free poker games

poker games

2005-06-09T02:03:00.000-07:00

Poker Games Proceeds As Planned January 8, 2005
The Chez Paree poker tournament proceeded as scheduled Friday night but building owner Butch Levell wondered if threats of shutting the game down didn't keep some players away.
About 30 poker players were ready to go at 7 p.m. but Larry Ringenberg, who is consulting with tournament organizers, held off another 10 minutes. "I got four calls from people who are on their way," he said.
The Texas Hold'em tournament has been the source of legal maneuverings with the Department of Inspections threatening to block the poker game and Pottawattamie County Attorney Matt Wilber saying the tournament, as structured, is legal in his opinion.
Players chomped on free hot dogs and chips and drank cola as they waited for the action to start.
Ringenberg said attorney Richter told him he had talked with Wilber and they decided to go ahead and hold the event. There were no signs of Inspection personnel in the early stages of the evening.
Ringenberg said for right now, the Chez Paree plans to hold Friday night and Saturday and Sunday afternoon tournaments.
But Friday's early turnout was lower than the 200 hoped for. Players pay a $35 buy-in and $15 entry fee. Prizes are split among winners at the end of the tourney. "If we got 200 people, the winner would get almost $3,000," Ringenberg said.
Brian Battistone, one of the players awaiting the tournament start said he thought it was great and was not concerned about arrest. "I think even if anyone came they would just tell us to leave."
Battistone said poker tournaments are big with students and a good alternative to some of the partying that goes on among the college-age crowd. He said he recently graduated from UNO.
Although the casinos have not said much about the tournament, Ringenberg said he thought they might welcome the poker tournament. "The wives can drop their husbands off and then go to the casino," he said.
Wilber said he thinks the Legislature needs to look at gambling laws and close, what he said, is a loophole.
There was no liquor in site and Levell said he is not planning to have any right now. "We may offer free beer at some point," he said.

Know when to hold 'em and fold 'em.

2005-05-13T12:34:00.000-07:00

Don't miss the free Texas Hold 'em poker party at 5 p.m. at the Glenwood Springs Center for the Arts. Sometimes even the best-laid plans go awry at the last minute. I am hooked on Texas Hold 'Em, a fun game that's easy to learn and even easier to win.

I love the terms. I love to play with the terms "Take me to the river!"Got me a couple of cowboys? I thought, what a great way to raise some funds for the Glenwood Springs Center for the Arts, have a little fun, bring in a different crowd, etc. I was really excited, and so was our board. I checked with our local gaming person and proceeded to get the word out. Well, it turns out the Colorado Division of Gaming was not so excited.

Even our police chief said he would love to come play if he didn't have to arrest the whole bunch of us. Not a pretty sight or a good message to send our kids. There have been so many illegal poker games around the state that they have to crack down. But, we are still very pleased to present a Texas Hold 'Em poker party tonight. We have approval from the Colorado Gaming Division and the blessing of Glenwood Springs Police Chief Terry Wilson. It doesn't get much better than that!So poker players, come on down and join us with a tax-deductible donation.

Come play for self-esteem and win the title, "You da Poker Man," "Pocket Cowboy," or even "Fishhook," among others. Come down to learn the game or practice for your next trip to Vegas or Black Hawk. Refreshments and snacks will be available. We're looking for 80-plus poker players to come down here and know when to hold 'em or know when to fold 'em.

The wonderfully talented members of the Glenwood Springs Art Guild have filled the gallery of the center with great renditions in all classic mediums, including textile art. The Art Guild is that organization that puts on the huge Fall Art Festival every September. The guild's membership includes many seasoned professionals. Many guild members have published works in books and other print media, many have work on display throughout the state on a continuing basis, and many are have works in galleries around the state.

The guild has more than 200 members. Showing from now until May 30, we hope you will join us for the artist reception at 6 p.m. Saturday here at 601 E. Sixth St. Be inspired by their renditions, and then register for a great art class from the Center.

Online Poker Games Review

2005-05-12T12:17:00.000-07:00

Online poker is the fastest growing aspect of the poker world. It provides poker players around the world the opportunity to play against each other and enjoy many good free poker games from the comfort of their own house.
It’s a fact that online poker rooms and land based poker rooms have unique advantages weighing in their own favor. But, while they share some similarities, they are different in a number of ways, and some of those differences are the reason poker lovers lean for the online poker way.
You need to compare, so, below we give you a list of some ways in which online poker is better than the offline poker opponent. These are just some of the many advantages online poker has.
Play online poker game for freeWhen you decide to play online, you can choose from playing for Real Money or for Play Money. Play poker with play money is not a facility you will find if you go to a casino. By doing this, beginners get the chance to learn a new game, increase theirs skills, see how the betting works, learn the procedures of online poker or just play for fun when you don’t feel like betting real money.
FREE games are the best learning tools. After playing for play money, we recommend you that once you feel confident enough go and try your best playing for Real Money. Poker is a game designed to be played for "something". And tournaments are fun, exciting, and affordable.

You can play more

Online poker rooms will deal about 60 hands per hour (or up to 100 hands per hour in shorthanded games) compared with most B&M casinos that will deal about 30 hands per hour.

You can choose to play from a better selection of online poker games: There is usually a game of any type and any level going at any time.
Lees travel time or not travel at all. You don't have to spend long hours to drive to and from the casino. This gives you more time to play the game. It also allows you to have short sessions - sometimes you feel like sitting and playing for 20 minutes or so but wouldn't drive to a casino just to play for 20 minutes.
There’s no toking You don’t have to tip the dealer.
Multiple tables at onceThis increase you win rate but it also might race your profits as you are playing anywhere from 150-250 hands per hour.
Chance to get bonuses Online poker rooms give away lots of money in bonuses for you to play at their site.

There are no dealer mistakes

Dealer mistakes can distort the real results in brick & mortar and these mistakes don't happen online.
You have time to plan your moveWhen you are playing online time is on your side, that’s because you can play at your own ease, and be secure in the knowledge that when you play a hand, you've put some thought into it, and have not played as a result of impulse or peer pressure. You don’t need to wait too long to start playing at the tables
Most of the time there are no waits for an online room (occasionally you may have to wait 5 minutes).
Feel good about being a bad player Bad players are intimidated to play brick & mortar in fear of making mistakes or looking bad to people. The anonymity of playing online allows them more comfort and allows you to make more money.
Play with no pressure: Sitting at a table brings lots of external pressures. While you play online in the secure and comfort of your home, the only pressures come from within yourself.

Choosing an Online Poker Room

2005-05-11T10:02:00.000-07:00

We often get asked who "we think" the best free poker games sites. When choosing an online poker room, there are many things to consider such as: sign up bonus offered, the user friendliness of the site, are there enough players playing at this particular online poker room to assure that your going to get into a game that suits your needs and more. Below, we'll highlight some of the things you should consider when looking for an online poker room that will suit your needs. Enjoy!

Learning and playing free poker games at home.

2005-05-07T18:37:00.000-07:00

I am simply amazed at the amount of people I see at the casino who are willing to plunk down their hard earned money on games that they haven’t a clue how to play. The same people who will comparison shop, clip coupons or drive across town to save a few cents on a gallon of gas, will sit at a blackjack table and bet $25 a hand without knowing basic strategy. I often wonder why they don't bother to learn the game before they play.
There once was a time when visitors to the casino had limited resources available to help them learn to play the games. I started my casino education back in the “Stone Age”. It was somewhere around 10 BC. That’s BC ...as in Before Computers. I don’t mean that computers weren’t invented, (I’m not THAT old) however the personal computer was barely affordable and all of the software programs were business related.
VCRs were also a luxury item (DVD’s were not invented) and movies were the main fare for those wishing to view at home. The self-help and educational tapes weren't being produced. That left a few books about gambling for those who wanted to learn how to play casino games.
When I first learned basic strategy for blackjack, I used hand-printed flashcards that I made. I would put the player's hand on one side and the rule for the hand on the other side. I would sit and practice for hours until I knew all the strategy rules by heart and could recite them instantly. It was very efficient, but also very boring. Things have changed drastically since those days.
Over the last few years with the rapid growth of personal computers, more and more gambling software has been developed. The software ranges from fun games with no educational value, to some really powerful training programs. Games that require strategy and decision making on the part of the player can be practiced at home with the use of the software programs. These games include Blackjack, Video Poker and live poker. Even software for games such as craps, and roulette can be helpful in teaching you the mechanics of the game. Now learning to play free poker games can be as easy as sitting down in front of your computer in the comfort of your own home. Well, almost.
Actually you will need a little more than software to learn to play a casino game. I recommend what I call the Three-Step approach to learning a casino game at home. The three steps for learning to play casino games are: reading, watching and practicing.
The Cost How expensive is it to visit the casino and constantly lose money because you don't know how to play the game correctly? All education comes with a price. Getting your education betting real money at a gaming table can be a lot more expensive that the price of a book and software program. Many good gambling books cost less than twenty dollars. Videotapes and DVDs can cost you another thirty dollars. The price of tutorial software varies depending on the casino game and the sophistication of the program. There are good programs that range from thirty to a hundred dollars. You start can start learning at home for around $100. You will save this much money by playing correctly during future visits to the casino.

Practicing Free Online Poker Games.

2005-05-06T13:26:00.000-07:00

Paying Attention
You should be watching the other players at the showdown to see what hands they are playing. This is something you should be doing in live games. Get in the habit of doing it every time you play. It will help you develop your attention to the game and the other players. Try to determine who is a serious player online and who is not. Just as in real games you should be able to determine who is playing tight or lose by the hands they are showing at the end.
Pot Odds
You can practice figuring pot odds by counting the money as it goes into the pot. Some of the free poker games sites actually show the amount of money in the pot. If this is the case you can cover the total on the screen. Other sites just show a pile of chips that you can click on to see the total. After the rounds you can peak at the total and see if your count matches the actual money in the pot. Its good practice and will sharpen your ability to figure pot odds during a live game.
Emotional Toughness
When you play against the really bad players online you will experience bad beats much more frequently. This is because more of the players are staying to the end looking for the miracle draw. While you will never get used to them you will have a better understanding that it is part of the game when you are dealing with this type of player. If you can learn to accept it as part of the game it will not have as great of effect your emotional stability when it happens at the tables in the card room.
Private Games
There are sites where players can hold private games or play one on one with each other. This is an excellent opportunity to get together with some of your serious poker friends for some practice. While there is no real money exchanging hands, if everyone considers their cyber chips to be as valuable as real money and plays the game as such, it will make for a great learning experience. The knowledge shared and experience gained will be invaluable.
It's Your Call
Practicing online can be like any other endeavor. You get out of it what you put into it. If you treat these free games as if you were playing with real money, then you can learn from it. If you decided to just play any two cards to the river, you are defeating the purpose. You are also wasting your time and running the risk of developing bad habits.

Practicing Free Poker Online Games!

2005-05-03T19:56:00.000-07:00

Paying Attention
You should be watching the other players at the showdown to see what hands they are playing. This is something you should be doing in live games. Get in the habit of doing it every time you play. It will help you develop your attention to the game and the other players. Try to determine who is a serious player online and who is not. Just as in real games you should be able to determine who is playing tight or lose by the hands they are showing at the end.

Pot Odds
You can practice figuring pot odds by counting the money as it goes into the pot. Some of the online sites actually show the amount of money in the pot. If this is the case you can cover the total on the screen. Other sites just show a pile of chips that you can click on to see the total. After the rounds you can peak at the total and see if your count matches the actual money in the pot. Its good practice and will sharpen your ability to figure pot odds during a live game.

Emotional Toughness
When you play against the really bad players online you will experience bad beats much more frequently. This is because more of the players are staying to the end looking for the miracle draw. While you will never get used to them you will have a better understanding that it is part of the game when you are dealing with this type of player. If you can learn to accept it as part of the game it will not have as great of effect your emotional stability when it happens at the tables in the card room.

Private Games
There are sites where players can hold private games or play one on one with each other. This is an excellent opportunity to get together with some of your serious poker friends for some practice at a free poker game. While there is no real money exchanging hands, if everyone considers their cyber chips to be as valuable as real money and plays the game as such, it will make for a great learning experience. The knowledge shared and experience gained will be invaluable.

It's Your Call
Practicing online can be like any other endeavor. You get out of it what you put into it. If you treat these free games as if you were playing with real money, then you can learn from it. If you decided to just play any two cards to the river, you are defeating the purpose. You are also wasting your time and running the risk of developing bad habits.

Free Poker Games - Beating Bad Poker Players!

2005-04-29T10:33:00.000-07:00

Free Poker Games - Beating Bad Poker Players!

Over the last year Poker has become the hottest game in the world. To say there is a fascination with the game would be an understatement. The new found interest in poker by millions of people this year can be attributed to a couple of events.
Television has brought Poker out of the cardrooms and into the living rooms of millions of people who have become fascinated with the reality game shows. The Travel channel gambled that the World Poker Tour would attract some viewers. It hit the jackpot when it turned into the Networks top rated show. This was the start of more Poker on Television. In past years ESPN would reduce the annual World Series of Poker into a two hour program. This year they turned it into a multi-program series. There was a six hour broadcast of the Showdown at the Sands Poker Tournament on Thanksgiving Day.

The Bravo Network is broadcasting a Celebrity Poker Tournament and more poker tournaments are set to be televised in the future. Recently, it seems that every broadcasting network is trying to get a poker show on the air. This year should see the poker continue to grow.
Online Poker rooms have been springing up on the Internet and they have been growing as more and more people log on to play poker with players from around the world. When Chris Moneymaker won the 2.5 million dollar first prize at the World Series of Poker in 2004 and Greg Raymer won 5 million in 2005 after winning their entries on an Internet Poker site, millions of would be players dreamed of becoming the next World Champion. Millions of new players flocked to the online poker rooms to try their hand at playing Poker. Many of them have been playing in the freerolls or low limit games in which the players are not very knowledgeable or serious about the game.

The combination of Internet players and television viewers has led to an increased number of new players making their way to the casino card rooms. The Poker Rooms in Tunica have seen the influx of these new players who want to try their hand in a live game. Most of these new players have little or no knowledge of the game other than the basic rules. Many of them have gotten all of their education from watching the tournaments on TV. Texas Hold’em is the game of choice because it is easy to learn the basic rules and this is what they have been watching on TV.

On television they see the pros making huge raises with trash hands and figure that this is the way the game is supposed to be played. Few of them are savvy enough to note that the players are either initiating a raise or re-raising with the trash hands. You will not see the pros merely calling with garbage hands. In addition, what they are seeing on TV is the final table that has been edited down to two hours. The hands shown on TV have been picked for their dramatic outcomes. They don’t see the boring hands where the majority of players have been folding time and time again. They also don’t realize that they are watching a short handed game that starts with six players.

Two Types of Players
Some of these players with their TV education make their way to the cardrooms in the casino or log on to an internet poker site confident that they know how to play the game. They sit down in a Low Limit game and play the way the have seen players play the final table of a televised No Limit tournament. They think that they can win a low limit game by bluffing and raising and they play like maniacs. This is one of the types of new players you will see in the Poker room these days. They are really easy to spot. Other players who have had their interest piqued by TV or have played a little on the internet are a meeker type. They are weak passive players who will sit down in a game and play a lot of hands but rarely raise of fold.

Both the maniac and the passive players have something in common. They don’t know how to play the game properly. They rarely have any concept of starting hand requirements, pot odds or even how to read the board. Some of them will use the any two will do strategy while others will be more selective and wait for two suited cards. Many of the new players think that a single ace is the Holy Grail and constitutes a raise every time they have one. They will cold call raises with hopeless hands and chase all the way to the river looking for a miracle card.

The number of new players has actually been a double edge sword for the knowledgeable player. Bad players are profitable for good players. In low limit games you will make more money from your opponent’s mistakes than you will from your own fancy play. This is because most of the new players are only interested in their own cards. Few of them even notice what type of hands the other players are playing.

free poker games just a click away at alamopoker.net !

2005-04-28T10:35:00.000-07:00

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Free Poker games info!

2005-04-27T08:31:00.000-07:00

Online poker continues to be the hottest trend in internet gaming. Thousands of people are playing online free poker games online every day and winning real money. Most Texas Holdem poker sites offer software downloads at no charge, along with competitive promotions when you sign-up. Whether you enjoy tournaments, regular poker tables, real money poker games or playing just for fun, there are plenty of sites that can meet your online poker needs. You can even choose from several popular poker game variations, including texas hold'em, 7 card stud, and omaha high poker.

Free Poker Games Info!

2005-04-26T18:38:00.000-07:00

Online Poker, the royal flush of the Internet. Whether you are searching for online poker, video poker, strip poker, or free poker games, allow us to be your guide thru the wide world of internet poker. Brush up on the latest in Poker terminology and learn the latest tips and strategies. Guaranteed not to fold, we will locate the best website that fulfills your every poker need.

Playing Free Poker Games free poker games

2005-04-22T18:52:00.000-07:00

free poker games 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 free poker games it is essential to achieving high performance. This paper describes and evaluates the implicit and explicit learning in the free poker games 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 free poker games, 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 free poker games. 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 free poker games 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 free poker games programs has lagged behind the advances in other games. However, it is also the reason why these games promise higher potential research benefits.

free poker games has a rich history of scientific investigation. Economists and mathematicians have applied a variety of analytical techniques to certain free poker games-related problems. However, since "real" free poker games 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" free poker games 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 free poker games. However, free poker games 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 free poker games 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 free poker games-playing program for simplified 5-card draw free poker games [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 free poker games (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 free poker games 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 free poker games 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 free poker games, and it is unlikely that we will ever be able to do so." In theory, their approach could be used to build an optimal free poker games player for a real variant of free poker games. 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 free poker games. We have chosen to study the game of Texas Hold'em, the free poker games variation used to determine the world champion in the annual World Series of free poker games. Hold’em is considered to be the most strategically complex free poker games variant that is widely played.

Our experiences with our first free poker games 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 free poker games 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 free poker games, 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 free poker games 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 free poker games Player

We have identified several key components that address some of the required activities of a strong free poker games 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 free poker games, but may eventually be required for world-class play.

Opponent modeling is integral to successful free poker games 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 free poker games, 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 free poker games 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 free poker games 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 free poker games 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 free poker games 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 free poker games 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 free poker games. 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 free poker games. 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, free poker games 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 free poker games, it can be the distinguishing feature between players at different skill levels. If a set of players all have a comparable knowledge of free poker games 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 free poker games, 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 free poker games 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 free poker games 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 free poker games-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 free poker games 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 free poker games 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 free poker games, 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 free poker games-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.free poker games

free poker games 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.free poker games

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