<p><div><div><div><div data-width="100" data-show-faces="false" data-send="true" data-layout="button_count" data-height="21" data-href="https://www.r-bloggers.com/learning-scrabble-strategy-from-robots-using-r/"></div></div><div></div></div><div></div></div>
<div>
(This article was first published on <strong><a href="http://blog.revolutionanalytics.com/2017/03/scrabblr.html"> Revolutions</a></strong>, and kindly contributed to <a rel="nofollow" href="https://www.r-bloggers.com/">R-bloggers)</a> </div>
<div>
<p>While you might think of Scrabble as that game you play with your grandparents on a rainy Sunday, some people take it <em>very</em> seriously. There's an <a target="_blank" rel="nofollow" href="https://fivethirtyeight.com/features/what-makes-nigel-richards-the-best-scrabble-player-on-earth/">international competition</a> devoted to Scrabble, and no end of guides and strategies for competitive play. James Curley, a psychology professor at Columbia University, has used an interesting method to collect <a target="_blank" rel="nofollow" href="http://rpubs.com/jalapic/scrabblr">data about what plays are most effective in Scrabble</a>: by having robots play against each other, thousands of times.</p>
<p>The data were generated with a Visual Basic script that automated two AI players completing a game in <a target="_blank" rel="nofollow" href="http://people.csail.mit.edu/jasonkb/quackle/">Quackle</a>. Quackle emulates the Scrabble board, and provides a number of AI players; the simulation used the &quot;Speedy Player&quot; AI which tends to make tactical scoring moves while missing some longer-term strategic plays (like most reasonably skilled Scrabble players). He recorded the results of 2566 games between two such computer players and provided the resulting plays and boards in an <a target="_blank" rel="nofollow" href="http://rpubs.com/jalapic/scrabblr">R package</a>. With these data, you can see some interesting statistics on long-term outcomes from competitive Scrabble games, like this map (top-left) of which squares on the board are most used in games (darker means more frequently), and also for just the Q, Z and blank tiles. Scrabble games in general tend to follow the diagonals where the double-word score squares are located, while the high-scoring Q and Z tiles tend to be used on double- and triple-letter squares. The zero-point blank tile, by comparison, is used fairly uniformly across the board.</p>
<p> </p>
<p><a target="_blank" rel="nofollow" href="http://rpubs.com/jalapic/scrabblr"><img title="Tile position" alt="Tile position" src="http://revolution-computing.typepad.com/.a/6a010534b1db25970b01b8d27092f5970c-800wi" border="0"></a></p>
<p>Further analysis of the actual plays during the simulated games reveals some interesting Scrabble statistics:</p>
<p><strong>It's best to play first</strong>. Player 1 won 54.6% of games, while Player 2 won 44.9%, a statistically significant difference. (The remaining 0.4% of the games were ties.) </p>
<p><strong>Some uncommon words are frequently used</strong>. The 10 most frequently-played words were QI, QAT, QIN, XI, OX, EUOI, XU, ZO, ZA, and EX; not necessarily words you'd use in casual conversation, but all words very familiar to competitive scrabble players. As we'll see later though, not all are high-scoring plays. Sometimes it's a good idea to get rid of a high-scoring but restrictive letter (QI, the life energy in Chinese philosophy), or simply to shake up a vowel-heavy rack for more opportunities next turn (EUOI, a cry of impassioned rapture in ancient Bacchic revels).</p>
<p><strong>For high-scoring plays, go for the bingo</strong>. A Scrabble Bingo, where you lay down all 7 tiles in your rack in one play, comes with a 50-point bonus. The top three highest-scoring plays in the simulation were all bingo plays: REPIQUED (239 points), CZARISTS (230 points), and IDOLIZED. (Remember though, that this is from just a couple of thousand simulated games; there are many many more potentially high-scoring words.)</p>
<p><strong>High-scoring non-bingo plays can be surprisingly long words</strong>. It's super-satisfying to lay down a short word like EX with the X making a second word on a triple-letter tile (for a 9x bonus), so I was surprised to see the top 10 highest-scoring non-bingo plays were still fairly long words: XENURINE (144 points), CYANOSES (126 pts) and SNAPWEED (126 points), all using at least 2 tiles already on the board. The shortest word in the top 10 of this list was ZITS.</p>
<p><strong>Some tiles just don't work well together</strong>. The pain of getting a Q without a U seems obvious, but it turns out getting <strong>two</strong> U's is way worse in point-scoring potential. From the simulation, you can estimate the point-scoring potential of any pair of tiles in your rack: lighter is better, and darker is worse.</p>
<p><a target="_blank" rel="nofollow" href="http://rpubs.com/jalapic/scrabblr"><img title="Tile synergy" alt="Tile synergy" src="http://revolution-computing.typepad.com/.a/6a010534b1db25970b01b7c8e62c5c970b-800wi" border="0"></a></p>
<p>Managing the scoring potential of the tiles in your rack is a big part of Scrabble strategy, as we saw in <a target="_blank" rel="nofollow" href="http://blog.revolutionanalytics.com/2011/07/scrabble-luck-and-skill.html">another Scrabble analysis using R</a> a few years ago. The lowly zero-point blank is actually worth a lot of potential points, while the highest-scoring tile Q is actually a liability. Here are the findings from that analysis:</p>
<ul>
<li>The blank is worth about 30 points to a good player, mainly by making 50-point &quot;bingo&quot; plays possible.</li>
<li>Each S is worth about 10 points to the player who draws it.</li>
<li>The Q is a burden to whichever player receives it, effectively serving as a 5 point penalty for having to deal with it due to its effect in reducing bingo opportunities, needing either a U or a blank for a chance at a bingo and a 50-point bonus.</li>
<li>The J is essentially neutral pointwise.</li>
<li>The X and the Z are each worth about 3-5 extra points to the player who receives them. Their difficulty in playing in bingoes is mitigated by their usefulness in other short words.</li>
</ul>
<p>For more James Curley's recent Scrabble analysis, including the R code using his scrabblr package, follow the link to below.</p>
<p>RPubs: <a target="_blank" rel="nofollow" href="http://rpubs.com/jalapic/scrabblr">Analyzing Scrabble Games</a></p>
</div>
<p>
<div>
<div>To <strong>leave a comment</strong> for the author, please follow the link and comment on their blog: <strong><a href="http://blog.revolutionanalytics.com/2017/03/scrabblr.html"> Revolutions</a></strong>.</div>
<hr>
<a rel="nofollow" href="https://www.r-bloggers.com/">R-bloggers.com</a> offers <strong><a rel="nofollow" href="https://feedburner.google.com/fb/a/mailverify?uri=RBloggers">daily e-mail updates</a></strong> about <a title="The R Project for Statistical Computing" rel="nofollow" href="https://www.r-project.org/">R</a> news and <a title="R tutorials" rel="nofollow" href="https://www.r-bloggers.com/search/tutorial">tutorials</a> on topics such as: <a title="Data science" rel="nofollow" href="https://www.r-bloggers.com/search/data%20science">Data science</a>, <a title="Big Data" rel="nofollow" href="https://www.r-bloggers.com/search/Big%20Data">Big Data, <a title="R jobs" rel="nofollow" href="https://www.r-users.com/">R jobs</a>, visualization (<a title="ggplot and ggplot2 tutorials" rel="nofollow" href="https://www.r-bloggers.com/search/ggplot2">ggplot2</a>, <a title="Boxplots using lattice and ggplot2 tutorials" rel="nofollow" href="https://www.r-bloggers.com/search/boxplot">Boxplots</a>, <a title="Maps and gis" rel="nofollow" href="https://www.r-bloggers.com/search/map">maps</a>, <a title="Animation in R" rel="nofollow" href="https://www.r-bloggers.com/search/animation">animation</a>), programming (<a title="RStudio IDE for R" rel="nofollow" href="https://www.r-bloggers.com/search/RStudio">RStudio</a>, <a title="Sweave and literate programming" rel="nofollow" href="https://www.r-bloggers.com/search/sweave">Sweave</a>, <a title="LaTeX in R" rel="nofollow" href="https://www.r-bloggers.com/search/LaTeX">LaTeX</a>, <a title="SQL and databases" rel="nofollow" href="https://www.r-bloggers.com/search/SQL">SQL</a>, <a title="Eclipse IDE for R" rel="nofollow" href="https://www.r-bloggers.com/search/eclipse">Eclipse</a>, <a title="git and github, Version Control System" rel="nofollow" href="https://www.r-bloggers.com/search/git">git</a>, <a title="Large data in R using Hadoop" rel="nofollow" href="https://www.r-bloggers.com/search/hadoop">hadoop</a>, <a title="Web Scraping of google, facebook, yahoo, twitter and more using R" rel="nofollow" href="https://www.r-bloggers.com/search/Web+Scraping">Web Scraping</a>) statistics (<a title="Regressions and ANOVA analysis tutorials" rel="nofollow" href="https://www.r-bloggers.com/search/regression">regression</a>, <a title="principal component analysis tutorial" rel="nofollow" href="https://www.r-bloggers.com/search/PCA">PCA</a>, <a title="Time series" rel="nofollow" href="https://www.r-bloggers.com/search/time+series">time series</a>, <a title="finance trading" rel="nofollow" href="https://www.r-bloggers.com/search/trading">trading</a>) and more...
<img height="1" alt="" width="1" src="http://feeds.feedburner.com/~r/RBloggers/~4/GZRR3Yifa5k"></a></div>