{"id":324,"date":"2020-04-27T06:30:09","date_gmt":"2020-04-27T06:30:09","guid":{"rendered":"https:\/\/sites.ps.uci.edu\/mathceo\/?page_id=324"},"modified":"2020-05-16T22:16:42","modified_gmt":"2020-05-16T22:16:42","slug":"tic-tac-toe","status":"publish","type":"page","link":"https:\/\/sites.ps.uci.edu\/mathceo-old\/meeting-3\/tic-tac-toe\/","title":{"rendered":"Game 1: Tic-Tac-Toe"},"content":{"rendered":"\n<h3 class=\"wp-block-heading\">Starters: 3 questions<\/h3>\n\n\n\n<ul class=\"wp-block-list\"><li>What game(s) do you like to play?  For instance, a board game, a card game, or some computer game?  <\/li><li>What makes the game you play fun?<\/li><li>Do you have a strategy for winning the game?<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<!--nextpage-->\n\n\n\n<h3 class=\"has-text-align-center wp-block-heading\">Tic-Tac-Toe<\/h3>\n\n\n\n<p class=\"has-large-font-size wp-block-paragraph\"><strong>Games Rules<\/strong><\/p>\n\n\n<ul>\n<li>\n<p>2 Players, X and O, take turn marking up a 3 x 3 grid.<\/p>\n<\/li>\n<li>\n<p>The first player gaining three marks in a row (vertical, horizontal, or diagonal) wins.<\/p>\n<\/li>\n<li>If all 9 spaces are marked up without a winner, then the game ends in a draw.<\/li>\n<\/ul>\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Play Tic-Tac-Toe<\/strong> on the Google Sheets <a href=\"https:\/\/docs.google.com\/spreadsheets\/d\/1ZBN3suYh5kA72_UavKhfMgNULJFMVK7W8szDP9KLtIo\/edit?usp=sharing\" target=\"_blank\" rel=\"noreferrer noopener\">Worksheet<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<!--nextpage-->\n\n\n\n<h3 class=\"has-text-align-center wp-block-heading\">Strategy for Winning Tic-Tac-Toe?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">We&#8217;ll use the Google Sheet to answer the following questions:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question 1<\/strong>:  How many different winning 3-in-a-rows (vertical, horizontal, and diagonal) are there on the 3 x 3 grid?  These are the winning positions.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question 2:<\/strong>  For each of the 9 spaces on the grid, how many winning positions goes through it?  Can you determine which space give you the optimal chance of winning?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question 3:<\/strong>  Could you develop a strategy?  <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Tic-Tac-Toe is a game that if you play &#8220;<a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Tic-tac-toe#Strategy\" target=\"_blank\">perfectly<\/a>,&#8221; you are guarantee to never lose, that is, you either win or draw every game.  Have you found the strategy?   <\/p>\n\n\n\n<!--nextpage-->\n\n\n\n<h3 class=\"has-text-align-center wp-block-heading\">Tic-Tac-Toe on a 4&#215;4 Grid<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now let&#8217;s change the rule of Tic-Tac-Toe.  An easy change is to play on a 4 x 4 grid.  Give it a try on the Google Sheet.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question:<\/strong>  How many winning 3-in-a-rows are there now?  Can you find the winning strategy?  (Can you see the step prior to winning the game?)<\/p>\n\n\n\n<hr class=\"wp-block-separator\" \/>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s use the 4 x 4 board but change the rule to <strong>4-in-a-row<\/strong> to win.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question: <\/strong>Now, how many 4-in-a-row winning positions are there?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Question:<\/strong> Do you think there is a strategy to always win this game?   <\/p>\n\n\n\n<p class=\"wp-block-paragraph\">You can find the answer in this <a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/M,n,k-game\" target=\"_blank\">Wikipedia entry<\/a> where requiring 4-in-a-row on a 4 x 4 grid is known as the (4,4,4) game. <\/p>\n\n\n\n<!--nextpage-->\n\n\n\n<h3 class=\"has-text-align-center wp-block-heading\">Variants of Tic-Tac-Toe<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">There are many games that are very similar to Tic-Tac-Toe.  <\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/3D_tic-tac-toe\" target=\"_blank\"><strong>3D Tic-Tac-Toe<\/strong>:<\/a> This is Tic-Tac-Toe played on a three-dimensional grid.  The game is usually played on a 4 x 4 x 4 board with the first 4-in-a-row win.  The brand name for this game is called Qubic.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><a href=\"https:\/\/en.wikipedia.org\/wiki\/Ultimate_tic-tac-toe\">Ultimate Tic-Tac-Toe<\/a><\/strong>: This game involves nine Tic-Tac-Toe games arrange in a 3 x 3 grid.  The winner must win the Tic-Tac-Toe in the large 3 x 3 grid.  Play <a rel=\"noreferrer noopener\" href=\"https:\/\/ultimate-t3.herokuapp.com\/\" target=\"_blank\">here<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Read about other variants of the Tic-Tac-Toe game on Wikipedia <a rel=\"noreferrer noopener\" href=\"https:\/\/en.wikipedia.org\/wiki\/Tic-tac-toe_variants\" target=\"_blank\">here<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Starters: 3 questions What game(s) do you like to play? For instance, a board game, a card game, or some computer game? What makes the game you play fun? Do you have a strategy for winning the game?<\/p>\n","protected":false},"author":16,"featured_media":0,"parent":1909,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_vp_format_video_url":"","_vp_image_focal_point":[],"footnotes":""},"class_list":["post-324","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/pages\/324","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/users\/16"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/comments?post=324"}],"version-history":[{"count":15,"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/pages\/324\/revisions"}],"predecessor-version":[{"id":381,"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/pages\/324\/revisions\/381"}],"up":[{"embeddable":true,"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/pages\/1909"}],"wp:attachment":[{"href":"https:\/\/sites.ps.uci.edu\/mathceo-old\/wp-json\/wp\/v2\/media?parent=324"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}