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The assignment includes basic exercises about modifying dice by adding dots, choosing optimal faces under informed changes, and analyzing conditional strategies. A main exercise guides students to play against DiceBot digitally, run at least 300 trials, switch dice, and evaluate win rates. Additional tasks cover win probability w(A;B) using tables and compute w(A;B) and w(B;A).",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/mathematics-b-day-2016-dice-game-assignment-win-probability-and-strongest-dice/510313/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/mathematics-b-day-2016-dice-game-assignment-win-probability-and-strongest-dice/510313.png","ImageObject",300,407,{"name":92,"@type":93},"Indoniesian Boy","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-05","2026-10-05",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the core game and what does it mean to have a strongest die?","Question",{"text":112,"@type":113},"Each player throws a die; the die with the higher number of dots wins. A set of dice can lack a strongest die when there is no single die that wins most often against all others.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do Exercises 1 and 2 change the dice, and what decisions must be analyzed?",{"text":117,"@type":113},"Exercise 1 adds an extra dot to a specific face of Susanne’s die and asks how this affects long-run winning. Exercise 2 introduces three new dice (T, U, V) and asks which die Rogier should pick first and, given that choice, which die Susanne should pick next.",{"name":119,"@type":110,"acceptedAnswer":120},"How is win probability w(A;B) determined in Exercise 4?",{"text":121,"@type":113},"w(A;B) is the fraction of outcomes where die A beats die B. Students compute it by filling a table of faces and then calculating the corresponding proportion of wins for A versus B and vice versa.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},510313,1792170202,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},962090760608,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","A nice set of dice  \nMathematics B-day 2016, Friday 18 November, 9:00h-16:00h  \nIntroduction  \nAbout the assignment  \nA soccer competition is often exciting until the end. Some strange results can occur along the way. For example, if Ajax beats PSV and PSV beats Feyenoord it does not imply that Ajax then beats Feyenoord. It is not unthinkable that Feyenoord still beats Ajax. In this case, which of these three teams is the strongest team remains unclear. But that's soccer: : : During the Mathematics B-day this year, we examine whether this also occurs when you are rolling dice. We study this using a simple game of dice: both players have a die, they throw it, and the one with the highest number of dots wins. Sets of dice where there is no strongest dice exist, and for the main exercise you will make such a set.  \nThe structure of the day  \nThis Mathematics B-day assignment consists of basic exercises, extra exercises and a main exercise. Try to spend approximately half the day on the main exercise.  \nWhat to hand in?  \nYou will hand in a report by the end of the day. In this report you describe the results you found in the exercises and the main exercise. Tell your own story in such a way that it is clear and convincing. Of course, you will use relevant explanatory images as illustrations. Make sure you report is understandable for people who did not take part in the Mathematics B-day, but who do have su􀀎cient understanding of mathematics. That means that you must take care to introduce the exercises clearly, and that, where needed, you must refer back to what you found in previous exercises.  \nIn short: you write your own clear story, supported by mathematical arguments. The quality of your report will de􀀌nitely play a part in the assessment!  \nIt may be useful for your report to already start writing down the exercises and answers you found during the morning. Keep in mind that the whole report has to be handed in by 4 o'clock in the afternoon!  \nBasic exercises  \nExercise 1 (More dots)  \nSusanne and Rogier are both playing with `normal' six-sided dice with respectively 1, 2, 3, 4, 5 or 6 dots per face, they both throw it, and the one who throws the highest number of dots wins. Sometimes Rogieris the winner, sometimes Susanne is the winner. If they play often enough, they will, approximately, both win half of the games. Susanne doesn't like that...  \na) Susanne draws an extra dot on the face with two dots. So now she's playing with 1, 3, 3, 4, 5, 6. Rogier still playing with 1, 2, 3, 4, 5, 6 . In the long run, will Susanne now win more often, or doesn't it matter?  \nb) Rogier has found at that Susanne has put an extra dot on the face with two dots. Therefore, he is also going to add an extra dot on one of the faces. Which is the best face to draw an extra dot on to ensure he wins as often as possible, the one with 1, 2, 3, 4, 5 or 6? Why?  \nExercise 2 (Is more always better?)  \n\n| Rogier is also caught and they stop the game. Then Susanne comes up with three new dice, which we will simply call T , U and V. Susanne and Rogier may not both play with the same die.\u003Cbr>􀀏 T : 1 ; 2 ; 3 ; 4 ; 5 ; 6\u003Cbr>􀀏 U : 2 ; 3 ; 4 ; 5 ; 6 ; 7\u003Cbr>􀀏 V : 1 ; 1 ; 1 ; 1 ; 1 ; 100\u003Cbr>They start another game of dice, and Rogier chooses a die 􀀌rst. After that, Susanne chooses a die.\u003Cbr>a) Which die should Rogier choose, and why?\u003Cbr>b) Say that Rogier chooses die U. Which die is then the best option for Susanne, and why? |\n| --- |\n| Exercise 3 (Playing against the DiceBot) |\n\nIt is time for you to play dice. You will do so digitally. You will play the variant of the game where you get to pick a die 􀀌rst. Next, your opponent DiceBot will choose a die. DiceBot is a computer program that is remarkably good at this game.  \nGo to [http://www.fisme.science.uu.nl/wisbdag/opdrachten/dice/](http://www.fisme.science.uu.nl/wisbdag/opdrachten/dice/)  \n(short URL: [http://bit.ly/2euSHM7](http://bit.ly/2euSHM7) , or use the QR code shown below)  \nAs you can see, there ","cbCaijietHxY1xdG","https://ap.wps.com/l/cbCaijietHxY1xdG","pdf",1039850,15,"English","# Introduction\n## About the assignment\n## The structure of the day\n## What to hand in?\n# Basic exercises\n## Exercise 1 (More dots)\n## Exercise 2 (Is more always better?)\n## Exercise 3 (Playing against the DiceBot)\n## Exercise 4 (Win probability)\n# Main tasks and reporting","[{\"question\":\"What is the core game and what does it mean to have a strongest die?\",\"answer\":\"Each player throws a die; the die with the higher number of dots wins. A set of dice can lack a strongest die when there is no single die that wins most often against all others.\"},{\"question\":\"How do Exercises 1 and 2 change the dice, and what decisions must be analyzed?\",\"answer\":\"Exercise 1 adds an extra dot to a specific face of Susanne’s die and asks how this affects long-run winning. Exercise 2 introduces three new dice (T, U, V) and asks which die Rogier should pick first and, given that choice, which die Susanne should pick next.\"},{\"question\":\"How is win probability w(A;B) determined in Exercise 4?\",\"answer\":\"w(A;B) is the fraction of outcomes where die A beats die B. Students compute it by filling a table of faces and then calculating the corresponding proportion of wins for A versus B and vice versa.\"}]","Mathematics B-day 2016 - Dice game assignment - Win probability and strongest dice | PDF",1791240381,38]