[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571750-105":53,"doc-detail-571750-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","optimal-drawing-strategy-for-deuces-wild-video-poker","Optimal Drawing Strategy for Deuces Wild Video Poker","","Video poker is a popular computerized poker variant that enables rigorous mathematical evaluation of play. This report analyzes the Deuces Wild version to determine an optimal strategy that maximizes long-run winnings relative to the bet. The work outlines a method to compute expected value for each possible way to play a hand, accounting for wild cards and penalty cards that affect probabilities. A computer algorithm enumerates outcomes, applies symmetries to reduce complexity, and derives a final strategy from grouped expected-value results.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/optimal-drawing-strategy-for-deuces-wild-video-poker/571750/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/optimal-drawing-strategy-for-deuces-wild-video-poker/571750.png","ImageObject",442,249,{"name":88,"@type":89},"eBook King","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-21","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":47},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What game variant is analyzed and why does it add complexity?","Question",{"text":108,"@type":109},"The analysis focuses on the Deuces Wild video poker variant, where twos are wild and can substitute for other cards, making the probability and strategy structure more complex.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How is the optimal play for a hand determined?",{"text":113,"@type":109},"For each possible way to play a hand, the expected value is computed by enumerating draws, calculating probabilities of paid hands, multiplying by payoffs, and selecting the play with the highest expected value.",{"name":115,"@type":106,"acceptedAnswer":116},"What optimization reduces computation time?",{"text":117,"@type":109},"Suit symmetries are used so equivalent configurations across suits share expected values, reducing the number of distinct hands from about 2.6 million to around 130 thousand.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},571750,1792403786,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":47,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":135,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":76},962088006270,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Optimal Drawing Strategy for Deuces Wild Video Poker  \nStephen Jensen  \nAbstract  \nVideo poker, an extremely popular computerized version of the traditional game of poker, o®ers many opportunities for mathematical analysis. Often, an optimal strategy exists which can, in the long run, assure a player of winning more than he bet. As part of a summer undergraduate research project, Professor Ethier and I chose to analyze the \\Deuces Wild\" variant of video poker and to ¯nd its optimal strategy. Choosing this particular type of video poker was motivated by its exceptional popularity as well as the added challenge posed to the analysis by the presence of wild cards. Since this analysis has been done before[?], albeit with with much less precision than the present analysis, it provided a good problem for an undergraduate project since the results could be veri¯ed.  \n1 Introduction  \nVideo poker games are typically based on traditional ¯ve card draw poker. Many variants of video poker exists, and each have a particular set of rules. For \\Deuces Wild,\" the twos are wild, in that they can take the place of anyother card in a hand. A game of video poker is begun by placing a bet, usually one to ¯ve units of currency (such as quarters or dollars) . The machine then deals ¯ve cards from a randomized deck of 52 cards. The player can then choose which cards to keep and the machine replaces discarded cards from the top of the deck. A bet is won when the resulting hand is a \\paid hand\"illustrated below.  \nTable 1: Paid hands, examples, and their payo®s for a one unit bet  \n\n| Paid Hand | Example | Payo® |\n| --- | --- | --- |\n| Natural Royal Flush | 10|J|Q|K|A| | 800 |\n| Four Decues | 4~2~2|2Ä2} | 200 |\n| Wild Royal Flush | 10~J~K~2Ä2} | 25 |\n| Five of a Kind | 4Ä4|4~4}2| | 15 |\n| Straight Flush | 3|4|5|6|7| | 9 |\n| Four of a Kind | 6|6~6Ä6}J| | 5 |\n| Full House | 4|4}4~8Ä8~ | 3 |\n| Flush | 3~8~7~10~A~ | 2 |\n| Straight | 4|5Ä6Ä7~8} | 2 |\n| Three of a Kind | 8|8~8}J|3| | 1 |\n| Other | 3~9~7ÄJ}A| | 0 |\n\nAfter winnings are paid (or not paid) and another bet is placed, the machine creates a new random deck and deals another ¯ve cards. It should be noted that for the 800 for 1 payo®, a ¯ve unit bet is usually required.  \n2 Method  \nThe optimal strategy of a video poker game is the combination of the optimal ways to play each of the à 525 ! possible hands. The optimal play for a hand is found by computing the expected value for each of the 25 possible ways to play the hand and taking the play with the highest expected value. This is complicated by the presence of \\penalty cards\" which, when discarded, a®ect the chance of getting a certain paid hand, and therefore the expected value of the hand. It becomes obvious that doing this analysis entirely by hand isan extremely di±cult problem. Using a computer, though, it becomes much easier.  \nTo complete this on a computer, I devised an algorithm which would ¯nd the optimal play for all of the possible hands. For each possible play of each hand, the program would replace the discards from the remaining 47 cards in the deck and count how many of each paid hand it encountered. Using these quantities, it would divide the number of instances of the paid hands by à 47j !, j=number of cards drawn. This became the probability of getting  \nthat particular paid hand. Then, multiplying the probability of getting a paid hand by the associated payo®, and then adding these values together, the program arrived at the expected value. This was then repeated 31 more times and the greatest value found was kept as the optimal play. This process was then repeated for each of the approximately 2.6 million possible hands.  \nDone improperly (see below), even a fast computer would take a long time to ¯nish this problem. A major optimization which can be done, though, is to pare down the number of possible hands. This is feasible since there are symmetries in the suits. For instance, there are four possible ways to geta particula","cbCaiqtsAMqFTfuR","https://ap.wps.com/l/cbCaiqtsAMqFTfuR","pdf",66201,7,"English","# Introduction\n# Method\n# Strategy","[{\"question\":\"What game variant is analyzed and why does it add complexity?\",\"answer\":\"The analysis focuses on the Deuces Wild video poker variant, where twos are wild and can substitute for other cards, making the probability and strategy structure more complex.\"},{\"question\":\"How is the optimal play for a hand determined?\",\"answer\":\"For each possible way to play a hand, the expected value is computed by enumerating draws, calculating probabilities of paid hands, multiplying by payoffs, and selecting the play with the highest expected value.\"},{\"question\":\"What optimization reduces computation time?\",\"answer\":\"Suit symmetries are used so equivalent configurations across suits share expected values, reducing the number of distinct hands from about 2.6 million to around 130 thousand.\"}]","Optimal Drawing Strategy for Deuces Wild Video Poker | PDF",1791923553]