timothyweber.org - dieroller
http://timothyweber.org/taxonomy/term/46/0
A machine for rolling and reading dice, to measure their fairness.enDie Roller intro
http://timothyweber.org/node/250
<p>The Die Roller<sup id="fnref:1"><a href="#fn:1" rel="footnote">1</a></sup> is a folly project I’ve been working on over the past couple of years to determine whether a given game-playing die or set of dice <a href="/node/254">are fair</a>. It consists of a machine that rolls a die over and over, a camera that takes a photograph of the die after each roll, a computer program that recognizes which die face is in each picture, and some <a href="/node/255">statistical analysis software</a>.</p>
<p>I’m interested in answering some simple questions, like “Are my (or your) favorite Dungeons and Dragons dice reasonably fair?”, as well as some deeper questions like “Which common design features help or hurt dice fairness?” and “What do we mean by ‘fair,’ anyway?”</p>
<p>I’ve enjoyed this project because it combines a lot of great stuff: Electronics, mechanical engineering, computer vision, statistics, user interface design, game theory, and 3D printing. Oh, and fig bars.</p>
<p>I hope to post about more detailed aspects of the project over time, including what I learn about die design. If some aspect of the project interests you, please comment - I’d like to see what purpose this could serve in the wider world.</p>
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<p>Needs a flashier name - any suggestions? Preferably with a domain name that’s not currently taken?? <a href="#fnref:1" rev="footnote">↩</a><span class="read-more"><a href="/node/250"><strong> read more...</strong></a></span></p>
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http://timothyweber.org/node/250#commentsdierollerTue, 01 Oct 2013 15:34:23 +0000tw250 at http://timothyweber.orgMathematical tests for fair dice
http://timothyweber.org/node/255
<p><a href="/node/254">My previous post on fair dice</a> focused on some intuitive ideas about die fairness, and the beginnings of a mathematical approach. Now I’d like to describe the tests my <a href="/dieroller">die roller</a> does. These are what I’ve settled on so far as a way to get some numbers to describe and compare the fairness of different dice.</p>
<h2>The chi-squared test</h2>
<p>First off, there’s the <a href="http://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test">chi-squared goodness-of-fit test</a>. This is a test that looks at the deviations in the histogram to get a total number (the chi-squared statistic) that characterizes how far the histogram deviates from ideal. You can also compare the result statistic to a mathematically-determined threshold that will give you a confidence value for the test; a 95% confidence is often chosen.</p>
<p>So hey, that’s great! We can reduce the whole set of results and its histogram to a single number for a given die, and then find out whether that die is fair or not with 95% confidence! Super! Right?<span class="read-more"><a href="/node/255"><strong> read more...</strong></a></span></p>
http://timothyweber.org/node/255#commentsdierollerTue, 15 Oct 2013 17:26:57 +0000tw255 at http://timothyweber.orgWhat are fair dice?
http://timothyweber.org/node/254
<p>If you like games, you’ve probably played games with dice, and you’ve probably thought about fair and unfair dice.</p>
<p>You might have seen “trick dice” advertised in the back of a comic book, for instance, or you might have flipped a string of heads on a coin and thought your way into <a href="http://en.wikipedia.org/wiki/Gambler's_fallacy">the Gambler’s Fallacy</a> or an instinctive <a href="http://en.wikipedia.org/wiki/Bayesian_inference">Bayesian</a> sense that the coin is biased towards heads.</p>
<p>If you have studied statistics, you’ve encountered more mathematical ways to treat these human observational instinct<span class="read-more"><a href="/node/254"><strong> read more...</strong></a></span></p>
http://timothyweber.org/node/254#commentsdierollerThu, 03 Oct 2013 20:35:09 +0000tw254 at http://timothyweber.orgNew overview video of the Die Roller
http://timothyweber.org/node/251
<p>Thought I should post an update to the <a href="/taxonomy/term/46">Die Roller</a> project. It’s getting kind of useful and a lot of fun! If, you know, you’re into those sorts of things - games, statistics, computer vision, mechatronics, Fig Newtons.</p>
<p><a href="http://youtu.be/FVWqVM4xyRU" title="http://youtu.be/FVWqVM4xyRU">http://youtu.be/FVWqVM4xyRU</a></p>
http://timothyweber.org/node/251#commentsdierollerTue, 01 Oct 2013 20:40:53 +0000tw251 at http://timothyweber.orgDie Roller is rolling
http://timothyweber.org/node/239
<p><a href="http://youtu.be/fHL1VMb2SS0" title="http://youtu.be/fHL1VMb2SS0">http://youtu.be/fHL1VMb2SS0</a></p>
<p>It rolls a die, controlled by USB. It’s not done yet.</p>
<p>Working on this project makes me hungry for some reason.</p>
http://timothyweber.org/node/239#commentsdierollerTue, 31 Jan 2012 20:40:29 +0000tw239 at http://timothyweber.org