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</div> </header> <div id="main" class=" main"> <div id="loop-meta" class=" loop-meta-wrap pageheader-bg-default loop-meta-withtext"> <div class="hgrid"> <div class=" loop-meta archive-header hgrid-span-12" itemscope="itemscope" itemtype="https://schema.org/WebPageElement"> <h1 class=" loop-title entry-title archive-title" itemprop="headline">chess</h1> </div> </div> </div> <div class="hgrid main-content-grid"> <main id="content" class="content hgrid-span-8 has-sidebar layout-wide-right " role="main"> <div id="content-wrap" class=" content-wrap theiaStickySidebar"> <div id="archive-wrap" class="archive-wrap"> <article id="post-2081" class="entry author-uwhitcher post-2081 post type-post status-publish format-standard has-post-thumbnail category-147 category-bill-casselman category-math-and-social-sciences tag-chess tag-game-theory tag-tic-tac-toe archive-block archive-block2 hcolumn-1-2" itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost"> <div class="entry-grid hgrid"> <div itemprop="image" itemscope itemtype="https://schema.org/ImageObject" class="entry-featured-img-wrap"><meta itemprop="url" content="https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2024/07/cropped-FC1380x500x2.png?resize=690%2C288&ssl=1"><meta itemprop="width" content="690"><meta itemprop="height" content="288"><a href="https://mathvoices.ams.org/featurecolumn/2024/09/01/payoffs-and-strategies/" class="entry-featured-img-link"><img width="690" height="288" src="https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2024/07/cropped-FC1380x500x2.png?resize=690%2C288&ssl=1" class="attachment-hoot-large-thumb entry-content-featured-img entry-grid-featured-img wp-post-image" alt="Feature Column" itemscope="" decoding="async" fetchpriority="high" srcset="https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2024/07/cropped-FC1380x500x2.png?resize=690%2C288&ssl=1 690w, https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2024/07/cropped-FC1380x500x2.png?zoom=2&resize=690%2C288&ssl=1 1380w" sizes="(max-width: 690px) 100vw, 690px" itemprop="image" /></a></div> <div class="entry-grid-content"> <header class="entry-header"> <h2 class="entry-title" itemprop="headline"><a href="https://mathvoices.ams.org/featurecolumn/2024/09/01/payoffs-and-strategies/" rel="bookmark" itemprop="url">Payoffs and strategies</a></h2> </header> <div class="screen-reader-text" itemprop="datePublished" itemtype="https://schema.org/Date">2024-09-01</div> <div class="entry-byline"> <div class="entry-byline-block entry-byline-author"> <span class="entry-byline-label">By:</span> <span class="entry-author" itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person"><a href="https://mathvoices.ams.org/featurecolumn/author/uwhitcher/" title="Posts by Ursula Whitcher" rel="author" class="url fn n" itemprop="url"><span itemprop="name">Ursula Whitcher</span></a></span> </div> <div class="entry-byline-block entry-byline-date"> <span class="entry-byline-label">On:</span> <time class="entry-published updated" datetime="2024-09-01T00:01:05-04:00" itemprop="datePublished" title="Sunday, September 1, 2024, 12:01 am">September 1, 2024</time> </div> <div class="entry-byline-block entry-byline-cats"> <span class="entry-byline-label">In:</span> <a href="https://mathvoices.ams.org/featurecolumn/category/2024/" rel="category tag">2024</a>, <a href="https://mathvoices.ams.org/featurecolumn/category/columnists/bill-casselman/" rel="category tag">Bill Casselman</a>, <a href="https://mathvoices.ams.org/featurecolumn/category/math-and-social-sciences/" rel="category tag">Math and Social Sciences</a> </div> <div class="entry-byline-block entry-byline-tags"> <span class="entry-byline-label">Tagged:</span> <a href="https://mathvoices.ams.org/featurecolumn/tag/chess/" rel="tag">chess</a>, <a href="https://mathvoices.ams.org/featurecolumn/tag/game-theory/" rel="tag">game theory</a>, <a href="https://mathvoices.ams.org/featurecolumn/tag/tic-tac-toe/" rel="tag">tic-tac-toe</a> </div> <div class="entry-byline-block entry-byline-comments"> <span class="entry-byline-label">With:</span> <a href="https://mathvoices.ams.org/featurecolumn/2024/09/01/payoffs-and-strategies/#respond" class="comments-link" itemprop="discussionURL">0 Comments</a> </div><span class="entry-publisher" itemprop="publisher" itemscope="itemscope" itemtype="https://schema.org/Organization"><meta itemprop="name" content="Feature Column"><span itemprop="logo" itemscope itemtype="https://schema.org/ImageObject"><meta itemprop="url" content=""><meta itemprop="width" content=""><meta itemprop="height" content=""></span></span></div> <div class="entry-summary" itemprop="description"><p>It turns out that the game with alternate moves can be converted into a game with just one move... Payoffs and strategies Bill Casselman University of British Columbia Payoffs and strategies In a recent Feature Column I discussed a basic search tool used by computers to explore options in playing<span class="more-link"><a href="https://mathvoices.ams.org/featurecolumn/2024/09/01/payoffs-and-strategies/">Read More →</a></span></p> </div> </div> </div> </article> <article id="post-2011" class="entry author-uwhitcher post-2011 post type-post status-publish format-standard has-post-thumbnail category-147 category-bill-casselman category-math-and-social-sciences tag-chess tag-game-theory tag-tic-tac-toe archive-block archive-block2 hcolumn-1-2" itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost"> <div class="entry-grid hgrid"> <div itemprop="image" itemscope itemtype="https://schema.org/ImageObject" class="entry-featured-img-wrap"><meta itemprop="url" content="https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2024/07/cropped-FC1380x500x2.png?resize=690%2C288&ssl=1"><meta itemprop="width" content="690"><meta itemprop="height" content="288"><a href="https://mathvoices.ams.org/featurecolumn/2024/07/01/looking-ahead/" class="entry-featured-img-link"><img width="690" height="288" src="https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2024/07/cropped-FC1380x500x2.png?resize=690%2C288&ssl=1" class="attachment-hoot-large-thumb entry-content-featured-img entry-grid-featured-img wp-post-image" alt="Feature Column" itemscope="" decoding="async" srcset="https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2024/07/cropped-FC1380x500x2.png?resize=690%2C288&ssl=1 690w, https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2024/07/cropped-FC1380x500x2.png?zoom=2&resize=690%2C288&ssl=1 1380w" sizes="(max-width: 690px) 100vw, 690px" itemprop="image" /></a></div> <div class="entry-grid-content"> <header class="entry-header"> <h2 class="entry-title" itemprop="headline"><a href="https://mathvoices.ams.org/featurecolumn/2024/07/01/looking-ahead/" rel="bookmark" itemprop="url">Looking ahead</a></h2> </header> <div class="screen-reader-text" itemprop="datePublished" itemtype="https://schema.org/Date">2024-07-01</div> <div class="entry-byline"> <div class="entry-byline-block entry-byline-author"> <span class="entry-byline-label">By:</span> <span class="entry-author" itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person"><a href="https://mathvoices.ams.org/featurecolumn/author/uwhitcher/" title="Posts by Ursula Whitcher" rel="author" class="url fn n" itemprop="url"><span itemprop="name">Ursula Whitcher</span></a></span> </div> <div class="entry-byline-block entry-byline-date"> <span class="entry-byline-label">On:</span> <time class="entry-published updated" datetime="2024-07-01T00:01:57-04:00" itemprop="datePublished" title="Monday, July 1, 2024, 12:01 am">July 1, 2024</time> </div> <div class="entry-byline-block entry-byline-cats"> <span class="entry-byline-label">In:</span> <a href="https://mathvoices.ams.org/featurecolumn/category/2024/" rel="category tag">2024</a>, <a href="https://mathvoices.ams.org/featurecolumn/category/columnists/bill-casselman/" rel="category tag">Bill Casselman</a>, <a href="https://mathvoices.ams.org/featurecolumn/category/math-and-social-sciences/" rel="category tag">Math and Social Sciences</a> </div> <div class="entry-byline-block entry-byline-tags"> <span class="entry-byline-label">Tagged:</span> <a href="https://mathvoices.ams.org/featurecolumn/tag/chess/" rel="tag">chess</a>, <a href="https://mathvoices.ams.org/featurecolumn/tag/game-theory/" rel="tag">game theory</a>, <a href="https://mathvoices.ams.org/featurecolumn/tag/tic-tac-toe/" rel="tag">tic-tac-toe</a> </div> <div class="entry-byline-block entry-byline-comments"> <span class="entry-byline-label">With:</span> <a href="https://mathvoices.ams.org/featurecolumn/2024/07/01/looking-ahead/#comments" class="comments-link" itemprop="discussionURL">2 Comments</a> </div><span class="entry-publisher" itemprop="publisher" itemscope="itemscope" itemtype="https://schema.org/Organization"><meta itemprop="name" content="Feature Column"><span itemprop="logo" itemscope itemtype="https://schema.org/ImageObject"><meta itemprop="url" content=""><meta itemprop="width" content=""><meta itemprop="height" content=""></span></span></div> <div class="entry-summary" itemprop="description">Tic-tac-toe is a very simple game, which even humans can figure out completely by using elementary reasoning, and yet a computer first approaching it would face these huge numbers… Looking ahead Bill Casselman University of British Columbia Looking ahead The question of whether the beginning position … is for one<span class="more-link"><a href="https://mathvoices.ams.org/featurecolumn/2024/07/01/looking-ahead/">Read More →</a></span></div> </div> </div> </article> <article id="post-653" class="entry author-uwhitcher post-653 post type-post status-publish format-standard has-post-thumbnail category-4 category-discrete-math-and-combinatorics category-tamsyn-morrill tag-chess tag-generating-functions archive-block archive-block2 hcolumn-1-2" itemscope="itemscope" itemtype="https://schema.org/BlogPosting" itemprop="blogPost"> <div class="entry-grid hgrid"> <div itemprop="image" itemscope itemtype="https://schema.org/ImageObject" class="entry-featured-img-wrap"><meta itemprop="url" content="https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2022/03/cropped-cropped-mathvoices-banner-feat-col-1.png?resize=690%2C279&ssl=1"><meta itemprop="width" content="690"><meta itemprop="height" content="279"><a href="https://mathvoices.ams.org/featurecolumn/2022/01/01/rook-polynomials/" class="entry-featured-img-link"><img width="690" height="279" src="https://i0.wp.com/mathvoices.ams.org/featurecolumn/wp-content/uploads/sites/2/2022/03/cropped-cropped-mathvoices-banner-feat-col-1.png?resize=690%2C279&ssl=1" class="attachment-hoot-large-thumb entry-content-featured-img entry-grid-featured-img wp-post-image" alt="Banner for the AMS Feature Column" itemscope="" decoding="async" itemprop="image" /></a></div> <div class="entry-grid-content"> <header class="entry-header"> <h2 class="entry-title" itemprop="headline"><a href="https://mathvoices.ams.org/featurecolumn/2022/01/01/rook-polynomials/" rel="bookmark" itemprop="url">Rook Polynomials: A Straight-Forward Problem</a></h2> </header> <div class="screen-reader-text" itemprop="datePublished" itemtype="https://schema.org/Date">2022-01-01</div> <div class="entry-byline"> <div class="entry-byline-block entry-byline-author"> <span class="entry-byline-label">By:</span> <span class="entry-author" itemprop="author" itemscope="itemscope" itemtype="https://schema.org/Person"><a href="https://mathvoices.ams.org/featurecolumn/author/uwhitcher/" title="Posts by Ursula Whitcher" rel="author" class="url fn n" itemprop="url"><span itemprop="name">Ursula Whitcher</span></a></span> </div> <div class="entry-byline-block entry-byline-date"> <span class="entry-byline-label">On:</span> <time class="entry-published updated" datetime="2022-01-01T00:01:31-05:00" itemprop="datePublished" title="Saturday, January 1, 2022, 12:01 am">January 1, 2022</time> </div> <div class="entry-byline-block entry-byline-cats"> <span class="entry-byline-label">In:</span> <a href="https://mathvoices.ams.org/featurecolumn/category/2022/" rel="category tag">2022</a>, <a href="https://mathvoices.ams.org/featurecolumn/category/discrete-math-and-combinatorics/" rel="category tag">Discrete Math and Combinatorics</a>, <a href="https://mathvoices.ams.org/featurecolumn/category/columnists/tamsyn-morrill/" rel="category tag">Tamsyn Morrill</a> </div> <div class="entry-byline-block entry-byline-tags"> <span class="entry-byline-label">Tagged:</span> <a href="https://mathvoices.ams.org/featurecolumn/tag/chess/" rel="tag">chess</a>, <a href="https://mathvoices.ams.org/featurecolumn/tag/generating-functions/" rel="tag">generating functions</a> </div> <div class="entry-byline-block entry-byline-comments"> <span class="entry-byline-label">With:</span> <a href="https://mathvoices.ams.org/featurecolumn/2022/01/01/rook-polynomials/#respond" class="comments-link" itemprop="discussionURL">0 Comments</a> </div><span class="entry-publisher" itemprop="publisher" itemscope="itemscope" itemtype="https://schema.org/Organization"><meta itemprop="name" content="Feature Column"><span itemprop="logo" itemscope itemtype="https://schema.org/ImageObject"><meta itemprop="url" content=""><meta itemprop="width" content=""><meta itemprop="height" content=""></span></span></div> <div class="entry-summary" itemprop="description"><p>Rook Polynomials: A Straight-Forward Problem For an integer $k$, is it possible to place $k$ rooks on a chess board so that no piece sits on the same row or column as any others? We wouldn’t want them stepping on each others’ toes. Tamsyn Morrill Trine University In the game<span class="more-link"><a href="https://mathvoices.ams.org/featurecolumn/2022/01/01/rook-polynomials/">Read More →</a></span></p> </div> </div> </div> </article></div><div class="clearfix"></div> </div> </main> <aside id="sidebar-primary" class="sidebar sidebar-primary hgrid-span-4 layout-wide-right " role="complementary" itemscope="itemscope" itemtype="https://schema.org/WPSideBar"> <div class=" sidebar-wrap theiaStickySidebar"> <section id="search-2" class="widget widget_search"><div class="searchbody"><form method="get" class="searchform" action="https://mathvoices.ams.org/featurecolumn/" ><label class="screen-reader-text">Search</label><i class="fas fa-search"></i><input type="text" class="searchtext" name="s" placeholder="Type Search Term …" value="" /><input type="submit" class="submit" name="submit" value="Search" /><span class="js-search-placeholder"></span></form></div></section><section id="blog_subscription-2" class="widget widget_blog_subscription jetpack_subscription_widget"><h3 class="widget-title"><span>Subscribe to Feature Column via Email</span></h3> <div class="wp-block-jetpack-subscriptions__container"> <form action="#" method="post" accept-charset="utf-8" id="subscribe-blog-blog_subscription-2" data-blog="202620863" data-post_access_level="everybody" > <div id="subscribe-text"><p>Enter your email address to subscribe to Feature Column and receive notifications of new posts by email.</p> </div> <p id="subscribe-email"> <label id="jetpack-subscribe-label" class="screen-reader-text" for="subscribe-field-blog_subscription-2"> Email Address </label> <input type="email" name="email" required="required" value="" id="subscribe-field-blog_subscription-2" placeholder="Email Address" /> </p> <p id="subscribe-submit" > <input type="hidden" name="action" value="subscribe"/> <input type="hidden" name="source" value="https://mathvoices.ams.org/featurecolumn/tag/chess/"/> <input type="hidden" name="sub-type" value="widget"/> <input type="hidden" name="redirect_fragment" value="subscribe-blog-blog_subscription-2"/> <input type="hidden" id="_wpnonce" name="_wpnonce" value="bba917ef41" /><input type="hidden" name="_wp_http_referer" value="/featurecolumn/tag/chess/" /> <button type="submit" class="wp-block-button__link" name="jetpack_subscriptions_widget" > Subscribe </button> </p> </form> </div> </section><section id="block-3" class="widget widget_block"><div class="wp-block-group"><div class="wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow"><h2 class="wp-block-heading">Recent Posts</h2><ul class="wp-block-latest-posts__list wp-block-latest-posts"><li><a class="wp-block-latest-posts__post-title" href="https://mathvoices.ams.org/featurecolumn/2024/12/01/capturing-the-invisible-hopping-rabbit/">Capturing the Invisible Hopping Rabbit</a></li> <li><a class="wp-block-latest-posts__post-title" href="https://mathvoices.ams.org/featurecolumn/2024/11/01/strung-out-on-automorphic-forms/">Strung Out on Automorphic Forms</a></li> <li><a class="wp-block-latest-posts__post-title" href="https://mathvoices.ams.org/featurecolumn/2024/10/01/people-and-computers-compared/">People and Computers Compared</a></li> <li><a class="wp-block-latest-posts__post-title" href="https://mathvoices.ams.org/featurecolumn/2024/09/01/payoffs-and-strategies/">Payoffs and strategies</a></li> <li><a class="wp-block-latest-posts__post-title" href="https://mathvoices.ams.org/featurecolumn/2024/08/01/welcome-to-the-fold/">Welcome to the Fold</a></li> </ul></div></div></section><section id="categories-2" class="widget widget_categories"><h3 class="widget-title"><span>Categories</span></h3> <ul> <li class="cat-item cat-item-2"><a href="https://mathvoices.ams.org/featurecolumn/category/2020/">2020</a> </li> <li class="cat-item cat-item-3"><a href="https://mathvoices.ams.org/featurecolumn/category/2021/">2021</a> </li> <li class="cat-item cat-item-4"><a href="https://mathvoices.ams.org/featurecolumn/category/2022/">2022</a> </li> <li class="cat-item cat-item-112"><a href="https://mathvoices.ams.org/featurecolumn/category/2023/">2023</a> </li> <li class="cat-item cat-item-147"><a href="https://mathvoices.ams.org/featurecolumn/category/2024/">2024</a> </li> <li class="cat-item cat-item-5"><a href="https://mathvoices.ams.org/featurecolumn/category/columnists/adam-a-smith/">Adam A. 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