Researchers "Solve" Texas Hold'Em, Create Perfect Robotic Player 340
Jason Koebler writes The best limit Texas Hold'Em poker player in the world is a robot. Given enough hands, it will never, ever lose, regardless of what its opponent does or which cards it is dealt. Researchers at the University of Alberta essentially "brute forced" the game of limit poker, in which there are roughly 3 x 10^14 possible decisions. Cepheus runs through a massive table of all of these possible permutations of the game—the table itself is 11 terabytes of data—and decides what the best move is, regardless of opponent.
I guess that means ... (Score:5, Funny)
...they got banned by 6241 online casinos and bragging here is the only thing left?
Re:I guess that means ... (Score:5, Insightful)
Re:I guess that means ... (Score:5, Insightful)
Maybe so, but a lot of online casinos have some reason to kiss their feet. You see, a lot of countries have laws against "gambling", which is usually defined as playing games for money where luck is the deciding factor.
And these people just proved that luck plays no role.
So playing poker is no longer gambling. Scientifically proven.
Re:I guess that means ... (Score:5, Interesting)
What happens if someone else creates an identicly perfect robotic player and joins the table? If, as the researches claim, winning limit Texas Hold'em is a directly solvable problem then anybody else who tries to solve the problem will come up with the exact same solution.
If these two robots played each other wouldn't the winner be determined by pure luck?
Re:I guess that means ... (Score:5, Informative)
"What happens if someone else creates an identicly perfect robotic player and joins the table?"
Not that I know so much about Texas Hold'em but, by the look of the text, "...Given enough hands, it will never, ever lose, regardless of what its opponent does or which cards it is dealt." these researchers have discovered the equivalent of a Nash equilibrium in the game.
"If these two robots played each other wouldn't the winner be determined by pure luck?"
Key words here are "given enough hands". This means that given enough hands, they would tie.
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Re:I guess that means ... (Score:5, Insightful)
Casinos take a small amount of money out of each hand, the "rake". So if two perfectly matches robots play, the casino wins, as they slowly bleed all the money away from them both. These guys could have saved a lot of time. If you want a poker game where you always win, all you have to do was is the casino.
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A strange game. The only winning move is not to play.
How about a nice game of chess?
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The issue is that ignoring the betting element of poker when claiming a system is perfect or optimal is nonsense. A 'perfect' poker system would need to be able to decide based on opponent behaviour etc the right amounts to bid to minimise losses and max
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And these people just proved that luck plays no role.
A perfect player at a table with nine other players, when the perfect player is being dealt rags consistently (based on luck -- poor luck), and the others are being dealt good cards, will lose despite being perfect. Being perfect only means that he'll lose at something less than (10*ante + big blind + small blind) per round, since there is a chance a bluff will succeed. The chance that the bluffs will succeed depends in large part on ... luck. Luck that the opponents have hands that they can be bluffed off
Re:I guess that means ... (Score:5, Insightful)
This doesn't prove it at all. You shouldn't have been modified +5 Insightful. Over the course of a game, luck is very important. Like you get dealt the card you already have, or you get dealt crap.
Blackjack also has a perfect strategy, and of course blackjack has a great amount of luck.
I guess if you planned on playing an infinite amount of games, luck wouldn't be a part of Texas Hold Em. For somebody playing a finite amount, luck is key.
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...they got banned by 6241 online casinos and bragging here is the only thing left?
The problem with online casinos (the ones that are not regulated) is that if the online casino decides you're winning too much, they can just decide to make you lose when you're betting the most (this has actually happened a lot).
It's just like three card Monte, it looks like it's an easy game to beat when other people are playing it, but unbeknownst to you, those other people are friends of the dealer, and the game becomes rigged for you to lose when you start playing it.
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what is ridiculous is that the so-called "researchers" were on the radio today here in Edmonton, and made the bizarre claim that their system could be converted to deal with terrorism by just programming in terrorist scenarios that their software would then solve...
hello defense spending budget!
Perfect? Really? (Score:5, Interesting)
Re: Perfect? Really? (Score:2, Interesting)
It's called playing game theory optimally. You can make decisions that are profitable OVER TIME no matter what your opponent does. An important caveat is that when opponents make mistakes, the game theory optimal approach may be LESS profitable because you assume your opponent is playing correctly.
Most importantly, no one is even close to solving no limit -- where you are allowed to vary your bet size. That changes everything.
Re: Perfect? Really? (Score:4, Insightful)
To the average joe poker player, I'd say what's most important here is that the perfect solution is only for a two player game.
Things become much more complicated when players>2.
Re:Perfect? Really? (Score:5, Informative)
The thing about this robot is that it only wins over time and many hands. The best you can do with another robot is to tie. But that's all in the long run and assumes you have deep enough pockets to keep playing through the losing hands. The odds don't hold up for individual games played in isolation. Texas Hold'Em is very dependent on the draw of the cards and that randomness makes it impossible to win every time. This robot won't win every single hand so it's maybe not so hard to beat in the short term over a few hands if you get a lucky draw. But in the long run it will win (or tie if it's playing another robot).
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The thing about this robot is that it only wins over time and many hands...
Indeed. The finite probability of long term loss never goes to zero no matter now perfectly the odds are played, so "never, ever lose" is grossly inaccurate.
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The best you can do with another robot is to tie.
Poppycock. Pure nonsense.
Another bot with the same 3 x 10^14 possible decisions could beat it over time based on play-style alone.
What's your decision tree say to do here when you're check-raised? Oh, it says fold? I've discovered that? Guess what happens now...
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What's your decision tree say to do here when you're check-raised? Oh, it says fold? I've discovered that? Guess what happens now...
Exactly. If you can predict what your opponent will do in poker, you can win easily.
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You're underestimating how big 3 x 10^14 is.
Your "here" is in a specific game state. That's current game state. It probably won't come up again unless you play another 3 x 10^14 games.
Re: Perfect? Really? (Score:4, Insightful)
Uh, if you can't see my cards, how would you have any idea what my decision tree said?
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As others have said, there's no way for you to know what the other player (in this case the other computer) holds, so you can't have any additional data with which to make a different decision. All you know is whether they bet, call, raise, or fold.
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As others have said, there's no way for you to know what the other player (in this case the other computer) holds, so you can't have any additional data with which to make a different decision. All you know is whether they bet, call, raise, or fold.
I had friends over for Texas Hold'em last night. When I picked up my chips as though I was going to raise substantially, I watched his face in the reflection off the glass table, and when it twitched towards a smile for a split second, I knew he had the straigh
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Wouldn't another robot which knows of all possible decisions of this particular robot be better that this "Perfect Robotic Player"?
No, the best that should happen is they both win the same amount after a large number of hands (note the phrase "given enough hands" so the law of large numbers is involved). Since the decisions are based on probability given the known cards (or so I assume since I haven't read the article), any decisions by the second robot trying to beat the first that went against the probability tree would be sub-optimal and cause it to slowly lose.
Re:Perfect? Really? (Score:5, Informative)
Mathematically speaking, all these games which are based around predicting what your opponent might do (and possibly a random factor, like in poker) have a perfect strategy, but that perfect strategy has random factors. For instance, the mathematically perfect strategy for rock/paper/scissors is to pick "rock", "paper", and "scissors" each with 1/3 probability. There is nothing an opponent can do to get more than a 50:50 chance of beating this strategy.
Rock/paper/scissors is unusual in that the game is symmetrical: a perfect strategy can't get any better than 50:50 against anyone. That's not true of poker, though; in such a case, a perfect strategy will have a better than 50% chance of beating anyone who plays imperfectly, and a 50% chance against a perfect strategy (due to symmetry).
I'm actually quite interested in the theory of this sort of game (where there are random factors and outguessing opponents involved), and even in simple cases, the calculations can be hard. I'm reasonably interested in whether this poker strategy is a probabilistic one (that can't be outpredicted as long as the random number generator used is sufficiently high-quality), or whether it just takes the best option without randomizing (which is much easier to implement, but which can be outplayed via knowledge of the algorithm like you suggest).
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the difference is in poker you can use intuition and body language to very your bets higher or lower than what the simple odds are.
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Rock/paper/scissors is unusual in that the game is symmetrical: a perfect strategy can't get any better than 50:50 against anyone.
That's because the perfect strategy is suboptimal. Play with someone. Watch them. When they go scissors, are the more or less likely to go with scissors the next time? If you can find patterns and probability in the others, then you can get better odds than "perfect". "Perfect" only is perfect against other perfect players, otherwise, there's likely a more optimal choice.
Re: Perfect? Really? (Score:2)
according to the summary, this research used brute force, which means the must have simulated all possible permutations for each given situation.
then, whichever outcome with the highest expected value would be chosen. since they had already solved it. the robot might just be looking up the opimal call for any situation from the database.
so there might be no probability calculations at all, just lookups.
this is a big handicap, because if you know the robots mind, you also know what cards he has, based on h
Re:Perfect? Really? (Score:5, Insightful)
Wouldn't another robot which knows of all possible decisions of this particular robot be better that this "Perfect Robotic Player"?
There may still be ways to beat it. For instance, two or more opponents could collaborate. So someone with a poor hand could be running up the pot so his teammate can win. Just knowing the odds isn't enough, because all bets are not for the same amount*. If your opponent suddenly makes a big bet, what does that mean? He could have a hot hand, he could be bluffing, or he could just be trying to run up the pot. Without some knowledge of the guy's history, and his relationship with the other players, it is hard to say. I play very differently against my amateur coworkers on "poker night", than I would against a pro in Vegas. Amateurs are way more likely to bluff, or stay in the game with a mediocre hand.
*I just RTFA, and I now understand that the robot plays a limited game where only certain fixed amount bets were allowed ... but that really means they didn't solve it, because that is not how real poker is played. Also, it looks like it only plays one opponent, rather than at a table of four. So this is like solving "queens and pawns" and claiming you have "solved chess".
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Limit hold'em is real poker, and people actually do play it, at real casinos and everything.
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Limit hold'em is real poker, and people actually do play it, at real casinos and everything.
Meh, it's nothing more than advanced blackjack... In real poker, you don't share cards with your adversaries, have wildcards, etc... This "hold'em" poker is just a bunch of tripe to make things look ok for TV.
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The beauty of Holdem is how easy it looks. But don't kid yourself, it is real poker. Two minutes to learn, a lifetime to master. It draws in less skilled players because they think they can play this easy game as well as anyone else. Then they slowly get bled dry.
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What do any of those things have to do with limit hold'em?
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Try actually playing the game, preferably against a highly skilled player. You might just discover that it is a lot more complicated than you think it is. Sharing cards is one of the things that allows skilled players to excel. BTW, there are no wild cards in hold'em.
Seriously, play the game and see for yourself. I would love to have such a clueless opponent.
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Re: Perfect? Really? (Score:2)
exactly. as a poker robot, it is rather useless. it would make some money in heads up limit against weak amateur players. it would lose big against PRO players, because it has a tell. the tell is that he plays optimal poker, which means we know what hand he has. he will never fold has 2 pair aakk if we can convince him we hold qqq, even tho we only hold 2 7. and contrary to popular belief, in limit poker you have to force yourself to even more gut wrenching aggressive play than in no limit poker. you have
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If you can say, "oh, the computer just bet $100, that means it thinks it has a 73% chance of winning," you can look at your own hand, and say, "I have an 82% chance of winning, I'll stay in." The computer not only has to be able to bet and fold, it also has to be able to hide its actions from its opponent. Also note that it only calculated the strategy for a two player game, obviously the odds change with more
Rock paper scissors (Score:5, Insightful)
You can better understand what is going on by considering the much simpler game Rock paper scissors. 'Perfect' here basically means the strategy gives you the best possible worst case.
For RPS, the perfect strategy (using the term in the same sense as it is used for the poker bot) is to play completely randomly. There is no way to gain an edge over this strategy, no counter-strategy which will give you more than 50% chance of winning, even if you know your opponent's strategy. (In this case, there is also no strategy which will give you less than 50% chance of winning against the 'perfect' strategy.)
For the poker bot, there is no strategy that will give you greater than 50% chance of winning against it in a two player game. If you know its strategy perfectly (but of course you don't know its cards) the best you can do is to equal that 50% chance (which is what happens if it plays itself.) Unlike RPS, you can can lose to the perfect poker bot by playing poorly. Also, as noted in the article, the perfect poker bot always plays as if it were playing against perfect opposition. A good human player will fleece you faster then the perfect bot, because the human player will notice your peculiar imperfections and exploit them, choosing to play in a way which would be suboptimal against a perfect opponent, but superior against you.
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umm, no, you have never played poker before in your life. you play the people, not the cards. you rely on visual and verbal cues to guide you on when to hold 'em and when to fold 'em. In fact, this robot would be very easy to beat because its moves would always be predictable. it will never bluff
Re:Perfect? Really? (Score:4, Interesting)
"Tells," for short, are hardly the end-all be-all of poker play.
Further, a well written poker robot would bluff a certain percentage of hands.
My only objection with the computer picking the best play strategy for 3 x 10^14 possible decisions is that in exactly the same situation, the right move would be, often, to make different choices, especially based on the makeup of the table, how your previous hands played, how the table reacted to those hands, etc. "Regardless of what its opponent does" leaves me skeptical.
I have no doubt that this can beat the field and win at poker. Bots have been doing that forever.
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They have found a non-exploitable strategy, not a maximally exploiting one.
This strategy will win less from an imperfect opponent than a strategy which maximally exploits that opponent's weaknesses. However, there is no strategy which can exploit a weakness in the strategy they have developed.
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We are talking about limit poker here. Bluffing doesn't really come into play.
Wrong. Either you've never played, or you've never played against anyone good.
If visual cues are such a big part of the game, how come most pros can go back and forth between online and live play with no real difference in performance?
Citation required. Nobody I've ever heard talk about it says this is true.
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Like there would likely no absolutely no situation that the robot would ever show a folded hand, not true for humans.
In other words, if it plays against idiots, it can win.
No such thing in real gambling (Score:2, Insightful)
Re:No such thing in real gambling (Score:5, Informative)
That is why it is limit poker. Besides all games have limits acknowledged or not.
Think of the robot as the house, it might not win everytime but it always wins in the long run.
Re:No such thing in real gambling (Score:4)
That is why it is limit poker. Besides all games have limits acknowledged or not.
Think of the robot as the house, it might not win everytime but it always wins in the long run.
But that's exactly the point. They didn't solve anything. So it plays the cards perfectly, but that's not the game. If the human walks in and due to chance gets several great hands in a row, then gets up and walks out, the robot doesn't win. They say right in the article "Given enough hands" well that's the entire point of the game! You don't give the opponent enough hands to win. Quit while you're ahead? There are so many gambling sayings that cover this very topic, I don't think I could remember them all. There's even a damned song about it!
You've got to know when to hold 'em
Know when to fold 'em
Know when to walk away
And know when to run
You never count your money
When you're sittin' at the table
There'll be time enough for countin'
When the dealin's done
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"They say right in the article "Given enough hands" well that's the entire point of the game! You don't give the opponent enough hands to win."
So you just played once, but still playing once was enough to master the game, you won by chance and then you don't return to the game never again?
Correction: you _may_ not give AN opponent enough hands to win, but of course you return to the game. That's what pros do, after all: they win sometimes and lose sometimes, it's only they tend to win more than lose. That
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The definition of "No Limit Poker" is a poker game where any amount up to the amount you have in front of you can be bet at any point of a betting round. If all of the chips you have are present, you are "all-in" and can multiply your stake times the number of people who called you if you win.
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Limit Poker is like having a low bandwidth connection the betting compared to No Limit. In No Limit, a player can pick any point they can make with chips win a minimum usually enforced. In Limit Poker, the player must either Bet the first increment amount, call exacttly the current bet, Raise to the exactly next the increment, or Fold and that means there's less stops in the option. Imagine the "Drag-able progress meter" in some online poker interface, it has much more stops in No Limit than Limit.
A bot is
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Sorry I can't agree that it will always come out on top, the flawed assumption here is that it is playing against something or someone that are making sufficient number of mistakes to profit from. It is also playing from incomplete data, so while it can always make calculated decisions based on odds, that is not always the correct decision in poker.
Re:No such thing in real gambling (Score:5, Informative)
From the article: "So, is online poker now dead? Destined to be crushed by robots? Not quite: No limit Texas Hold'Em—in which any amount of bet in any dollar amount can be made—is by far the most popular, and while robots can play that game quite well, we're no where close to solving it. Limit poker has roughly 3 x 10^14 permutations; no limit poker has 3 x 10^48, which is many orders of magnitude harder to solve."
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Bets (Score:5, Insightful)
Recently I noticed that Texas Hold'em is only half of the game. The betting is the real strategic part. Unless the bot can do this well, I don't it will ever really "beat" a human player.
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Recently I noticed that Texas Hold'em is only half of the game. The betting is the real strategic part. Unless the bot can do this well, I don't it will ever really "beat" a human player.
If it can beat the game and win more time that it loses by simply playing chances optimally (or force a draw), then it can basically get the same benifits as the house; always winning over time.
I didn't think that would be possible with Poker, and would love to see that in practice, but it is what they claim.
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Yep, poker, like most casino card games, are a mix of luck and strategy. Whoever is trying to convince us robots are better than humans is trying to sell us something inferior.
Re:Bets (Score:5, Interesting)
In limit poker there is more often a correct play. The odds would dictate, in a large pot to call that last bet because it is only a fraction of the pot. As long as your pot odds are better than your card odds it is correct to call, even if you only have one or two outs. In no limit where you can adjust the size of your bet, the correct bet is to give your opponents worse pot odds then their card odds. No bot can ever master no limit, it's not a card game at all. it's a people game played with cards.
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A bot might eventually master 2-player no-limit (and this one is only optimal for 2-player limit, right?). The bot and the human will have equal luck in reading one another. A more sophisticated bot could detect common betting strategies, and play common bettering strategies, and switch strategies at a critical moment, again making it on par with the human trying the same trick to fool the bot. But 2-player poker is odd to begin with.
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Any good poker play knows that "playing the opponent" is only a small part of playing poker.
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If you don't know what I am talking about, buy any good book on poker theory.
I am not saying anything other than what Jennifer Harman is saying, and she is considered one of the strongest limit poker players in the world, and wrote the chapter on Limit Holdem in Doyle Brunsen's Supersystem 2 book.
So let me toss that ball back to your court and ask why you think you know better than one of the best? Or if you were just guessing that you had an idea about proper Limit Holdem strategy.
Also, that it is LIMIT,
Nonsense! (Score:2)
First, robots can't play poker. Computer programs called "bots" are hated by online poker sites. They're fun for an offline game like Poker Academy, but they don't play perfectly.
How do the creators of this thing say it's perfect? When handed the lowest hand in the game, how does it not lose? Bluff too badly and that's a loss This makes no sense to me.
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How do the creators of this thing say it's perfect?
They have computed every possible game of limit hold'em poker. Based on these computations, the bot will always pick the optimal hand for the given situation (or possibly fold). Yes, it may lose a hand here or there, but the point is that over the long term, given enough hands, it will always beat imperfect (read human) players.
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bot will always pick the optimal hand
You don't get to pick your hand in poker, and your max win is controlled by how much the other players bet. There's billions (more than 32 bits) of combinations between 20 down cards (2 per player) and 5 community cards under Texas Hold 'em rules.
is it useless? (Score:2)
thats the time limit on most online tables
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But can it hold its liquor? (Score:2)
Yes, but... (Score:5, Informative)
I'm a former professional poker player, now semi-pro and working again in the IT industry. In a game like poker, to "solve" the game, from a mathemartcal and game theory point of view, means to develop a strategy that is "unexploitable", which basically means "mistake free". If two game-theory perfect players were to play against each other, then their "expectation" would be zero, as if they were flipping a coin between each other. Neither would make a mistake, so only te randomness of the cards would determine the winner of a given hand. In the long run, both perfect players would win as often as they lose.
But in a real poker game, human players make lots of mistakes. A player who adjusts their strategy to exploit these mistakes will win vastly more than this (formerly theoretical) "perfect player". The game-theory optimal strategy is focused on not losing, rather than exploiting mistakes and winning the most.
So in an actual game, the expert human player will outperform the computer because the other humans in the game are exploitable.
In live play, especially in tournaments, computer solutions are used in poker. In particular, when the game is "heads up" (only two players), and the chips are not deep, which happens at the end of every tournament, then the correct strategy is to "jam or fold" all hands. The solution to this has been determined in a computer and top players have the table memorized.
If this subject interests you, I HIGHLY recommend "The Mathematics of Poker", by Chen and Ankenman.
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But in a real poker game, human players make lots of mistakes. A player who adjusts their strategy to exploit these mistakes will win vastly more than this (formerly theoretical) "perfect player". The game-theory optimal strategy is focused on not losing, rather than exploiting mistakes and winning the most.
In real life, the human player can feign a mistake as well. So you aren't playing the cards, but the person.
I'm not a poker player, but I am a bridge champion. The bridge techniques for humans guess the locations of cards based on where they are likely to be. There's also guessing where the cards are to guess what the opponents will bet (as bets are exclusive and competitive). Full knowledge of all the cards lets you make the perfect bet. So you communicate with your partner via your bets, and try t
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In particular, when the game is "heads up" (only two players), and the chips are not deep, which happens at the end of every tournament, then the correct strategy is to "jam or fold" all hands.
I never understood this. It just seems to ruin the game. Can you elaborate?
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Whether it ruins the game or not is not relevant: It's just optimal strategy at the very end of a tournament. 2 players, and there are only two outcomes: The tournament only ends when one player runs out of chips.
So you are sitting there, with your cards. At any time, the other player can go all in. He can do that to start, or he can do that after you bet something. In either case, you either match, or fold. If you bet a small amount, then either it doesn't matter (if you call), or it does, negatively to yo
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So in an actual game, the expert human player will outperform the computer because the other humans in the game are exploitable.
No, it won't. Read the article. The game they solved is heads-up limit hold 'em.
There will never be other humans in the game. That's not what they solved.
Ok, so it knows Texas Hold'Em... BUT (Score:3)
...does it know when to fold 'em? When to walk away? When to run?
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...does it know when to fold 'em? When to walk away? When to run?
Yes, it does. However it inexplicably insists on counting its money while it's sitting at the table, even though there's time enough for counting when the dealing's done.
Perfect poker strategy... uhm, maybe. (Score:2)
Always bet and win with the high hands, and fold when you do not have the highest hand.
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Not that simple. A good player will win with the worst hand at times. A good player will also sometimes fold with the best hand due to uncertainty and risk management. Good players sometimes fold to a bluff for perfectly good reasons. They also sometimes bluff and lose. But, the good player will learn from these decisions so that they make better decisions next time. You never know what your opponent holds, but you try to understand their strategy over time to exploit their play.
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My post was a joke... it's similar to a "Score more points" way of winning games.
obligatory (Score:2, Funny)
Lookup when to fold 'em
Lookup when to walk away
Lookup when to run
You never lookup your money
When you're sittin' at the lookup table
There'll be time enough for lookups
When the dealin's done
Poker isn't really about math (Score:2)
It's about psychology: guessing what your opponents hold, whether you can beat what you think they hold, or whether you can bluff them into folding.
I'm betting that a good human player could pretty quickly learn how this bot plays, and learn how to react to various scenarios to defeat it...regardless of the math.
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Hmmm... I'll take that bet.
Theories put to the test (Score:2)
Pretty useless research (Score:2)
heads up limit Holdem is something you in practice never play, unless you are in the last table in a limit tournament.
besides, being able to beat or play even with the perfect player will in fact make you broke in the long run. the casino rake will clean you out , it is just a matter of how many hands.
the only claim to fame this robot could make is that it is the best ever limit heads up novice. there have been plenty of pokerbots before, making good money, playing low stakes online poker. it does not take
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Yep... big blind plus losing hand means you've got to get all the other players to fold, or that's a loss.
There are already 4 computers that beat it easily (Score:5, Funny)
And then there is the computer that deals the cards and takes 4% of the pot every round, muttering "House always wins".
The third computer that can beat it keeps giving it complimentary alcoholic beverages until it gets a buffer overrun.
The fourth computer doesn't "believe in no win situations" and reprograms the computer to lose, but then Spock finds out and he gets kicked out of the Academy.
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There is no way to perfectly play a fair game of poker. You don't get to see mucked cards... so you have no way of knowing if you blundered unless you go to the showdown and lose.
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This is like the "Let's see what would have happened if you didn't quit..." round of some game shows. In poker, you can't find out if you would have won if the hand was bet/folded differently, so how do you confirm you're "perfect"?
Since there can be as many as nine different strategies around you, how do you perfect your game?
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It already isn't. One of my friends is a pro-player, and he says that it was never allowed anywhere close to tournaments - not because of being singled out, but because it is banned by at least two different, preexisting rules.
Poker is far from the only gambling activity that could be helped a lot by a computing device. Hell, there are rules against doing math in your head, let alone an app.
Rake: a 4 percent tax on pot (Score:3)
even in a fair game, the house wins.
Not always. Poker isn't played against the house; it's played against other players. The house just gets about 4 percent of any pots that flop [wikipedia.org].
Blackjack is the other casino game that can be "beaten". It's played against the house, but the house plays like a robot, and its only advantage is that it takes double busts (hands where both the the player's cards and the dealer's cards total more than 21). The player has plenty of advantages, including double payout for player A-10, the "insurance" side bet on dea
Re: (Score:2)
Adverse selection (Score:2)
When there's no mandate, people will buy insurance if they see their situation as particularly risky. It's called adverse selection [wikipedia.org], and you can make it work for you in Blackjack.
Insurance [wikipedia.org] is offered when the dealer shows an ace. It's a 2:1 bet that the dealer's hole card is 10. On a fresh shuffle of multiple decks, this is a loser because only 4 out of every 13 cards are 10. But if you can prove a high proportion of 10s left in the library, more than one-third of the remaining cards, it becomes advantageou
Re: (Score:3)
Poker, for humans, is luck and psychology in the main. It's about convincing the other guy that your hand is better/worse than it is.
But the problem is that if you're playing against a robot, he doesn't care what you want him to think. He knows exactly what the odds are of you having any particular card, and what that means in terms of him beating you. Playing the odds will win on average. It's how it works. It's how casinos get rich enough to have marble floors and air conditioning in the middle of th