[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-571422-105":3,"detail-sidebar-cat-1-en-105":81,"doc-detail-571422-en":127},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","imperfect-information-games-poker","Imperfect Information Games - Poker","","Imperfect Information Games: Poker explains key distinctions between perfect vs. imperfect information and deterministic vs. stochastic outcomes. It defines endogenous uncertainty from hidden player holdings and exogenous uncertainty from chance events such as card dealing. The document develops strategy concepts in normal-form games, including pure, mixed, and behavioral strategies, and formalizes best responses, Nash equilibrium, and Pareto dominance. It further introduces information sets as the context for action selection and contrasts them with perfect information games.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/presentations/","Presentations",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/template/imperfect-information-games-poker/571422/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/imperfect-information-games-poker/571422.png","ImageObject",442,249,{"name":42,"@type":43},"Jacob","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-22","2026-10-13",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",6,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What is the difference between perfect information and imperfect information games?","Question",{"text":63,"@type":64},"Perfect information games make the actions and holdings of other players fully known at all times, while imperfect information games withhold some information about the arena or player holdings.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How do deterministic and stochastic games differ?",{"text":68,"@type":64},"Deterministic games have certain outcomes for any action, while stochastic games include actions with probabilistic outcomes such as dealt cards or rolled dice.",{"name":70,"@type":61,"acceptedAnswer":71},"What is a Nash equilibrium and why is it stable?",{"text":72,"@type":64},"A Nash equilibrium is a pair (or profile) of actions where each player’s action is the best response to the other’s, so neither can switch to improve its payoff given the opponent’s fixed strategy.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},571422,1792171601,{"code":4,"msg":82,"data":83},"success",[84,88,93,98,103,108,113,118,123],{"id":85,"doc_module":22,"doc_module_name":25,"category_name":29,"show_sort_weight":86,"slug":87},11,90,"presentations",{"id":89,"doc_module":22,"doc_module_name":25,"category_name":90,"show_sort_weight":91,"slug":92},12,"Resumes",80,"resumes",{"id":94,"doc_module":22,"doc_module_name":25,"category_name":95,"show_sort_weight":96,"slug":97},14,"Invoices",70,"invoices",{"id":99,"doc_module":22,"doc_module_name":25,"category_name":100,"show_sort_weight":101,"slug":102},15,"Posters",60,"posters",{"id":104,"doc_module":22,"doc_module_name":25,"category_name":105,"show_sort_weight":106,"slug":107},16,"Social Media",50,"social-media",{"id":109,"doc_module":22,"doc_module_name":25,"category_name":110,"show_sort_weight":111,"slug":112},17,"Forms",40,"forms",{"id":114,"doc_module":22,"doc_module_name":25,"category_name":115,"show_sort_weight":116,"slug":117},18,"Letters",30,"letters",{"id":119,"doc_module":22,"doc_module_name":25,"category_name":120,"show_sort_weight":121,"slug":122},21,"Paper Templates",5,"papers-templates",{"id":124,"doc_module":22,"doc_module_name":25,"category_name":125,"show_sort_weight":4,"slug":126},158,"General","general-158",{"code":4,"msg":82,"data":128},{"doc_id":79,"user_id":129,"nickname":42,"user_avatar":130,"doc_module":22,"category_id":85,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":136,"language":137,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":138,"faqs":139,"seo_title":140,"seo_description":12,"update_tm":141,"read_time":142},962084931830,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Imperfect Information Games: Poker  \nKeith L. Downing  \nJanuary 17, 2023  \nKeith L. Downing Imperfect Information Games: Poker  \nPerfect Info-state of playing arena and other players holdings known at all times.  \n Imperfect Info-some info about arena or players not available.  \n Deterministic-outcome of any action is certain.  \n Stochastic-some actions have probabilistic outcomes, e.g. dealt cards, rolled dice, etc.  \nPerfect Imperfect  \nInformation Information  \n\n| Stratego\u003Cbr>Battleship\u003Cbr>Scotland Yard | Bridge Risk\u003Cbr>Hearts\u003Cbr>Poker\u003Cbr>Scrabble |\n| --- | --- |\n| Chess\u003Cbr>Othello\u003Cbr>Checkers\u003Cbr>Go | Monopoly Backgammon\u003Cbr>Ludo 2048 |\n\nDeterministic Stochastic  \nKeith L. Downing Imperfect Information Games: Poker  \nThe terminology is slightly different.  \nImperfect Information Games  \n Games in which players make moves without knowing either a) the actions or holdings of other players, or b) the results of external processes (aka nature or chance) .  \n Endogenous Uncertainty-that related to the actions or holdings (e.g. hole cards, hidden pieces, etc.) of other players. This includes games  \nwhere players make moves simultaneously, such as rock-scissors-paper and prisoner’s dilemma.  \n Exogeous Uncertainty-that arising from external stochastic processes, such as the roll of dice, dealing of cards, etc.  \n In these games, a player’s beliefs about the possible opponent’ states and actions, as well as possible outcomes of chance events, are crucial in determining behavior.  \n Thus, a player’s strategy will normally a) account for probability distributions over endogenous states and exogenous events, and b) constitute a probability distribution over possible actions  for that player.   \nKeith L. Downing Imperfect Information Games: Poker  \nPure Strategies  \nA single fixed action for each state.  \nGame States  \nActions  \nBehavioral Strategy  \nMixed Strategy  \n0.3  \nStochastically pick a pure strategy, then play it the whole game.  \nAction length = probability  \nStochastically pick an action at each state.  \n Pure-For each game situation, a pure strategy has ONE particular action.  \nDeterministic mapping from states to actions.  \n Mixed-Probability distribution over complete, pure strategies.  \n Behavioral-Probability distributions over actions at each game state.     \nKeith L. Downing  Imperfect Information Games: Poker   \nKey Features of a Normal-Form Game  \n A set of two or more players.  \n A set of legal actions for each player.  \n A set of payoffs: a mapping from each combination of player actions to rewards for each player.  \n\n| Player 1\u003Cbr>Actions | Player 2 Actions |  |  |\n| --- | --- | --- | --- |\n|  | X Y Z |  |  |\n| X\u003Cbr>Y\u003Cbr>Z | (3,3) | (0,4) | (0,3) |\n|  | (4,0) | (3,3) | (0,4) |\n|  | (3,0) | (4,0) | (3,3) |\n\n Cell entries / pairs = payoffs to players 1 and 2 .  \n Best-Response (BR) action-bold font-BRi(k) = highest-paying action choice for player i when opponent chooses action k.  \n BR1 (X ) = Y; BR1 (Y ) = Z; BR1 (Z ) = Z  \n BR2 (X ) = Y; BR2 (Y ) = Z; BR2 (Z ) = Z  \n Nash Equilibrium-blue font-a pair of actions, k1 and k2 , where BR1 (k2) = k1 and BR2 (k1) = k2 , i.e. , BR1 (BR2 (k1)) = k1. Intuitively: a situation where neither player can choose a better action to counter that of its opponent.      \nKeith L. Downing Imperfect Information Games: Poker  \nDefine a strategy profile as a set of strategies (s), one for each player, e.g. s = (Y,X) in the game above.  \n Let v1 (s) and v2 (s) be the payoffs for players 1 and 2 for profile s.  Profile s pareto dominates s’when ∀i : vi (s) ≥ vi (s′) and  \n∃k ∋ vk (s) > vk (s′) . I.e., payoffs for each player are at least as good with s as s’, and at least one player does better with s than with s’.  \n A pareto optimal profile is one that is not pareto dominated by anyother profile. Note: This does not mean that it must pareto dominate all other profiles.  \n In game above, there are 7 pareto optimal payoffs: 2 x (0,4), 2 x (4,0), 3 x (3,3), but each only dominates one other ","cbCaiiVQYYTd5rkD","https://ap.wps.com/l/cbCaiiVQYYTd5rkD","pdf",1747136,88,"English","# Imperfect vs. Perfect Information\n## Deterministic vs. Stochastic\n## Endogenous and Exogenous Uncertainty\n# Strategies and Uncertainty\n## Pure, Mixed, and Behavioral Strategies\n# Normal-Form Game Concepts\n## Key Features of a Normal-Form Game\n## Best Response (BR)\n## Nash Equilibrium\n## Pareto Dominance and Pareto Optimality\n# Information Sets\n## Definition of Information Sets\n## Perfect Information as Singleton Sets","[{\"question\":\"What is the difference between perfect information and imperfect information games?\",\"answer\":\"Perfect information games make the actions and holdings of other players fully known at all times, while imperfect information games withhold some information about the arena or player holdings.\"},{\"question\":\"How do deterministic and stochastic games differ?\",\"answer\":\"Deterministic games have certain outcomes for any action, while stochastic games include actions with probabilistic outcomes such as dealt cards or rolled dice.\"},{\"question\":\"What is a Nash equilibrium and why is it stable?\",\"answer\":\"A Nash equilibrium is a pair (or profile) of actions where each player’s action is the best response to the other’s, so neither can switch to improve its payoff given the opponent’s fixed strategy.\"}]","Imperfect Information Games - Poker | PDF",1791916648,31]