By. It is possible to squeeze more people into one game, but the game is less fun with that many people and most online casinos and card rooms nowadays cap the game at 9 players per table. 1 However, heads-up limit Texas hold’em has fewer than 1014 decision points. There is a limit on how many starting. Hand Abbreviation. This is. cash game strategy tournament strategy beginner strategy no-limit hold’em bet sizing pot odds bluffing value betting live poker online poker In this Series 1 10 Texas Hold'em Tips: The Check-RaiseThis A. The Illustrated Guide to Texas Hold'em takes you from novice to skilled player fast. The dealer button in Texas Holdem poker is in the best position, and each position to the right of the button is the next best position. Therefore, players who implement GTO in their game will allow their opponents to make. For more, don’t miss Complete Texas Hold’em Strategy Guide | How To Play Poker. Texas Holdem for advanced players by David Sklansky and Mason Malmuth This was the bible for limit Holdem player in the late eighties on. In No-limit Texas Hold’em a player may bet all of his/her chips at any time At a $. 1. Pocket Aces AA. Bigger Pots: No-Limit is vastly more popular thanks to its propensity to create massive pots and huge swings in action. This chart is a GTO poker chart for hands to open-raise within a 6-max game. Spread limit Hold'em is stated as 2/10 or something similar. Not only will this get you extra cash and increase your overall win rate, but it will also give you more breathing space as you improve your skills, particular for no-limit texas. smallest variant of poker played by humans. As you might have already known, understanding the strategy involved in a game of poker is very crucial to your success in the game. A player raises to $7 from the button and it folds to you. There are 9 unknown cards left that could complete your flush so you have 9 outs out of 47 total unknown cards (52 cards in the deck – your 2 cards and – 3 more on the flop). Game selection is the process of choosing which game you’re going to play. Having an understanding of GTO poker is a requirement for succeeding at no-limit hold’em, to learn GTO there is no better place to start than with preflop strategy. You're UTG+1 in a 9-Max $1/$2 No Limit Hold'em cash game. The WSOP Main Event is a no-limit Texas Hold’em tournament, as are all the WPT TV final tables. Find out how to bet, bluff, read, exploit and win in NL with. Casino expert. 02. Time to get to the heart of the Big Stack Strategy: playing after the flop. No-Limit Hold'em is a dynamic, situational game. Poker News. Don’t Call All the Time. 6. It also. No-Limit Texas Hold’em Poker. Make solid 3 or 4 BB raises when entering an un-opened pot. As technology continues to advance, it’s exciting to envision where the future of online Texas Hold’em will lead! 18 Nov 2023 Internet Texas Holdem offers free poker strategy advice, articles, and discussion forum!In a 9-handed cash game, the standard open-raise size is usually around 3 blinds. We previously discussed the top-20 starting hole cards, button strategy and how to count outs. Texas hold’em is a game of strategy, like any poker game. Annie Duke & John Vorhaus. 1: Strategic Play. Texas Hold'em No Limit Advanced Optimal Overbetting Strategy in Poker. $3495. +. Don’t limp into pots ever. In the development of artificial intelligence (AI), games have often served as benchmarks to promote remarkable breakthroughs in models and algorithms. The base strategy was computed in eight days, and at market rates would cost about $144 to produce, much smaller than contemporary superhuman game-playing milestones such as AlphaZero. decisively defeated four poker pros across 120,000 hands of two-player Texas Hold’em, but as the Facebook blog post explains, was limited by the fact that it only faced off with one. Most importantly, I’m going to share with you the key strategy we used during our consulting, which. 02. This is the best selection of hole cards on which you can win profitably. They also recognize how flops may or may not have helped their opponents, and play accordingly. 25BB open has to pick up the pot less than half of the time to show an immediate profit. The comparable variant of poker is heads-up no-limit Texas hold’em (HUNL). Recognize villain strength. Games like 7 Card Stud, Limit Hold'em, and Razz, use limit betting rules. Instead of just dictating a bunch of rules that work only some of the time, this book teaches you to become a great poker thinker and strategist, so that you can expertly navigate any poker challenge that you encounter. The invention of Texas Holdem is unclear but Robstown, Texas is the official birthplace of the game as declared by the Texas State Legislature. Annie Duke & John Vorhaus. Since this is a beginner poker strategy series,. The Biggest Bluff: How I Learned to Pay Attention, Master Myself, and. (Note: sit and go’s are a type of poker tournament). This item: Decide to Play Great Poker: A Strategy Guide to No-Limit Texas Hold ' Em. A player raises to $7 from the button and it folds. Texas Hold'em Betting Rules: Limit, No-Limit & Pot-Limit; Players: Just as in Texas Hold’em there can be 2-10 players from heads-up to full ring. closer to the top of the chart), the betterNo Limit Texas Hold’em Rules. I cannot sweat enough how important this poker tip is! Your goal is to learn poker strategy and concentrate on seeing all the information. No longer does. 1. This phrase drove the pre-flop strategy of almost every tournament regular for years, and it still has some merit. Strategy Guide for No-Limit Texas Hold'em (Cash Game) Introduction; Key Advice and Common Mistakes; Pre-Flop Play; Flop Play; Specific Holdings at Flop Play; On the Turn; On the River; Special Moves; Odds; Introduction . Find out how to bet, fold, raise, and bluff your way to the pot with five community cards and two hole cards. 24. 2012 More Hold'em Wisdom for all Players. For even a simplified version of Texas Hold ’em, played “heads up” (i. In no limit holdem, you can bet as many chips as you want to, as long as you have the money in front of you. Page 1. The WSOP Main Event is a no-limit Texas Hold’em tournament, as are all the WPT TV final tables. It folds to the button in a $1/$2 No-Limit Hold’em cash game and he raises to $8. In Hold’em, there are a 169 combinations of hands of you can be dealt, not including hands of the same suit. No-limit Texas Hold’em (NLTH) is one of the most popular and challenging poker games. 3 MISTAKES To AVOID. No-Limit Hold’em…. If you flop Q♦ 2♥ 3♠ you lose your stack to AA and KK. “No Way To Prevent This” Says Only Player Who Regularly Gets Involved In Big Pots With Q3s. Basic Strategy. In part one of this article, we analyzed the play of drawing hands in heads-up situations and concluded an aggressive approach is usually best. You should 3-bet and 4-bet in Texas Holdem i f you’re dealt these hole cards:Welcome to Low Limit Holdem Strategy and Tactics. Seat 2: Small Blind (SB) - The Small Blind is directly to the right of the Big Blind. Cash games, tournaments, and sit and go’s, are the main three. In No-Limit Hold ’em, the oNo-Limity betting rule is that the minimum be at least the size of the big. In my no-limit Texas hold'em home games, players are allotted approximately $2500 worth of chips. 300 big blinds for Limit Hold'em. 99; $9. Just don't get crazy - keep your goal in mind. In no limit, there is no limit to how many chips you can bet at any point in the hand. This chart details the Hole Cards that we believe you should open with in an 8-max No-Limit Hold ‘Em tournament without antes – such as Match Poker Online’s™ Battle Royale tournament. Poker games; Texas Hold'em. As a result, players typically play fewer hands from early positions than later positions. Nothing brings out the adrenaline quite like a heads-up game in the No Limit Texas Hold’em world. Miscellaneous Poker books To. In. Many people dream of winning the World Series of Poker Main Event which crowns the unofficial best No Limit Texas Hold'em player every year. That can mean playing for much less than what one would find in a live casino. When to fold before the flop. It offers a really good, easy-to-follow, and detailed breakdown of sit and go strategy for every stage of the play. 1% chance to hit your flush on the turn. $3494. Something like: A-T, A-xs, K-Q, K-Js-K-9s, JT-89 both suited or not, 45s+, and 57s+. 0 5 Stars 36 4 Stars 2 3 Stars. $2695. The Pot-Limit Omaha Book by Tri (slowhabit) Nguyen. American players only . Updated: November 6, 2022. Phil Gordon took everything he learned during his 15 years as a professional poker player and as a highly sought-after Texas Hold’em teacher and poured it into this book. #3. RR or Fold against 1 Player, Call 3. Poker Tip #6. Everyone is going to have holes and weaknesses in their game. Check out my Full Contact Poker Podcast at head-to-head in Texas Hold’em is not the same as playing against multiple opponents. Menu; Strategy. 1. Cash games, tournaments, and sit and go’s, are the main three. Rounded to the nearest tenth of a percent, 9/47 = 19. However, to make it a winning one, you need to have more than a working knowledge of the game. Here is an example-hand to demonstrate how a 5-bet bluff works: Full Tilt Poker Game #10852419747: Table Worron (deep hu) - $0. Each of them possesses a probability to win. In No-Limit Hold'em, drawing hands can often be very profitable. Limit was THE way to play Hold’em until the poker boom took off in the early to mid 2000s. $1,500 No-Limit Hold'em, earning $262,502. Fundamental No Limit Hold'em Mathematics You Need To Know. Those games have a lot more variables. The WSOP Main Event is a no-limit Texas Hold’em tournament, as are all the WPT TV final tables. One of the goals of game theory is to "solve" games. The Secrets of Professional Tournament Poker, The Mental Game of Poker, and Ace on the River are also excellent titles for improving your strategies. But you can only use two of those cards, and must use exactly two cards to complete your poker hand. No-Limit Texas Hold’em can be played in several different formats. When it is played with just two players (heads-up) and with fixed bet sizes and a fixed number of raises (limit), it is called heads-up limit hold’em or HULHE ( 19 ). The game tree solve must be able to fit inside the RAM. Limping into pots, calling the preflop. 1 Introduction Texas Hold’em Poker is becoming closer and closer to being solved. However on the next hand the pot might be smaller, let’s say it’s just $12. 1. k. By Greg Walker. The Texas Hold'em games you find in the casino are generally very loose. 1. Rank. For all you skim-readers, here are the basic rules of bankroll management for Texas Hold'em. This never changes. Comments. 7. No-Limit Texas Hold’em. That’s why our go-to play with them is 3-betting. However, that is likely a result of the greediness of Q-learning, which could make it very exploitable for human players. Imagine holding a weak flush in Hold’em. The resulting program Cepheus is the first computer programNo-limit Texas Hold'em Top Advice. After every player has two hole cards, the. Use this simple formula in Texas Hold'em poker games to start winning much more consistently. Texas hold ‘em (còn được gọi là Texas holdem, hold ‘em hoặc holdem) là một trong những biến thể phổ biến nhất của game bài Xì Tố (Poker), trong đó mỗi người chơi được chia 2 lá bài tẩy và sẽ phải kết hợp với 5. One of the most overlooked strategies for Texas Hold’em cash games comes before you even sit down at a table. Fun, Fact & Strategy. Beyond his poker accomplishments, O'Kearney is. This is done to maintain a low rake. How to Crush $2/$5 No Limit Hold’em (In 8 Weeks) In this blog post, I’m going to share with you a case study from my client James who went from losing at $1/$3 No limit, to crushing at $2/$5, profiting over $40 per hour, in just 8 weeks. $1629. Live Events 2. Anyway, I would find my greatest success, and profits, playing this form of Texas Hold’em – No Limit ring games. 100% up to $600. In Exploitability and Game Theory Optimal Play in Poker, Jen Li introduces and explores the theory and briefly touches on the mathematics involved in understanding Nash equilibriums present in a 2-player game of no limit Texas hold’em. $2841. Top Ultimate Texas Hold 'Em - Rules and Strategy Chart Online Casinos UP TO $11,000 BONUS. While studying No-Limit Hold’em is a great idea for any poker player, it’s not the only way to learn about poker if you’re new to the game. Learn how poker players can take advantage of position when making decisions both before and after the flop. There is a lot of fixed limit based material out there, and being as these games haven't undergone the same level of evolution that NL Holdem and PLO has, there is still an enormous amount of scope for getting ahead of the crowd if you are prepared to put the. Texas Hold'em Poker is the most popular poker game, or poker variation, in the world and the one you've most likely seen played on TV. The resulting program Cepheus is the first computer programNo-Limit Texas Hold 'Em is such a complex system that "we cannot derive a dominant strategy in a closed form. More Texas Holdem Starting Hands. For Texas hold'em poker, "The Theory of Poker" by David Sklansky is highly recommended. Look, no one enters a casino or logs on to an online game with the intention of folding hand after hand. The best. 2. Mark Patrickson • 789 Views • on 14/6/23. Hands like 83 should not be played past the preflop betting round. The most common mistake made by limit hold’em players is that they play too many hands. 1: Strategic Play. Poker betting strategy overview. The Portable Poker Pro: Winning Tips For Texas Hold'em. Mostly bet when you flop a strong hand. Don’t limp into pots ever. We will share a complete list of 30 top Texas Hold ’em strategy books! 1. Hold'em Poker for Advanced Players, 21st Century Edition by David Sklansky and Mason Malmuth Texas Hold 'em is not an easy game to play well. But where you’re sitting in relation to the action becomes part of your strategy when playing hold’em. The Chevy Cavalier of Poker. Poker Strategy; Rules; Poker Games. $0. IE, you can go all in. Go back to the awesome Texas Hold'em Strategy. It is possible to squeeze more people into one game, but the game is less fun with that many people and most online casinos and card rooms nowadays cap the game at 9 players per table. No-limit Texas Hold’em (NLTH) is one of the. Although the format is simple, there are a number of complex skills needed for a good Texas Hold’em strategy, including probabilities, psychology, positional play and chip dynamics. The Book of tells by Mike Caro. Six-Plus Poker began in the high-stakes poke r rooms of Macau casinos. Doyle Brunson went so far as to dub Texas Hold’em “the Cadillac” of poker in his book Super/System. Learn Texas Holdem tournament strategy from some of the game’s best professional players. In this game, the betting and raising limits are fixed and divided into small and big bets. PokerListings » Poker Strategy » No-Limit Texas Holdem Tournament Strategy. Fixed Limit Hold'em is a game of patience and. If you bet too small, you could end up facing a re-raise or a check-raise, depending on your position. For example, if it’s a $2/$4 No Limit Texas Hold’em poker game with a $4 big blind, it would cost $4 to. 1 10 Texas Hold'em Tips: The Check-Raise; 2 10 Texas Hold'em Tips: Playing Suited Connectors; 3 10 Hold'em Tips: The Fundamentals of Set Mining; 4 10 Hold'em Tips: Pot Odds Basics; 5 10 Hold'em. Stud is played as a limit game. 1. com, and partypoker have Texas Hold’em action as low as $0. Some prefer limit games, some like the no limit variety. Alice. Mark Patrickson • 4,090 Views • on 8/12/21. A♣-A♦ and A♠-A♥ are different hands), but that is more of a “just for fun” number as suits have no value over each other in Texas Hold’em. Any time you raise the bet during any of the betting rounds, you can add as many chips as you have to the pot. These hands will be immensely profitable when our loose, passive opponents enter the hand, and get trapped when we flop a set, or make a well-disguised straight. Watch a 22-minute video with. Find out how to bet, fold, raise, and bluff your way to the pot with five community cards and two. In Texas Hold ‘Em each player plays the 5 best cards between the table and your hole cards. Basic Texas Hold em Poker Advice. The standard buy-in for this game is $200. Making money in No-Limit Texas Holdem poker starts with the hands you choose to play and when you choose to play them. Fixed Limit Hold'em columns & quizzes. “No Way To Prevent This” Says Only Player Who Regularly Gets Involved In Big Pots With Q3s. So leave multi-tabling for the future, stick with one table, and try to absorb all the information you can get. If No Limit Hold’em is the Cadillac of poker, Limit Hold’em is the Toyota Camry. An intro to Texas Holdem, strategy, rules and styles of play, all combined for you to understand. Classic and forever relevant. For simplicity, we will focus on a 6-handed game, which is the most popular format in online poker. Every poker player dreams about playing in high-stakes games for millions of dollars. 10 of 10. The Poker Puzzle by Oliver (Improva) Marx. In No-Limit, gather the amount that you’re going to raise and either announce. With high cards like AK and AQ, the ideal situation is to be heads-up (1v1) on the flop. Examples: A♥ 2♥ vs K♣ Q♠ on a flop of K♥ T♣ 8♥; K♣ Q♠ vs 8♦ 7♥ on a flop of K♦ 9♣ 6♥. The difference between no limit and limit is that the betting increases exponentially in no limit, and only linearly in limit. PokerListings Author. If you’re sticking with the same bet size then, based on the pot, your bet should be $9. ) It’s unlikely that we have this type of system lying around. This includes a (1) bet, (2) raise, (3) re-raise, and (4) cap (final raise). Limit Holdem restricts the bets. RGPS Iowa;1. The general idea of ThePokerBank is to teach you how to play winning no limit Texas Hold'em and help you find a better room to play at. 9. There are three types of Texas Hold’em. The thing is, though, in poker, no one is going to play correctly. No Limit Texas Hold'em The minimum bet in No Limit Hold'em is the same as the size of the big blind, but players can always bet as much more as they want, up to all of their chips. Intermediate level Texas Hold'em strategy articles - Take your game to the next level through our free strategy library. Top strategy tips for preflop betting: Don’t be afraid to bet or raise. The differences in the three types of Hold’em are only in the way you can bet your chips. Learn how to play Texas Hold'em No Limit, the most popular format of poker, with articles, videos and tips from experts. 10 Hold'em Tips: Bluff Catching. The purpose of this article is to assist beginner/intermediate players to improve their game. One of the goals of game theory is to "solve" games. Daniel Negreanu. Best Poker. Phil Gordon's Little Green Book: Lessons and Teachings in. They have become the most popular game in poker and where the majority of professional players earn their profits. 200. However it still exists in limit play. Heads-up No-Limit Hold'em requires the mastery of all the classic elements of poker - maths, psychology, hand reading and heart. 9 out of 5. An overview of the most important no limit texas hold'em strategy fundamentals. Table selection: Beware of tight/aggressive tables (low profit, high volatility) and avoid strong players that can read you and take your money. Texas Hold’em is a rather complex game, so describing a. Overall. As a rule, a maximum of 10 players play at one table. Whether you are playing poker for fun or you want to make some extra income, these 10 tips will help you play a stronger game and make more money: Bluff-catch with your medium-strength hands. Suited hands contain two cards of the same suit, like J♣9♣, A ♥ K ♥, K. Every time you read a Texas Hold'em strategy article, you should be actively trying to absorb the information as you go along. 5% of your stack. ”. Find out how identifying and counting outs can help a poker player determine the. Poker strategy for Texas Hold’em. No limit is placed on the size of the bets, although there is an overall limit to the total amount wagered in each game . ) In Fixed-Limit Hold’em, this is not a big problem since we can keep the pot small by simply calling down our opponent’s bets. Mathew Janda's Applications of No-Limit Hold'em represents an excellent resource for everyone looking to improve their Texas Hold'em fundamentals. When your opponents play weak hands before the flop, they make weak hands after the flop. You will often see players at your limit holding on to one of their kickers and drawing only two. The dealer begins each game by distributing these cards one at a time to each player, starting with the player in the small blind position. You want to make big pot hands, not potentially dominated ones. This book is often considered a top poker book for players keen on understanding the theory and strategy behind the game. For example, in a $1/$2 no-limit hold’em game, the small blind is $1 and the big blind is $2. In part two, we'll discuss playing drawing hands in multi-way pots. 4. That’s why the WSOP Main Event is always decided in No-Limit Hold’em. However, in practice there is little difference between betting $200 and betting $201. Playing fewer hands is a strategy to win Hold’em that involves you waiting for the right cards. While this has some to do with which stakes you’ll play, it has more to do with picking a table within those stakes. A lot of players at the casino play 30% of hands or more. That means some pretty big changes to the poker hand rankings, game dynamics and to standard Texas Holdem. 5 out of 5 stars 4. 2. 2NL. Watch a 22-minute video with tips and examples from a professional poker coach and player. 99;. View Profile. Look, no one enters a casino or logs on to an online game with the intention of folding hand after hand. The mandatory blinds count as the first bet, the open-raise counts as the second bet, and any raise following this will be a 3 bet. 1 10 Texas Hold'em Tips: The Check-Raise; 2 10 Texas Hold'em Tips: Playing Suited Connectors; 3 10 Hold'em Tips: The Fundamentals of Set Mining; 4 10 Hold'em Tips: Pot Odds Basics; 5 10 Hold'em. Pot Limit. Against loose players, a tighter strategy. 1 10 Texas Hold'em Tips: The Check-Raise; 2 10 Texas Hold'em Tips: Playing Suited Connectors; 3 10 Hold'em Tips: The Fundamentals of Set Mining; 4 10 Hold'em Tips: Pot Odds Basics; 5 10 Hold'em. Doyle Brunson’s Super System. No-Limit Texas Holdem Cash Game Strategy Hold’em tournaments draw a lot of attention but the true test of a poker player’s mettle is at the cash-game tables. Game Theory Optimal (GTO) Texas Holdem Poker Theory Game Theory Optimal (GTO) poker is “an umbrella term players use to describe the holy grail of no-limit holdem playing strategy” (MasterClass). For this reason, many players call this Six-Plus Hold'em. You've come to the right place. 3. If you’re an action junkie, you’ll probably love speed. 10 Essential Texas Hold’em Strategy Moves: The Bluff Catcher. The relative hand strengths. Seat 1: Hero. Bluff on the flop when you have backdoor draws. That's essentially the meat and bones of bet sizing in Texas Hold'em for you. Cards DealtFor example, let’s suppose you’re playing in a no-limit cash game and the pot contains $20 after the flop. Bluff on the flop when you have backdoor draws. Zynga Poker ™ – Free Texas Holdem Online Card Games. Speed hold’em is always played as a no-limit game, and most casinos offer it at low stakes starting at $0. The Little Green Book will help you develop a singular style. • Limit Poker, which allows for a maximum of four wager during all wagering rounds, including Raise, Re-raise, and. This item: Harrington on Hold 'em Expert Strategy for No Limit Tournaments, Vol. No-limit players must revise strategy for limit games, starting with how they approach implied odds. There are 169 different combinations of starting hands. However, there are varying degrees of short stack poker as a 10BB stack will require a slightly different strategy than a 40BB stack, and it is important to be aware of these differences. Read Review Visit. 1. Holz is considered one of the best players in the game today, even in semi-retirement. Additional strategic. As the title suggests, each of these tips are at least somewhat advanced. #3. Low-stakes includes $1-$3 (or $1-$2, depending on the casino you play. Sitting at the top of the list is the cash game variant of the Cadillac of poker. 1) Top Pair vs Flush Draw or Straight Draw. Poker tournaments have extreme variance even when you are playing well, but cash games can provide a steady income. It's all well and good reading a whole bunch of articles, but if nothing is sinking in or making a real difference to the way you play, then it's going to be pretty useless. The purpose of this article is to shed more light on: How to play Limit Texas Hold’em. PokerListings Team . More Praise from the Pros “Trust me, this book will open your eyes again and again. This is why poker legend Doyle Brunson called No Limit Texas Hold’em the ‘Cadillac of Poker’ and why the game favours the fearless and aggressive. A respectable bet size would be $15. An ε-Nash equilibrium is a strategy for each player where no player can increase. You can also practice Omaha at PlayWSOP. No-Limit Hold’em cash game strategy. Basically, I want to help you win more money from playing Texas Hold'em online. Pluribus plays the poker variation no-limit Texas hold 'em and is "the first bot to beat humans in a complex multiplayer competition". Poker Tip #6. 50, and the maximum bet for all rounds is whatever you have at the table. These. Say for example you're playing $1/$2 no-limit hold'em and get dealt in the big blind. Bluffing Strategy: Texas Hold’em Poker By Jim Beviglia Published: Dec 01, 2017, Updated: Jun 14, 2023 Ahh, bluffing in no-limit Texas hold’em…the most incorrectly used and down-right abused facet of most players’ poker game. Texas Hold'em combines your two. 2A strategy we’ll discuss during the project. It’s not advanced but should be the starting point for any new player wanting to learn Texas. There was no competition in 2015. In AI, two. When playing online Texas Hold’em tournaments, you need to be aware of the bubble and how it affects the aggressiveness of players remaining in the event. Mark Patrickson • 789 Views • on 14/6/23. Basically, I want to help you win more money from playing Texas Hold'em online. With fewer cards in the deck, you’ll hit your outs more often too. Texas Hold'em No Limit Intermediate Big Blind Poker Strategy . The purpose of this article is to assist beginner/intermediate players to improve their game. Read everything you need to know about the game. Raises are usually capped in Limit Hold’em games to one bet and three raises per round. The heads -up (that is, two -player) variant prevents op-Here is a short list of all the poker hands in Texas Hold’em, ranked from the strongest to the weakest: #1. Applications of No-Limit Hold em – by Matthew Janda 1. In addition, the button is the position from which it is most effective to start bluffs before the flop - large raises against limpers. In most forms of poker, such as the most popular one of No-Limit Texas Hold’em, there are forced blind bets that must be put forward by the players to the immediate left of the button before any cards are dealt. There are the game-theoretic bots, that play according to a strategy that gives rise to an ap-proximate Nash equilibrium.