{"id":2655,"date":"2013-12-06T11:04:25","date_gmt":"2013-12-06T19:04:25","guid":{"rendered":"http:\/\/www.danamackenzie.com\/blog\/?p=2655"},"modified":"2013-12-06T11:04:25","modified_gmt":"2013-12-06T19:04:25","slug":"the-cheating-coach-redux","status":"publish","type":"post","link":"https:\/\/danamackenzie.com\/blog\/?p=2655","title":{"rendered":"The cheating coach redux"},"content":{"rendered":"

A few of you might remember a post I wrote last year about a really cool math problem that a friend sent to me. For those who don’t remember, here it is again:<\/p>\n

Two chess teams are going to play a chess match. The best players on each team are supposed to play on board 1, the second best players on board 2, etc. However, the coach of team B thinks he can win more games by putting his players in a different order. Is he right? If so, what is the best order for the cheating coach to put his players in?<\/em><\/p>\n

Fortunately, shenanigans like this are not possible in the actual chess world because we have a rating system that keeps the coach from intentionally putting the players in the wrong order. However, in a world with no rating system this would be a real problem. If there are 3 players on each team, it turns out that the best order to put them in is 3-1-2. If there are 4 players, the best order is 4-1-2-3. In each case the idea is to “throw” the game on the first board in order to improve your odds on the other boards. For example, in the four-player match, the cheating team will win on average by a score of 2.34-1.66 if they adopt this strategy.<\/p>\n

(Technical note<\/em>: The above calculation is only true in a world where upsets never happen, i.e., the better player always wins. If upsets do happen, I suspect the effect would be to reduce but not eliminate the cheating team’s advantage.)<\/p>\n

Now let me get to my news. Recently I wrote an article about the cheating coach problem for a science website called Nautilus<\/a>. If you’re interested, the article — which also explains the optimal strategy for teams of N<\/em> players — is now online<\/a>.<\/p>\n

But that’s not all! The problem is also going to be featured in the New York Times<\/em> “Numberplay” blog<\/a>, written by Gary Antonick. Even if you’ve read my Nautilus article, I think you will find Antonick’s post to be interesting because we pose the problem in a different way. Gary thought that the original version was a little bit too complicated for readers to understand, and I kind of agree with him. The fine print about no upsets is, unfortunately, a necessary assumption to get a unique solution, and that assumption is both unrealistic and detracts from the simplicity of the problem.<\/p>\n

So we worked out a different way to pose the problem, in terms of a card game, which I think is simple and elegant and really the best way to do it. It distills the problem to its essence and also, I think, greatly enhances the surprise factor. The card game seems as if it must be fair, when in fact it is biased in favor of one player. It should be a hustler’s delight!<\/p>\n

Anyway, I won’t say any more about Gary’s article now, because I don’t want to scoop him, but it think it will be really, really cool. I’ll let you know when it comes out.<\/p>\n

P.S. As an unrelated aside, this blog got 305 hits on Tuesday, the day of my “Anatomy of a Meltdown” post. That’s the first time that I have topped 300 hits in one day except during the 2010 and 2012 world championship matches. (During those matches I was translating GM Sergey Shipov’s commentary, and got as many as 2143 visitors in a single day.) Thanks to all 305 of you! In general there seems to be a subtle but unmistakable increasing trend in the number of readers of “dana blogs chess,” so I must be doing something right.<\/p>\n","protected":false},"excerpt":{"rendered":"

A few of you might remember a post I wrote last year about a really cool math problem that a friend sent to me. For those who don’t remember, here it is again: Two chess teams are going to play a chess match. The best players on each team are supposed to play on board […]<\/p>\n","protected":false},"author":80,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[14,235,171,12],"tags":[2758,2335,801,2754,2438,2336,2755,2757,2756],"class_list":["post-2655","post","type-post","status-publish","format-standard","hentry","category-literature","category-off-topic","category-ruminations","category-tournaments","tag-entertainment","tag-gary-antonick","tag-math","tag-nautilus","tag-new-york-times","tag-numberplay","tag-publications","tag-puzzle","tag-shenanigans"],"_links":{"self":[{"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/2655","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/80"}],"replies":[{"embeddable":true,"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2655"}],"version-history":[{"count":3,"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/2655\/revisions"}],"predecessor-version":[{"id":2658,"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/2655\/revisions\/2658"}],"wp:attachment":[{"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2655"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2655"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/danamackenzie.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2655"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}