raise or fold) - your job is to calculate a strategy that makes either of those decisions have the same expected value for your opponent. That is doable, but quite complex, because it requires you to consider not only what your opponent has, but also what possible hands you could have based on your previous actions.
The complexity is obviously enormous (hence why it hasnt been computed yet) but it is not impossible to compute by any definition.
http://www.econ.ohio-state.edu/jpeck/gametheory/gameL8.pdf
http://robotics.stanford.edu/~koller/Papers/Koller+Pfeffer:I...
It's a problem that is incredibly challenging.
Moreover, if we could, the opponent may choose a different strategy. It may be like a game with nontransitive dice: if you figure out which dice I use, you can beat me, but if I figure out that you figured that out, I can pick different dice and beat you (http://en.wikipedia.org/wiki/Nontransitive_dice)
I think it is possible to write software that statistically beats any opponent, but proving that it does is way harder.
The definition of solvable is "Does there exist a strategy that, regardless of opponents play, is not a losing strategy" though (because the game is symmetrical). It is not possible to solve for "Does there exist a strategy that, regardless of opponents play, guarantees maximum profits". You can solve it for not losing money, but you cant solve it for making the max amount of money.
Trivially it's not possible to write software that beats any opponent (because what would it do playing against itself?) . Less trivially, any game that has a finite amount of decisions (and limit hold-em does) has at least one Nash equilibrium, so there exists a strategy that will at least have you break even.
The way to solve the game is to calculate your odds of winning based on previous actions and ensure that you take actions that make any future decision of the opponent have the same outcome (to reach a Nash equilibrium).
That strategy hasnt been calculated yet, but the best limit players are most likely playing very close to it, at least if you compare to the best no-limit players playing no-limit (the variable amounts possible to bid in no-limit multiplies the possible strategies massively).
Given two strategies, you can determine which one is expected to win and by how much. That allows you to find the strategy that's hardest to take advantage of. In the case of non-transitive dice, the hardest strategy to take advantage of is likely to be "pick each die with equal chance".
That being said, solving these games is extremely expensive. Super-exponential in the size of the game, if I remember correctly. Way worse than games like chess. See this paper: http://www.sciencedirect.com/science/article/pii/00220000849...
Let's say for all the possible hand/board combinations and betting patterns you evaluate all of them (with current computing power this is not possible) then you can take the line that maximizes your value assuming your opponent maximizes his. Then you both end up close to even over a long period of play.
But it's even more simple than that: Nash equilibrium strategy says that you have to bluff 1/3 of the time on the river in a certain spot and have a highly valued hand 2/3 of the time.
It doesn't matter whether your opponent calls you or not. If he calls you too much, your value hands get paid off more often. If he doesn't call you enough, he loses too much to your bluffs. If the bet is the size of the pot, then he has to call one half of the time as part of his Nash equilibrium strategy to not get exploited. If he deviates, he will lose to the bot in the long term.
And since this is limit it's actually very simple. Bet sizes in regards to the pot are tiny (1/5 to 1/10 of the pot) and there is no having to choose the bet size or allowing for players to overbet the pot (make a bet larger than the pot)
No limit is a much bigger challenge than limit for computers, because a small edge in limit is too hard to exploit since you'll get tired of exploiting a computer for pennies per hand
The earlier part of the article (when it was full strength and in testing) has no mention of it being beaten.
Computers can easily calculate probabilities and expected values for every hand. So why they are not beating professionals?
Poker has no optimal strategy that wins against all other strategies. To play poker in higher level you must model the strategies of others, including them trying to model your strategy.
1. In the lowest level it's just maximizing expected value based on hand probabilities.
2. In the second level you try to learn the strategy of your opponents and maximize value against those strategies.
3. In third level you try to figure out how much your opponents have figured out your strategy and you change the strategy so that you maximize value when your opponents play against what they have learned from your strategy so far.
4. ... and so on. It' goes meta.
If you want to create ultimate pokerbot, it has to be able to model the minds of it's opponents. it hast to be able to detect leaks in it's own game and close them down. It must go meta all the time. It must learn how to understand how others think and how they think about it and change it's behaviour constantly.
Opponent modeling is purely advantageous, but not necessary
You can solve equilibrium for simplified poker games like just Heads Up with only shove or call an all-in options though.
It's theoretically possible to find Nash equilibrium over all possible strategies but that's not winning strategy. You just lose as little as possible. You lose against most/all strategies.
Take for example Kuhn poker (https://en.wikipedia.org/wiki/Kuhn_poker). It's very simple but first player has several optimal strategies.
* Q: What’s a Nash Equilibrium or “game theory optimal” strategy? – Failed Math, Port Perry, Ontario A: An equilibrium strategy is one that wins the most money possible against a perfect opponent (this does not mean an opponent who can see your cards, but one who always knows your range whenever you take an action and makes the best choice against that range). In the game “rock, paper, scissors,” the equilibrium strategy is to randomly choose between the three options, choosing each one a third of the time in the long run. Finding equilibriums in poker is much more complicated, but the concept can be useful when you’re playing lots of hands against tough opponents. For example, if your opponent bets half the pot on the river after a particular series of actions, the pot is offering him 2-1 on his bluff. If he were a perfect player, the right thing to do would be to call his bet a third of the time, since if you called more he’d exploit you by never bluffing and if you called less he’d exploit you by always bluffing. In reality, of course, our opponents are never perfect, and so the idea of playing an equilibrium strategy at the table is usually pretty academic. *
http://pokerpromagazine.com/proscorner/bryce-paradis/
You can certainly use Nash equilibrium when you have figured out the strategies your opponents are using. This is what Bryce Paradis is talking about. It can have practical value when playing Heads Up.
But If we are talking game theory and "solving poker", there is no single winning strategy that works against all other strategies and you can't calculate single Nash equilibrium that would be optimal in actual game against specific strategies.
Your opponent has 1352 different hand combinations. Assume he is playing the Nash equilibrium strategy. Make the perfect plays based on this. If he plays worse than the Nash equilibrium strategy, you beat him. If he plays perfectly, you tie.
Assuming your opponent plays perfectly works in chess. Chess programs are stronger than the best humans now.
You you can't do that assumption because you don't know what the strategy is. You can calculate Nash equilibrium only if you know the strategy your opponent is using. In full no limit hold em there is no single strategy winning strategy, so you don't know the strategy your opponents are using.
An optimal strategy’s goal is to loose the least against any arbitrary strategy. It is a strategy that is impossible to exploit in poker because poker has antes.
Poker players must seek maximal strategy. A maximal strategy’s goal is to win as much as possible against a specific strategy.
For example, you would raise more often when the antes are higher, regardless of the other player's strategy.
The optimal strategy beats everything but an equally good strategy, and ties against itself, but it doesnt necessarily maximise profits against other bad strategies.
If you are able to identify flaws in your opponents strategy then you can play non-game theory optimal to increase your profits against that perceived strategy. Doing so comes at the cost of you yourself no longer playing the best strategy though.
There exists strategies that gives higher yields vs certain unbalanced strategies than the game theory optimal strategy (or strategies - for all we know there are several optimal strategies in limit hold'em).
For instance - in limit poker if your opponent will never raise, call every street, but not call the river with anything less than a pair, regardless of what you do, then bluffing every river is a more winning strategy than the game theory optimal strategy. The game theory optimal strategy would include times when you do not bet the river, for balance, but knowledge of your opponent's flawed strategy would tell you that betting 100% of the time has a higher yield.
I'd like to add that how poker players generally define as their main goal, to maximize expected value: http://en.wikipedia.org/wiki/Expected_value
But ultimately, the whole enterprise just seems distasteful: "Look, there was a 24-year-old who had beaten it for a while. Now he’s broke. And I think this machine had something to do with his demise."
There's more poker situations than amount of atoms in the universe
Yet the article states that the machine has multiple personalities (passive, aggressive, etc) and will sometimes throw hands.
In other words, machines are allowed to shark $player, but not allowed to target John Doe specifically.
I will never forget the feeling of "you've got to be kidding me" when the code I had written was able to successfully classify a huge percentage of the validation image set. I really should head back in that direction and get with the machine learning.
Re: poker software. Before the feds crushed online poker, I had already given up on low-limit limit hold-em. It had clearly become a bot and augmented-player race. I would assume given game theory and Bill Chen's book that some enterprising hackers would encode pretty decent no-limit bots as well. If any hackers know anything about successful no-limit bots, I'd enjoy reading about it.
2. When this machine showed up ~2? years ago, there was a thread on 2+2 about it, and it would sometimes do some weird things like not value bet in obvious situations. They explain it in this article by saying it's, "playing dumb" but that seems like it would be a huge leak against Limit Hold'em HU specialists. I am guessing that they assume that they can make up for it in the weaker players losing consistently against this machine.
3. It is kind of annoying that the guy is proud that he "broke" a 24 year old player.