<story><title>Go First Dice</title><url>http://www.ericharshbarger.org/dice/go_first_dice.html</url></story><parent_chain></parent_chain><comment><author>munificent</author><text>I love that they put so much work into trying to solve this when there is an equally trivially simple mechanical solution that works just as well and easily scales up to any number of users:&lt;p&gt;1. Put consecutive numbered tiles in an opaque bag.&lt;p&gt;2. Each person reaches in and blindly grabs a tile.&lt;p&gt;3. Play proceeds in the order of tiles.&lt;p&gt;You can think of dice rolling as simple random sampling with replacement. It&amp;#x27;s naturally good at generating combinations. Drawing from a bag is random sampling without replacement. It&amp;#x27;s naturally good at generating permutations.&lt;p&gt;Using a system that generates combinations to generate uniformly distributed random permutations is a super fun mathematical exercise and I&amp;#x27;m sure this brought plenty of joy to the authors. But if you&amp;#x27;re just trying to design a physical mechanism to generate permutations, it&amp;#x27;ll be an easier starting point if you do sampling without replacement.&lt;p&gt;In fact, if you do want to generate permutations with dice, a simple (but laborious) way to do it is:&lt;p&gt;1. Choose an arbitrary ordering for the players.&lt;p&gt;2. For each player, roll a die. If the value rolled is the same as any value rolled by a previous player, re-roll. Continue to re-roll until a unique value is rolled.&lt;p&gt;3. Play proceeds in the order of values each player rolled.&lt;p&gt;You&amp;#x27;ll probably want to use d20 or some dice with a large number of faces relative to the number of players in order to minimize collisions and re-rolling.&lt;p&gt;I&amp;#x27;m not 100% certain, but I believe this will generate an unbiased ordering where the order of players in step 1 has no effect on the resulting order determined in step 3.</text></comment>
<story><title>Go First Dice</title><url>http://www.ericharshbarger.org/dice/go_first_dice.html</url></story><parent_chain></parent_chain><comment><author>pessimizer</author><text>Reiner Knizia uses distributions that are meant to have this quality (or get close enough to make people happy), most notably in Ra. Ra is an auction game where each player gets the name number of bidding tokens. Each token has a unique number on it, and you can only use a single token to bid, ensuring that there are never ties.&lt;p&gt;Ra is an example, but he uses it elsewhere. He&amp;#x27;s a math PhD who often writes in his books about how to break down these problems, and I wonder if he approached it the same way or reached the same conclusion.&lt;p&gt;&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;boardgamegeek.com&amp;#x2F;boardgame&amp;#x2F;12&amp;#x2F;ra&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;boardgamegeek.com&amp;#x2F;boardgame&amp;#x2F;12&amp;#x2F;ra&lt;/a&gt;</text></comment>