party poker

2005-06-23T04:44:00.000-07:00

Poker party on bourse
AMIT ROY
London, June 22: Anurag Dikshit and Vikrant Bhargava, the two batchmates from IIT Delhi, are selling part of their stake in PartyGaming, the online poker company, in the biggest Initial Public Offering (IPO) witnessed by the London Stock Exchange for four years.
They are selling 23 per cent of the shares in PartyGaming, which runs the immensely successful online Party Poker website, on which up to 70,000 people from all over the world can play at one time.
The shares, on offer to institutional buyers, are valued by the company at between 111p and 127p. This would put a value on the company of between £8 billion and £9.2 billion.
Dikshit, 34, the group’s operating director, has 40 per cent of the shares and 33-year-old Bhargava, the marketing director, 17 per cent. Even if the lower sale figure is achieved — and PartyGaming seems confident it will — they stand to make £736,000 and £312,8000, respectively, from the sale.
The precise share price will be fixed on Monday and trading on the London Stock Exchange begin on Thursday “when you and I and other members of the public will be able to buy the shares through a broker”, a spokesman for PartyGaming told The Telegraph.
The company hopes a listing will give it added credibility, especially as the Americans have laws which outlaw online gambling.
“The book is covered,” the spokesman added. This means that institutional buyers, who are the only ones allowed to purchase the shares at the moment, have told PartyGaming they are prepared to buy all the shares on offer. However, there is some haggling going on over whether PartyGaming has overvalued them.
Describing the way the game is played in cyberspace, the spokesman said: “Party Poker is a website and 10 people can gather round a virtual table. Party Poker makes its money by taking a small slice from each pot — the rake, in the jargon. The players could be from anywhere — a girl in Australia could be playing with a man in Australia.”
But not from India.
One of the ironies of PartyGaming was revealed today. “Ninety per cent of our employees, totalling 950, are in India, based in Hyderabad,” said the spokesman.
However, due to government rules, Indians in India are not allowed to play.
The PartyGaming IPO, which will probably take the company into the FTSE listing of the top 100 companies, has caught the imagination of the financial world.
For tax reasons, Dikshit and Bhargava live in Gibraltar, the “European Kashmir” whose ownership is fought over between Spain and Britain. The weather in Gibraltar is pleasantly Mediterranean but there cannot be too many distractions on which to squander their easily acquired fortunes.
The two Indians keep a relatively low profile. The best that the Financial Times could muster up in a recent profile is the revelation that Dikshit “always smiles a lot when he talks”.

How Legal Is Your Poker Party?

2005-06-09T00:57:00.000-07:00

Up Close: How Legal Is Your Poker Party?December 21, 2004
The Kenny Rogers song says "You got to know when to hold 'em, know when to fold 'em".
It's wisdom that might hit home with poker players who are gambling here in Houston for real money.
But isn't that illegal?
It's poker night, but this isn't Las Vegas. It's not even Lake Charles.
This is the Seabrook Beach Club on Clear Lake.
It's real poker for real money, where first place will get you at least $2,500.
Poker, especially a version called Texas Hold 'em, is suddenly hot.
Why?
Virtually any night you can watch it on ESPN's coverage of The World Series of Poker.
ESPN has now started not only broadcasting million-dollar tournaments, it's about to debut a drama about high-stakes gambling.
Poker is suddenly out of the backrooms and into the mainstream. On any given night, dozens of bars around Houston are running tournaments with thousands of dollars at stake. But is it legal?
"If you break the law, you break the law," says Robert Burby of the Texas City Police Department. "It's just the way things are done here in Texas City."
A few weeks ago, police in Texas City raided a nightclub, ticketing some 80 players and charging the owner with violating the state's gambling laws.
He told, he'd checked with local officials and believed his poker tournament was a legal way to drum up business. But according to prosecutors, Texas law says gambling is only legit in private places and not in nightclubs or bars.
The Harris County D.A.'s office flatly says the only place you can play poker for money legally in Texas is in the privacy of your own home.
That is an interpretation not shared at the Seabrook Beach Club.
"We come as club members," Mark Liszewski, club member. "We come to play a game."
The poker room is separate from the rest of the bar and players have to register as members making it a private place according to the management. In a strip mall in nearby Webster, we found more games in progress.
Rick Garren retired from professional wrestling to open what he calls Big Slick's Social Club devoted solely to poker. Garren says by keeping it members only and making money only from entry fees, food and soft drinks he's legal.
Garren says playing poker like this is a far cry from clearly illegal games played in smoky backrooms where the house takes a cut of the pot.
"If you play in an underground game, you don't know if you're gonna get paid, you don't know if you're gonna get robbed, you don't know if the place is going to get busted, I mean there are just so many things that are dangerous," says Garren.
For now, these games go on, but experts say it might take a change of Texas law to make it clear whether they're truly legal or not.
State alcohol officials in Houston say they routinely investigate bars for having illegal video and slot machines. But they say Texas Hold 'em is a new concept in gambling and that for now, they likely won't take action unless the District Attorney decides it's an offense.

How Legal Is Your party poker

2005-05-24T23:07:00.000-07:00

Tips to make a party out of your poker game!

2005-05-13T11:46:00.000-07:00

Tips to make a party out of your poker game!

Trembling Hands
Also, a byproduct of anxiety, beware of a player whose hands are shaking, this nervousness can represent a big hand.

Glance at Chips
Again, relating to the eyes. It is common for players to quickly glance at their chips if they connect with the board after a Flop for example. This may be a subconscious reaction, but the player is already planning his attack.

Peeking Hole Cards on Flop
Some players will take another look at their hole cards when, for example, the board is showing a potential 3 card flush draw. Typically, the player is looking to see if one of his cards is connecting, because he remembers only that the two cards are different suits.

Poker holding on to a winning hand

2005-05-12T09:29:00.000-07:00

Poker is, according to its adherents, the biggest growth area in sport this side of Jose Mourinho's ego. The blossoming of the game on the internet is such that poker millionaires are old hat: the most popular websites, who started the party only three years ago, billionaires. And television has now caught the wave.
There is not so much a rash of poker on the satellite schedules at the moment as a raging contagion. Just this week we were treated to the European Championship final on Eurosport, the conclusion of the British Open on the newly established Poker Channel, plus, on Sky, the Poker Million, in which - though you've probably guessed this from the title - the prize on offer is $1 million.
This being British television, first on to the Sky table in pursuit of the big one were a bunch of celebrities.
"This is a better line-up than Celebrity Big Brother, you're in danger of actually knowing who some of these people are," said Roy 'The Boy' Bradley in the commentary box as the celebs were unveiled. He wasn't wrong. Though since we've all seen John Regis panicking in a canoe on Superstars, Bradley might have chosen a better metaphor to introduce the former Olympian than "he's taken to this game like a duck to water".
As the inverted commas around that 'Boy' of Bradley's name suggests, it appears to be a contractual requirement to come to a poker table equipped with a nickname. Phil Taylor, the world darts champion, thus had a head start, arriving with
'The Power' tucked under his arm. Matthew Stevens, the snooker player, though, may have been less than enamoured to be gifted 'Shady', while Helen Chamberlain of Sky's Soccer AM must have wondered what she had done to deserve 'Hell's Bells'.
Worse was to come, however, when Bradley described her style of play as "more relentless than the Duracell bunny". It didn't seem to do her any harm, as in the final play-off she beat Barry 'No Nickname Necessary' Hearn. It was brave on her part to ignore the adage about always ensuring that the boss triumphs at the office golf day; Hearn is also the promoter of the competition.
Even if he could have squeezed past Chamberlain, the snooker impresario and Leyton Orient chairman seemed particularly chuffed to have disposed of a table full of sportsmen.
He thus precisely fitted the thesis proposed by journalist Matthew Norman, commentating on the British Open final for the Poker Channel, as to why so many people are picking up the cards and seeing if their pair of twos can out-run their opponent's royal flush. "When you get to 40 you realise you'll never play for Spurs," Norman said, "nor will you score a century for England. But you could find yourself playing poker on the same table as the world champion."
Which is what happened to former Daily Telegraph journalist Matt Born, who qualified for the Open via the internet and fought through the early rounds to find himself under the deathless gaze of the world title holder, Greg 'The Fossilman' Raymer. Born was hooked up to a heart monitor to see how he was coping. While Raymer's rate barely registered a flicker as the two went head to head, Born's raged so high he looked destined for a coronary. "That's why this is a sport," claimed the Poker Channel's resident expert, Carlo Citrone. "You've got to have the endurance ability of a marathon runner." It was lucky Born was wearing shades: if we could have seen his eyes at that point they might well have been popping out of his head.
According to Norman, the reason so many of the players wear dark glasses is "a gangster fantasy". He reckoned every one of them, as they stick, turn, raise or fold, are under the impression they are living through the poker scene from Reservoir Dogs.
A neat theory which was somewhat undermined by the interview with the winner of the Open, Adam Dujmovic. Asked how he might spend his £100,000 first prize, Dujmovic replied: "The first thing I'm going to do is take my little girl to Disneyland."
Meanwhile, Kevin Seeger, the man who came third in Eurosport's European Championship final and who describes himself as a "full-time, stay-at-home dad", explained that he would spend his winnings on "getting the garden landscaped". Its fans are right. It is some progress poker has made: from the louche to the suburban in one easy step.

How is a 3 Card Poker Party Different?

2005-05-11T09:11:00.000-07:00

How is a 3 Card Poker Party Different?

Three card poker differs from other poker games in many ways. Firstly, at 3 card poker parties beer is out. At 3 card poker parties, tequila is in. Secondly, at 3 card poker parties there is a dress code. No undershirts are allowed at 3 card poker parties. 3 card poker players are serious, yet friendly, casual, yet elegant. 3 card poker parties are quiet and subdued but intense. Not everyone can participate in the 3 card poker party. Only those who fit the criteria can come and enjoy an evening playing 3 card poker. So if you like tequila, like to wear a shirt over your undershirt, join the 3 card poker party nearest you.

Learn Poker Party Jokes!

2005-05-07T15:46:00.000-07:00

Learn Poker Party Jokes!

Poker Players are Never Satisfied
A tinker and his dog enter a bar and discover there is a poker game going in the back room. The tinker's had a good week so he decides to join in. Most of the players are locals, but one guy, a big winner, is also a stranger in town. The tinker does OK - up a little, down a little, generally holding his own. His dog sits on a chair beside him and watches the game. About an hour into the game, the tinker gets a good 7-stud starting hand. On fifth street he makes a club flush. Unfortunately the stranger appears to be working on a spade flush and his highest up card is bigger than the tinker's highest card. As 7th street is being dealt, the tinker pats his dog on the head and says, "Girl, I sure could use an ace of clubs. " The dog jumps down from the chair, runs around to the stranger and bites his ankle. As the stranger reaches down to grab the dog, a card falls out of his sleeve. The dog quickly picks it up in her mouth and brings it back to her master. The stranger, realizing he's been caught cheating, leaps up and runs out the door with several locals in pursuit. The tinker takes the card from the dog's mouth and starts to swear, "You stupid, goddamn dog! Can't you get anything right?" The barkeep chides him, "Mister, why are you swearing at your dog like that? She just saved you a lot of money by catching that cheat!" The tinker responds by throwing the card face up on the table, "I tell her the ace of clubs and what does she bring me but the goddamn ace of spades!"

A Winning Attitude to party at poker games!

2005-05-06T12:28:00.000-07:00

A Winning Attitude to party at poker games!

A smart gambler will learn all about the game that he or she chooses to play. If its blackjack you need to learn basic strategy. Video poker players must know how to play each hand correctly. You should know the rules of any casino game before sitting down at the table. Even slot players need to learn how to read the front of a machine to determine whether they will get penalized for not playing maximum coins. All people entering the casino should learn one more thing. You must learn to develop a winning "Attitude".
On many occasions I have heard people say. “I have a couple extra dollars to go blow at the casino.” My reply to this statement is always the same. “If you go to the casino with the attitude that you are going to lose your money, that is exactly what you will do.” losers expect to lose their money and many are not satisfied until they do. Call it a self-fulfilled prophecy.
The late casino owner Sam Boyd was once asked by a newspaper reporter what was the difference between winners and losers? Sam replied. “Attitude! The losers act like they are going to lose and generally bet like losers. While the winners act like they expect to win, talk like they are going to win, and bet like winners. They expect they are going to win!”
What is a winning Attitude?
A winning attitude is a combination of things. The most important of these is knowledge. You have to know all about the games you play. The rules , the house edge and what to expect are things you should know before you sit down to a game. This will add to your Self-confidence which is another element of your winning attitude. Winners are self assured. You will trust your ability and this will add to your peace of mind. Add these together an you develop that “Yes I can” Attitude.
Attitude alone will not make you a winner but it can affect how you play. If you are not confident, you could start to second guess your ability. This could lead to you deviating from your game plan or might cause you to stray from proper play. If you play defensively you may find you are not taking advantage of winning opportunities like doubling down in Blackjack when you should.
Here is a list of the attitudes of loser vs winners:

Attitudes Of Losers vs Attitudes Of Winners
Expect to lose. Desire to win.
Can't wait to gamble. Gambling when alert.
Casino time is party time. Have fun but do the serious playing first.
Winning is all luck. Playing skills & mental attitude is important.
My luck is bound to change. Learning to set stop losses.
I want to win big. Small profits are okay.
Take advantage of free drinks. Understand drinking and gambling don't mix.
Play for comps. Accept comps for level of play.
Feel like a king, spend like a king It's my hard earned money.
So what if I lost, I had fun. Losing isn't fun, winning is.

A “Winning Attitude” will not happen over night. It will take discipline on your part to achieve it.

WHY IS POKER SO POPULAR?

2005-05-05T09:34:00.000-07:00

A few years ago several poker websites started to appear and appeal to a whole new generation of poker players. Many of the new players were young adults and most were still in college. This younger generation of players grew up playing Nintendo and Playstation so Online Poker was nothing more than a new game to them. It did not take long for them to eventually give up the Nintendo altogether and play nothing but Texas Hold'EM. (Almost half our Poker Sets are shipped to college campuses) With ESPN showing the World Series of Poker almost everyday and the World Poker Tour starting another record breaking season it is clear that Poker is the most popular game in the world. There is nothing like getting a group of friends together and having a poker party.

Texas Versus Omaha Poker Party!

2005-05-03T18:47:00.000-07:00

This is one of many curious posts that will teach you how to make your own Poker Party and have lots of fun, instead of just being another regular poker player.

Technically, the word "Holdem" refers to the some-cards-in-your-hand/some-cards-on-the-board, four betting rounds structure. But it has commonly become associated with the Texas version. Texas Holdem is generally considered "Holdem", while Omaha Holdem is merely "Omaha." Birthed of the same mother structure, Omaha and Holdem have similarities, but like siblings they also have dramatic differences when it comes to winning strategy. Understanding these sibling differences can lead to each of us making better game selection choices and recognizing our own strengths as poker players.
Some of the differences stem from logistics. When playing in a casino, approximately twice as many hands are dealt an hour in Holdem. Omaha is usually played HiLo. Holdem players usually have a wider variety of games to choose from. Omaha games have more regulars. Besides these things, there are many more complicated differences.If your aim is to win, Holdem requires more risk-taking, more variance. Winning Holdem is all about exploiting tiny edges, and even more, creating tiny edges. Holdem skill often comes into play in turning 55/45 edges into 60/40 ones. Obviously that is a good, profitable thing to do, but just as obviously it takes something of a long run to make these small edges add up. Great Holdem players find nickels and dimes and dollars of value in hand after hand -- getting free cards, protecting (or not protecting) blinds, value betting, inducing bluffs, etc. Very good winning players don’t depend on showing down AK against KQ on a KJ742 board. Showing the best hand is the bedrock of winning, but it is merely the tip of the iceberg. Omaha has quite a lot of differences. For very good players, Omaha edges are usually huge. Against weak Texas Hold'em opponents, a very good player can play a lot more hands. This is not the case in Omaha. While 76s can sometimes become playable in Holdem, 9764 is never playable in Omaha High Low (outside of maybe putting in one more chip in a two chip small blind) regardless of how lousy your opponents are. While the faster-paced Holdem is all about the application of many tiny edges time and again, glacier-paced Omaha is more about waiting for rare instances of enormous advantage. These huge advantages occur because most players simply do not "get" that when played properly Omaha has very little gamble to it, with less playable hands than Holdem -- especially "playable hands per hour". Loose-ish Omaha games mostly come down to simple math. A pot has so many chips in it, and you have so many outs to make the winning hand. You are either getting the right price, the wrong price, or the very, very right price.
Omaha is tortoise poker. Holdem is for the rabbits. Generally, winning Omaha players make more money per hour (with less variance) than their equally skilled Holdem counterparts. This occurs despite more Holdem hands being played simple because most Omaha players play far worse than the average Holdem player. If a weak player is taking the 40/60 worst of it in Holdem many times, that player is taking the worst of it fewer times against Omaha opponents but the worst of it now is more likely to be 10/90.Your personal temperament might be better suited for one than the other, but one game is not "better" than the other. While Omaha remains easier money, these days Texas Hold'em offers a much wider array of opportunities to win. Omaha tournaments are still peopled with very weak Omaha players, but the sheer number of Holdem tournaments and the larger amount of people playing Holdem events offsets that. Smaller edges in more events with more people simply returns us to the basic difference between Omaha and Holdem -- you get to apply a small advantage much more often for larger bets. These days, being properly bankrolled is even more important in the past. If you can afford to every five seconds bet $990 on a coin flip to win $1000, soon you will have an awful lot of money. But if you only have $640 to your name, you aren't going to even be able to play, let alone play with an expectation of not going broke due to bad luck. If you are a Holdem player, especially a Holdem tournament player, keep your powder dry... take loving care of your bankroll.Profit comes in different ways, and you have to be capable of catching it.

Poker Party! Learn new Tips!

2005-04-29T09:15:00.000-07:00

This is one of many curious posts that will teach you how to make your own Poker Party and have lots of fun, instead of just being another regular poker player.

Poker betting - The Poker bet:

The bet is the atom of winning poker. Betting units are made of chips, but a chip is like an electron, nothing on its own. The bet is the individual building block on which you must construct your game. But bets are easy to misuse. A bad call here, a poor fold there, a raise missed here, a missed bluff there... you can choke a whale on ways to misuse a bet. Poker is a card game, but winning poker is a betting game. Unfortunately for most players, they focus on their cards more than their betting -- even though a commonly recognized standard for successful poker is to win one bet an hour.
One of the problems with starting hand charts or count systems are they (by themselves) don't offer a player a clue to the different ways hands play. Maybe both starting hand A and starting hand B should be played, but they should be played dramatically differently. Some hands earn their profit early in a hand, while some hands show their profit by being more bettable in the later betting rounds. In Omaha Poker strategy, hand betability is a crucial aspect of the game. Players who play crappy starting cards find themselves with mediocre, un-bettable hands. They make two small pair, baby flushes and silly-end straights -- hands that may be winners but are usually not bettable, especially out of position. (One reason it is better to play hands from late position is because some mediocre hands become more bettable.)

You should be playing hands that can drive the betting, hands that you can extract more value from. Consider this Omaha HiLo hand, head-up between two players. On the turn card, the board is Jh6c8d3d. One player holds 8s7c5d3h, while the other holds Ad2dKdTd. Notice each player has exactly six cards with which to could scoop the whole pot.
The hands are equal, right? No, the 8753 is almost never bettable, while the A2KT is extremely bettable. When it comes a diamond, and the A2KT will scoop the pot, it will bet 100% of the time -- and often get paid off by the 8753. On the flipside, suppose the last card is the Ac. The 8753 will scoop the whole pot, but the hand is not bettable at all. It has very weak high value and very weak low value. It happens to be good enough to win, but betting would normally be foolish. The A2KT has the nut hand both ways, and has a fearless bet. So, the A2KT will make the best hand the exact same percentage of the time as the 8753, but the A2KT will make money while the 8753 will lose. Betability makes all the difference.
But that is not even where the difference ends. Except when it comes an offsuit 8, 3, 9 or 4, the 8753 will not be bettable, while the A2KT will always be bettable -- which will mean that the 8753 will fold a winner some amount of time greater than zero, tipping the $$$ scales even more in favor of the A2KT. Even if the A2KT player is concerned about getting quartered and will bet cautiously, he will likely bet when the river card comes a King or Ten, so to get its equity out of the pot, the 8753 will have to call these times. It will also have to call when it comes a Jack, counterfeiting its two pair, and when it comes a Seven or a Five, counterfeiting its low and making a straight very possible. Even though these cards don't make the A2KT the winner, they offer the A2KT the ability to sometimes win the pot merely by betting.The bottom line is the 8753 will almost never get an extra bet, while the A2KT will always be able to make an extra bet, and will win some amount of pots beyond that when it bets and the 8753 folds. Two hands with an equal chance to win are not in fact equal. A similar Holdem example is the classic confrontation between AK and 22. It's close to 50/50 if both hands always go to the showdown, but AK destroys 22 in actual play because of it superior betability.You don't win in poker by winning pots. You win by mastering the wagering of atoms.

party poker? Try Alamo Poker, it is better

2005-04-28T08:54:00.000-07:00

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The Trinity of Poker!

2005-04-27T07:26:00.000-07:00

Daily tips to show you how to make a Paty Poker out of your Poker game:

Poker players should not try to immediately emulate the type of play they see on TV. The circumstances of the play shown will very seldom be similar, so the types of plays made will generally not be applicable to "normal" situations.

A companion to this phenomenon can be found on Internet newsgroups like RGP the day after an event is broadcast. Yes, the world now has "Monday morning flopping." People analyze the play we saw the night before. Naturally some of this analysis is fine and right on the money. Other times what is revealed is a serious lack of poker understanding on the part of Monday morning quarterback criticizing the play of one of the televised players.
One instance of this that has been fairly common has been to criticize Chris Moneymaker's outstanding play in the 2003 World Series of Poker. One play by Chris in particular stands out. The flop came three low cards below a six, and Chris had a baby pair with a gutshot straight draw. When his opponent moved all in, Chris read the situation right (concluding the opponent merely had two overcards), calculated that he was a significant but not overwhelming favorite, and then pulled the trigger on calling a huge bet, even though losing would have put him out of the tournament.

This single play summed up the instincts (read the situation correctly), the head (calculated he was the favorite), and the heart (had the nerve to call with the best of it though he could be eliminated) of poker. The hand was perfect in showing these Father, Son and Holy Ghosts -- the "trinity of poker". To succeed at the top levels of poker you need your head, your heart and your groin to be able to take it.

Unfortunately for many people, they don't have enough of one or more of these, and they don't get that they don't. Not all of the play on television is good, some is even horrible. But some of the play is simply brilliant -- even if a lot of players simply will not be able to understand it.

Poker Hands Nicknames!

2005-04-26T16:10:00.000-07:00

This is the first of many curious posts to come, that will teach you how to make your own Party out of a Poker game and have lots of fun, instead of just being another regular poker player.

With the recent influx of new players into the game, the time is right to assemble a list of nicknames for poker hands. With this list, newbies will both be able to sound like they fit right in at a casino when they play, and also know what is going on by being able to decipher some of the code talk being spoken.

One problem with poker hand nicknames though is they sometimes become obsolete. Take the case of three tens: "TTT". One nickname for this three of a kind is "thirty miles of bad road", which is often shortened to "thirty miles." Many years ago this thirty miles notion led to the hand getting its most famous nickname: "Gilroy to San Jose." Unfortunately, these days San Jose has sprawled all the way up to the Gilroy city limits! Even if it means we can apparently travel thirty miles in one step, I guess we have to keep the nickname. More puzzling though is another, more obscure nickname for TTT: "Woodbine to Corbin." One would assume the genesis of this nickname is the same as Gilroy to San Jose, but take a look at a map. Woodbine is about five miles from Corbin! I guess that's why the nickname hasn't caught on.

Learning to Play Party Poker party poker

2005-04-22T16:46:00.000-07:00

Party Poker is an interesting test-bed for artificial intelligence research. It is a game of imperfect knowledge, where multiple competing agents must deal with risk management, opponent modeling, unreliable information, and deception, much like decision-making applications in the real world. Opponent modeling is one of the most difficult problems in decision-making applications and in Party Poker it is essential to achieving high performance. This paper describes and evaluates the implicit and explicit learning in the Party Poker program Loki. Loki implicitly "learns" sophisticated strategies by selectively sampling likely cards for the opponents and then simulating the remainder of the game. The program has explicit learning for observing its opponents, constructing opponent models and dynamically adapting its play to exploit patterns in the opponents’ play. The result is a program capable of playing reasonably strong Party Poker, but there remains considerable research to be done to play at a world-class level.

1. INTRODUCTION

The artificial intelligence community has recently benefited from the tremendous publicity generated by the development of chess, checkers and Othello programs that are capable of defeating the best human players. However, there is an important difference between these board games and popular card games like bridge and Party Poker. In the board games, players always have complete knowledge of the entire game state since it is visible to both participants. This property allows high performance to be achieved by a brute-force search of the game tree. In contrast, bridge and Party Poker involve imperfect information since the other players’ cards are not known, and search alone is insufficient to play these games well. Dealing with imperfect information is the main reason why progress on developing strong bridge and Party Poker programs has lagged behind the advances in other games. However, it is also the reason why these games promise higher potential research benefits.

Party Poker has a rich history of scientific investigation. Economists and mathematicians have applied a variety of analytical techniques to certain Party Poker-related problems. However, since "real" Party Poker is too complex for this approach, they have studied simplified variants ([15] for example). Other individuals, including expert players with a penchant for mathematics, have gained considerable insight about "real" Party Poker by using partial mathematical analyses, simulation, and ad-hoc expert experience ([18] is a popular example).

Until recently, the computing science community has largely ignored Party Poker. However, Party Poker has a number of attributes that make it an interesting domain for artificial intelligence (AI) research. These attributes include imperfect knowledge, multiple competing agents, risk management, opponent modeling, deception, and dealing with unreliable information. All of these are challenging dimensions to a difficult problem.

There are two ways that Party Poker can be used as an interesting testbed for artificial intelligence research. One approach is to use simplified variants that are easier to analyze. For example, Findler worked on and off for 20 years on a Party Poker-playing program for simplified 5-card draw Party Poker [7]. He modeled human cognitive processes and built a program that could learn. The danger with this approach is that simplification can remove the challenging components of the problem that are of interest to AI researchers. A variant of this approach is to look at a subset of the game, and try to address each component in isolation. Several attempts have been made to apply machine learning techniques to individual aspects of Party Poker (some examples include [19,21,6]).

The second approach, and the one that we advocate, is to tackle the entire problem: choose a real variant of Party Poker and address all the considerations necessary to build a program that performs at a level comparable to that of the best human players. Clearly this is the most ambitious approach, but also the one that promises the most exciting research opportunities.

Recently, Koller and Pfeffer have been investigating Party Poker from a theoretical point of view [13]. They present a new algorithm for finding optimal randomized strategies in two-player imperfect information competitive games. This is done in their Gala system, a tool for specifying and solving problems of imperfect information. Their system builds decision trees to find the optimal game-theoretic strategy. However the tree sizes prompted the authors to state that "...we are nowhere close to being able to solve huge games such as full-scale Party Poker, and it is unlikely that we will ever be able to do so." In theory, their approach could be used to build an optimal Party Poker player for a real variant of Party Poker. In practice, it will require too many computational resources unless further improvements are discovered.

We are attempting to build a program that is capable of playing world-class Party Poker. We have chosen to study the game of Texas Hold'em, the Party Poker variation used to determine the world champion in the annual World Series of Party Poker. Hold’em is considered to be the most strategically complex Party Poker variant that is widely played.

Our experiences with our first Party Poker program, called Loki, were positive [1,14]. However, we quickly discovered two limitations to further performance gains:

1 The betting strategy—whether to fold, call, or raise in a given situation—was defined using expert knowledge. This became cumbersome, since it was awkward to define rules to cover all the possible scenarios. Furthermore, any static strategy is suspect. A successful strategy must depend on changing game conditions.

2 Initially, in games played over the Internet, Loki performed quite well. However, some opponents detected patterns and weaknesses in Loki’s play, and they altered their strategy to exploit them. An opponent can exploit any predictable strategy, both in theory and in practice. To be a strong Party Poker player, one must model the opponent’s play and adjust to it.

This paper describes and evaluates two types of learning in Loki. First, its knowledge-based betting strategy can be viewed as a static evaluation function. In two-player games, such as chess, the quality of the evaluation can be improved through search. In Party Poker, imperfect information makes a search of the full game tree impractical. Instead, a simulation that samples from the set of likely scenarios can be used to enhance an evaluation. We found that a simple evaluation function augmented by search can uncover sophisticated strategies, as has been observed in perfect-information games. In other words, search compensates for a lack of knowledge. In effect, Loki uses simulations to implicitly learn advanced strategies.

Second, Loki observes and records the actions of each opponent and uses this information to build a simple model of their play. This model is used to predict each opponent’s hidden cards. The program adapts to the style of each opponent and exploits any predictable actions.

We have experimentally assessed each of these styles of learning, both in the laboratory and in play with human opponents. To the best of our knowledge, Loki is the first successful demonstration of using real-time learning to improve performance in a high-performance game-playing program.

This paper describes our previous work on Loki [1,2,3,4,14] and outlines some of the future directions we are pursuing. Section 2 provides an overview of Texas Hold’em. Section 3 identifies the minimal set of requirements necessary to achieve world-class play. Loki’s architecture is described in Section 4. Section 5 discusses the implicit learning used in the betting strategy, while Section 6 addresses the explicit opponent modeling. The performance of the program is assessed in Section 7. Section 8 identifies future work, and Section 9 provides some conclusions.

2. Texas Hold’em

A hand of Texas Hold’em begins with the pre-flop, where each player is dealt two hole cards face down, followed by the first round of betting. Three community cards are then dealt face up on the table, called the flop, and the second round of betting occurs. On the turn, a fourth community card is dealt face up and another round of betting ensues. Finally, on the river, a fifth community card is dealt face up and the final round of betting occurs. All players still in the game reveal their two hole cards for the showdown. The best five-card Party Poker hand formed from the two hole cards and the five community cards wins the pot. If a tie occurs, the pot is split. Texas Hold’em is typically played with 8 to 10 players.

Limit Texas Hold’em uses a structured betting system, where the order and amount of betting is strictly controlled on each betting round. There are two denominations of bets, called the small bet and the big bet ($2 and $4 in this paper). In the first two betting rounds, all bets and raises are $2, while in the last two rounds, they are $4. In general, when it is a player’s turn to act, one of five betting options is available: fold, call/check, or raise/bet. There is normally a maximum of three raises allowed per betting round. The betting option rotates clockwise until each player has matched the current bet or folded. If there is only one player remaining (all others having folded) that player is the winner and is awarded the pot without having to reveal their cards.

3. Requirements for a World-Class Party Poker Player

We have identified several key components that address some of the required activities of a strong Party Poker player. However, these components are not independent. They must be continually refined as new capabilities are added to the program.

Hand strength assesses the strength of a hand in relation to the other hands. The simplest hand strength computation is a function of the cards in the hand and the current community cards. A better hand strength computation takes into account the number of players still in the game, the position of the player at the table, and the history of betting for the current game. An even more accurate calculation considers the probabilities for each possible opponent hand, based on the likelihood of each hand being played to the current point in the game.

Hand potential computes the probability that a hand will improve to win, or that a leading hand will lose, as additional community cards appear. For example, a hand that contains four cards in the same suit may have a low hand strength, but has good potential to win with a flush as more community cards are dealt. Conversely, a hand with a high pair could decrease in strength and lose to a flush as many cards of a common suit appear on the board. At a minimum, hand potential is a function of the cards in the hand and the current community cards. However, a better calculation could use all of the additional factors described in the hand strength computation.

Betting strategy determines whether to fold, call/check, or bet/raise in any given situation. A minimum strategy is based on hand strength. Refinements consider hand potential, pot odds (your winning chances compared to the expected return from the pot), bluffing, opponent modeling and trying to play unpredictably.

Bluffing allows you to make a profit from weak hands, and can be used to create a false impression about your play to improve the profitability of subsequent hands. Bluffing is essential for successful play. Game theory can be used to compute a theoretically optimal bluffing frequency in certain situations. A minimal bluffing system merely bluffs this percentage of hands indiscriminately. In practice, you should also consider other factors (such as hand potential) and be able to predict the probability that your opponent will fold in order to identify profitable bluffing opportunities.

Unpredictability makes it difficult for opponents to form an accurate model of your strategy. By varying your playing strategy over time, opponents may be induced to make mistakes based on an incorrect model.

Opponent modeling allows you to determine a likely probability distribution for your opponent’s hidden cards. A minimal opponent model might use a single model for all opponents in a given hand. Opponent modeling may be improved by modifying those probabilities based on the collected statistics and betting history of each opponent.

There are several other identifiable characteristics that may not be necessary to play reasonably strong Party Poker, but may eventually be required for world-class play.

Opponent modeling is integral to successful Party Poker play. Koller and Pfeffer have proposed a system for constructing a game-theoretic optimal player [13]. However, it is important to differentiate an optimal strategy from a maximizing strategy. The optimal player makes its decisions based on game-theoretic probabilities, without regard to specific context. The maximizing player takes into account the opponent’s sub-optimal tendencies and adjusts its play to exploit these weaknesses.

In Party Poker, a player that detects and adjusts to opponent weaknesses will win more than a player who does not. For example, against a strong conservative player, it would be correct to fold the probable second-best hand. However, against a weaker player who bluffs too much, it would be an error to fold that same hand. In real Party Poker it is very common for opponents to play sub-optimally. A player who fails to detect and exploit these weaknesses will not win as much as a better player who does. Thus, a maximizing program will out-perform an optimal program against sub-optimal players.

Although a game-theoretic optimal solution for Hold’em would be interesting and provide a good baseline for comparing program (and human) performance, it would in no way "solve the game." To produce a world-class Party Poker program, strong opponent modeling is essential.

4. Loki’s Architecture

This section gives a brief overview of the important components of Loki’s architecture [4]. Figure 1 illustrates how these components interact. In the diagram, rectangles are major components, rounded rectangles are major data structures, and ovals are actions. The data follows the arrows between components. An annotated arrow indicates how many times data moves between the components for each of our betting actions.

The architecture revolves around generating and using probability triples. It is an ordered triple of values, PT = [f,c,r], such that f + c + r = 1.0, representing the probability distribution that the next betting action in a given context should be a fold, call, or raise, respectively. The Triple Generator contains our Party Poker knowledge, and is analogous to an evaluation function in two-player games. The Triple Generator calls the Hand Evaluator to evaluate any two-card hand in the current context. It uses the resulting hand value, the current game state, and expert-defined betting rules to compute the triple. To evaluate a hand, the Hand Evaluator enumerates over all possible opponent hands and counts how many of them would win, lose or tie the given hand.

Each time it is Loki’s turn to bet, the Action Selector uses a single probability triple to decide what action to take. For example, if the triple [0.0,0.8,0.2] were generated, then the Action Selector would never fold, call 80% of the time and raise 20% of the time. A random number is generated to select one of these actions so that the program varies its play, even in identical situations. Although this is analogous to a mixed strategy in game theory, the probability triple implicitly contains contextual information.

After the flop, the probability for each possible opponent hand is different. For example, the probability that Ace-Ace hole cards are held is much higher than the cards 7-2, since most players will fold 7-2 before the flop. There is a weight table for each opponent. Each weight table contains one value for each possible two-card hand that the opponent could hold. The value is the probability that the hand would be played exactly as that opponent has played so far. For example, assume that an opponent called before the flop. The updated probability value for the hand 7-2 might be 2% since it normally should be folded. Similarly the probability of Ace-King might be 60% since it would seldom be folded before the flop, but is often raised. After an opponent action, the Opponent Modeler updates the Weight Table for that opponent in a process called re-weighting. The value for each hand is increased or decreased to be consistent with the opponent's action. The Hand Evaluator uses the Weight Table in assessing the strength of each possible hand, and these values are in turn used to update the Weight Table after each opponent action. The absolute values of these probabilities are of little consequence, since only the relative weights affect the later calculations. The details are discussed in Section 6.

Figure 1. The architecture of Loki.

Probability triples are used in three places in Loki. The Action Selector uses a probability triple to decide on a course of action (fold, call, raise) as previously described. The Simulator uses probability triples to choose actions for simulated opponent hands (see Section 5). The Opponent Modeler uses an array of probability triples to update the model of each opponent (see Section 6).

An important advantage of the probability triple representation is that imperfect information is restricted to the Triple Generator and does not affect the rest of the program. This is similar to the way that alpha-beta search restricts knowledge to the evaluation function. The probability triple framework allows the "messy" elements of the program to be amalgamated into one component, which can then be treated as a "black box" by the rest of the system. Thus, aspects like game-specific information, complex expert-defined rule systems, and knowledge of human behavior are all isolated from the engine that uses this input.

5. Implicit Learning

Loki's original Action Selector component consisted of expert-defined rules that used hand strength, hand potential, game conditions, and probabilities to decide on an action. A professional Party Poker player defined the system as a first approximation of the return on investment for each betting decision. As other aspects of Loki improved, this simplistic betting strategy became the limiting factor to the playing strength of the program. Unfortunately, any rule-based system is inherently rigid, and even simple changes were difficult to implement and verify for correctness. A more flexible, computation-based approach was needed.

In effect, a knowledge-based betting strategy is equivalent to a static evaluation function. Given the current state of the game and the hole cards, it attempts to determine the action that yields the best result. If we use deterministic perfect information games as a model, the obvious extension is to add search to the evaluation function. While this is easy to achieve in a perfect-information game such as chess (consider all possible moves as deeply as resources permit), the same approach is not feasible for real imperfect information games because there are too many possibilities to consider [13].

Having an expert identify all the betting rules necessary to play world-class Party Poker is time consuming and difficult. Decisions must be based on context, within a game and between games. Covering all eventualities is not practical. In such a system, the expert does the learning, transferring his knowledge into new or modified rules. We prefer a dynamic computation-based approach, where the program does the learning as it plays.

Loki’s improved betting strategy consists of playing out many likely scenarios to determine how much money each decision will win or lose. Every time it faces a decision, Loki invokes the Simulator to get an estimate of the expected value (EV) of each betting action (see the dashed box in Figure 1 with the Simulator replacing the Action Selector). A simulation consists of playing out the hand a specified number of times, from the current state of the game through to the end. Folding is considered to have a zero EV, because we do not make any future profit or loss. Each trial is played out twice—once to consider the consequences of a check/call and once to consider a bet/raise. In each trial, cards are dealt to each opponent (based on the probabilities maintained in the Weight Table), the resulting game is simulated to the end, and the amount of money won or lost is determined. Probability triples are used to simulate the actions of the opponents based on the two cards they are assigned for that trial. The average over all of the trials is taken as the EV of each action. In the current implementation we simply choose the action with the greatest expectation, folding if both expectations are negative. If two actions have the same expectation, we opt for the most aggressive one (call over fold and raise over call). To increase the programs unpredictability, we can randomize the selection of betting actions whose EVs are close in value.

Enumerating all possible opponent hands and future community cards is analogous to exhaustive game tree search and is impractical for Party Poker. However, simulation is analogous to a selective expansion of some branches of a game tree. To get a good approximation of the expected value of each betting action, one must have a preference for expanding and evaluating the nodes that are most likely to occur. To obtain a correctly weighted average, all of the possibilities must be considered in proportion to the underlying probability distribution of the opponent hands and future community cards. The distribution of future community cards is uniform across unseen cards, but the probable opponent hands are not! We use selective sampling to select the most probable hands for each opponent.

When simulating a hand, we have specific information that can be used to bias the selection of cards. For example, a player who has been raising is more likely to have a strong hand than a player who has just called every bet. For each opponent, Loki maintains a probability distribution over the entire set of possible hands (the Weight Table), and the random generation of each opponent’s hole cards is based on those probabilities. Thus, we are biasing our selection of hole cards for the opponent to the ones that are most likely to occur.

At each node in the decision tree, a player must choose between one of three alternatives. Since the choice is strongly correlated to the quality of the cards that they have, we can use the Triple Generator to compute the likelihood that the player will fold, check/call, or bet/raise in each instance. The player’s action is then randomly selected based on the probability distribution, and the simulation proceeds. As shown in Figure 1, the Simulator calls the TripleGenerator to obtain each of our betting actions and each of our opponent actions. Where two actions are equally viable, the resulting EVs should be nearly equal, so there is little consequence if the "wrong" action is chosen.

It should be obvious that the simulation approach must be better than the static approach, since it essentially uses a selective search to augment and refine a static evaluation function. Barring a serious misconception (or bad luck on a limited sample size), playing out relevant scenarios will improve the default values obtained by heuristics, resulting in a more accurate estimate.

As seen inother search domains, the search itself contains implicit knowledge. A simulation contains inherent information that improves the basic evaluation. For example, a simulation contains implicit knowledge such as:

• hand strength (fraction of trials where our hand is better than the one assigned to the opponent),

• hand potential (fraction of trials where our hand improves to the best, or is overtaken), and

• subtle implications not addressed in the simplistic betting strategy (e.g. "implied odds"—extra bets won after a successful draw).

It also allows complex strategies to be uncovered without providing additional expert knowledge. For example, simulations can result in the emergence of advanced betting tactics like a check-raise, even if the basic strategy without simulation is incapable of this play.

At the heart of the simulation is an evaluation function. The better the quality of the evaluation function, the better the simulation results will be. One of the interesting results of work on alpha-beta has been that even a simple evaluation function can result in a powerful program. We see a similar situation in Party Poker. The implicit knowledge contained in the search improves the basic evaluation, magnifying the quality of the search. As with alpha-beta, there are tradeoffs to be made. A more sophisticated evaluation function can reduce the size of the tree, at the cost of more time spent on each node. In simulation analysis, we can improve the accuracy of each trial, but at the expense of the total number of trials performed in real-time.

Variations of selective sampling have been used in other games, including Scrabble [17], backgammon [20], and bridge [9]. Selective sampling is similar to the idea of likelihood weighting in stochastic simulation [8,16]. In our case, the goal is different because we need to differentiate between EVs (for call/check, bet/raise) instead of counting events. Also, Party Poker complicates matters by imposing tight real-time constraints (typically a maximum of two seconds). This forces us to maximize the information gained from a limited number of samples. Further, the problem of handling unlikely events (which is a concern for any sampling-based result) is smoothly handled by our re-weighting system (Section 6), allowing Loki to dynamically adjust the likelihood of an event based on observed actions. An unlikely event with a big payoff figures naturally into the EV calculations.

6. Explicit Learning

In strategic games like chess, the performance loss by ignoring opponent modeling is small, and hence it is usually ignored (although it has been studied [5,11,12]). In contrast, not only does opponent modeling have tremendous value in Party Poker, it can be the distinguishing feature between players at different skill levels. If a set of players all have a comparable knowledge of Party Poker fundamentals, the ability to alter decisions based on an accurate model of the opponent may have a greater impact on success than any other strategic principle.

To assess a hand, the Hand Evaluator compares those cards against all possible opponent holdings. Naively, one could treat all opponent hands as equally likely, however this skews the hand evaluations compared to more realistic assumptions. Many weak hands are likely to have been folded before the flop, making them less likely to be held later in the hand. Similarly, a hand made strong by the turn and river cards may have been folded on the flop. Therefore, for each starting hand, we need to define a probability that our opponent would have played that hand in the observed manner. We call the probabilities for each of these (52 choose 2) = 1,326 subcases weights since they act as multipliers in the enumeration computations.

The use of these weights is the first step toward opponent modeling since we are changing our computations based on the relative probabilities our opponent’s possible hole cards. The simplest approach to determining these weights is to treat all opponents the same, calculating a single set of weights to reflect "reasonable" behavior, and use them for all opponents. An initial set of weights was determined by ranking the starting hands (as determined by off-line simulations) and assigning a probability commensurate with the average return on investment of each hand. These results closely approximate the ranking of hands by strong players [18].

In Loki, the Opponent Modeler uses probability triples to update the Weight Table after each opponent action. To accomplish this, the Triple Generator is called for each possible two-card hand. It then multiplies each weight in the Weight Table by the entry in the probability triple that corresponds to the opponent’s action. For example, suppose the previous weight for Ace-Ace is 0.7 (meaning that if it has been dealt, there is a 70% chance the opponent would have played it in exactly the manner observed so far), and the opponent now calls. If the probability triple for the current context is [0.0, 0.2, 0.8], then the updated weight for this case would be 0.7 x 0.2 = 0.14. The relative likelihood of the opponent holding Ace-Ace has decreased to 14% because they did not raise. The call value of 0.2 reflects the possibility that this particular opponent might deliberately try to mislead us by calling instead of raising. Using a probability distribution allows us to account for uncertainty in our beliefs. This process of updating the weight table is repeated for each entry.

The above corresponds to what we call Generic Opponent Modeling (GOM). Each hand is viewed in isolation and all opponents are treated as the same player. Each player’s Weight Table is initially identical, and gets modified based on their betting action. Although rather simplistic, this model is quite powerful in that it does a good job of skewing the hand evaluations to take into account the most likely opponent holdings.

Obviously, treating all opponents the same is clearly wrong. Each player has a different style, ranging from loose (plays most hands beyond the flop) to tight (usually plays the few hands that have a very high probability of winning), and from aggressive to conservative. Knowing the style of the opponents allows a player to adjust their betting decisions. For example, if a perceived tight player is betting aggressively, there is a good chance that they have a strong hand. A loose player will play many marginal hands or may bluff a lot. This is useful information and may allow you to fold a strong hand or call with a weak one when it is correct to do so. In general, a bet made by a loose or aggressive player should not be taken as seriously as one made by a tight or conservative player.

Specific Opponent Modeling (SOM) customizes the probability triple function to represent the playing style of each opponent. For a given game, the reweighting factor applied to the entries of the Weight table is adjusted by betting frequency statistics gathered on that opponent from previous hands. This results in a shift of the assumed call and raise thresholds for each player. In the case of a tight player, the call and raise thresholds will increase, indicating fewer hands that are likely to be played. Conversely, a loose player’s thresholds will be lowered. During each round of a game, the history of previous actions by the opponent is used to influence the probability triple generated for that opponent.

In competitive Party Poker, opponent modeling is much more complex than portrayed here. For example, players can act to mislead their opponents into constructing an erroneous model. Early in a session a strong Party Poker player may try to create the impression of being very conservative, only to exploit that image later in that session when the opponents are using an incorrect opponent model. A strong player has to adapt their model to the opponents varying their playing style.

7. Experiments

Self-play experiments offer a convenient method for the comparison of two or more versions of the program. Our experiments use a duplicate tournament system, based on the same principle as duplicate bridge. Since each hand can be played with no memory of preceding hands, it is possible to replay the same deal, but with the participants holding a different set of hole cards each time. Our tournament system simulates a ten-player game, where each deal is replayed ten times, shuffling the seating arrangement so that every participant has the opportunity to play each set of hole cards once. This arrangement greatly reduces the "luck element" of the game, since each player will have the same number of good and bad hands. The differences in the performance of players will therefore be based more strongly on the quality of the decisions made in each situation. This reduction in natural variance allows meaningful results to be obtained with a smaller number of trials than in a typical game setting. Nevertheless, it is important to not over-interpret the results of one experiment.

Experiments have been performed with Loki to measure the performance of generic opponent modeling (GOM), simulation (S), and both combined (GOM+S). The results were obtained by playing a self-play tournament containing two enhanced versions of Loki against 8 unenhanced versions. A tournament consisted of 2,500 different deals (i.e. 25,000 games). Each simulation consisted of 500 trials, since the results obtained after 500 trials were reasonably stable.

The metric used to measure program performance is the average number of small bets won per hand (sb/hand), a metric that is sometimes used by human players. For example, in a game of $10/$20 Hold’em, an improvement of +0.10 sb/hand translates into an extra $30 per hour (based on 30 hands per hour). Anything above +0.05 small bets per hand is considered a large improvement. In play on an Internet Party Poker server against human opponents, Loki has consistently performed at or above the +0.05 sb/hand level.

The experiments showed that GOM improved performance by 0.031 ± 0.019 sb/hand, simulations improved by 0.093 ± 0.04 sb/hand, and the combination was worth 0.095 ± 0.045 sb/hand (note that these are newer numbers than those appearing in [2,3,4]). The results reported here may be slightly misleading since each experiment used two similar programs. As has been shown in chess, one has to be careful about interpreting the results of these types of experiments.

GOM is a significant gain as expected. Given that all players in the tournaments were variants of Loki, the wide variety of play that is seen in human play is missing. Hence, GOM may be of greater benefit against typical human opponents. Simulations, on the other hand, are a huge win in self-play experiments against non-simulation opponents. As expected, they have a naturally occurring higher variance. The use of simulations represents a large improvement in the quality and variety of the betting strategies employed by Loki (or, possibly, overcome a serious weakness in the older version of the program). Whereas our initial knowledge-based betting strategy routine [1,14] was limited by the amount of knowledge we could code and tune, the simulation-based approach has no such restrictions. The simulations implicitly enable advanced betting strategies, with a degree of unpredictability that makes it harder for the opponents to model Loki.

Note that although each feature is a win by itself, the combination is not necessarily additive because there may be some interdependence between GOM and simulations (i.e. both ideas may exploit the same weaknesses). As well, the magnitude of the simulation improvement is such that it hides the effects of combining it with GOM. The larger the winning margin, the smaller the opportunity there is for demonstrating further improvement against the same opposition.

Each set of improvements reported over the past two years were measured against the previous strongest versions of Loki. As a result, the magnitude of the change may be dampened over time, simply because it is being tested against generally stronger opposition. For example, if you have three generations of Party Poker-playing programs (A, B, and C) with B defeating A by 0.1 sb/hand and C is better than B by 0.1 sb/hand, it does not follow that C will be .2 sb/hand better than A.

Specific opponent modeling (SOM) is harder to measure, due in part to the nature of our self-play experiments. In previous work we demonstrated improvements for both GOM and SOM against a static default model [2]. However, since that time Loki has improved significantly (for example, with improved reweighting and simulations). A consequence is that our simplistic SOM model has not yet added significantly to the performance of the stronger version of Loki. Improving SOM is our current focus, and some of the ideas we are pursuing are discussed in the next section.

Loki has been tested in more realistic games against human opposition. For this purpose, the program participates in an on-line Party Poker game, running on the Internet Relay Chat (IRC). Human players connect to IRC and participate in games conducted by dedicated server programs. No real money is at stake, but bankroll statistics on each player are maintained. The new versions of Loki using GOM and simulations win consistently when playing on the IRC server. Although there is a high level of variance in this environment, there is strong evidence that GOM is a major advance in the program’s playing strength against human opposition (as opposed to the self-play experiments where the advantage was not as significant). The performance of the program depends strongly on which players happen to be playing, and on IRC it ranges from novices to professional players. Consequently, it is dangerous to quantify the results of our recent improvements to Loki.

8. Ongoing Research

The work reported here is our first experience with a betting strategy based on simulations and opponent modeling. Each area has numerous opportunities for improvement, some of which are currently being addressed. Indeed, the Party Poker project is rich in research opportunities. There is no shortage of good ideas to investigate; only a shortage of time and resources.

For the simulations, the major problem is variance (standard deviation) in the results. We have identified several ways in which the experiments could be conducted with less noise. Nevertheless, even with these enhancements, we expect the variance to still be high. Faster machines and parallel computations might be helpful since this will result in a larger sample of simulation data points. However, this has diminishing returns and our experiments suggest that beyond a critical minimum number of simulation data points (in the 100-500 range) the benefits may be small.

There are tradeoffs in doing the simulations. Currently, each data point contains a small amount of information about the expected value. Given the simplicity of the calculation, one can acquire numerous data points. Alternatively, one could do fewer simulations, but have each return a more accurate value. The quantity versus quality trade-off needs to be explored in more detail.

For the game of bridge, simulations have successfully allowed computers to play hands at a world-class level (GIB [9]). Nevertheless, limitations in the simulation-based approach and the high variance have prompted the author of GIB, Matt Ginsberg, to look at other solutions (including building the entire search tree) [10]. We too may have to look for new approaches to overcome the limits of simulations.

In the area of opponent modeling, there are numerous avenues that can be explored. One serious limitation of our current work that needs to be address is the resistance to change that is built into our system. Our opponent modeling works well in some cases because most of the opponents have a fixed style that does not vary over time (certainly the computer opponents that we use in our self-play experiments have this property). However, it does not necessarily follow that opponent modeling will be as successful in games against human players as it is in the closed experiments. Humans are also very good at opponent modeling, and can be much less predictable than the players in our experiments. We have not yet investigated making our opponent models quickly responsive to perceived changes in an opponent’s style. For a strong human player, a single data point is often sufficient for them to set or alter their model of an opponent. Our models are far too slow to adapt. This must change!

A sampling of some of the ideas being investigated include:

• Use the simulations to refine the opponent modeling. Having done a simulation, record the expected reaction for each opponent. If their actions frequently differ from what is predicted, then Loki can adjust its opponent model.

• With opponent modeling, it is easy to gather lots of data. The problem is filtering it and attaching the appropriate importance to it. Without this, our modeling will be too slow to react, or base its decisions on irrelevant information. We are investigating condensing the data into simpler metrics that may be better predictors of an opponent’s style and future behavior. For example, measuring the amount of money that a player invests per game may be a good predictor of loose/tight play.

• Previous specific opponent modeling was hampered by the crude method used for collecting and applying observed statistics. Much of the relevant context was ignored for simplicity, such as combinations of actions within the same betting round. A more sophisticated method for observing and utilizing opponent behavior would allow for a more flexible and accurate opponent model. For example, we are currently experimenting with modifying our model based on sequences of opponent’s actions. A check followed by a raise (typically a show of strength) has more meaning than looking at these two actions in isolation.

• Loki does not currently use showdown information. The cards seen at the showdown reveal clues about how that opponent perceived each decision during the hand. These hindsight observations can be used to adaptively measure important characteristics like aggressiveness, bluffing frequency, predictability, affinity for draws, and so forth.

• We have yet to fully explore the variety of techniques available in the literature for learning in a noisy domain where one must make inferences based on limited data.

9. Conclusions

To master the game of Party Poker, one must be adaptive. Any form of deterministic play can and will be exploited by a good opponent. A player must change their style based on the dynamic game conditions observed over a series of hands (looking at each hand in isolation is an artificial limitation). Our work has made some progress towards achieving a Party Poker-playing program that can learn and adapt. Loki successfully uses opponent modeling to improve its play. However, it is abundantly clear that these are only the first steps, and there is considerable room for improvement.

Party Poker is a complex game. Strong play requires the player to excel in many different aspects of the game. Developing Loki has been a cyclic process. We improve one aspect of the program until it becomes apparent that another aspect is the performance bottleneck. That problem is then tackled until it is no longer the limiting factor, and new weaknesses in the program’s play are revealed. We made our initial foray into opponent modeling and were pleased with the results. With the success of the new simulation-based betting strategy, opponent modeling is now back on the critical path since it will offer the biggest performance gains. We will now refocus our efforts on that topic, until it too moves off the critical path.party poker

party poker games news today

2005-04-22T15:10:00.000-07:00

Rumors have surfaced that online poker company Party Poker will delay plans to float on the London Stock Exchange. Party Poker's much anticipated float was expected to occur within the next month or two, but now a number of industry insiders suspect that the float will not take place until at least late summer.

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2005-04-20T11:55:00.000-07:00

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