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<blockquote style="position: relative; padding-left: 55px;"><section><a href="https://dice.camp/users/Sophie/statuses/112904249720838177">Sophie 🎲🧩🏳️‍⚧️ (sophie@dice.camp)'s status on Monday, 05-Aug-2024 01:31:46 JST</a><a href="https://dice.camp/@Sophie" title="sophie@dice.camp"><img src="https://gnusocial.jp/avatar/96428-48-20230209085239.webp" width="48" height="48" alt="Sophie 🎲🧩🏳️‍⚧️" style="position: absolute; left: 0; top: 0;">Sophie 🎲🧩🏳️‍⚧️</a><div><ul><li></ul></div></section><article><p>I've been meaning to make an updated version of this for a while so here it is, every numerically-balanced d20 layout!</p><p>Feel free to share, especially with any dice makers you think may be interested!</p><p>There is a more detailed explanation video by <a href="https://mathstodon.xyz/@henryseg">@henryseg</a> for The Dice Lab (which use layout C, if you're curious!) <a href="https://youtu.be/Nh2H_4g6evc" rel="nofollow noreferrer">https://youtu.be/Nh2H_4g6evc</a></p><p><a href="https://dice.camp/tags/dice" rel="tag">#dice</a> <a href="https://dice.camp/tags/ttrpg" rel="tag">#ttrpg</a> <a href="https://dice.camp/tags/DnD" rel="tag">#DnD</a></p></article><footer><a rel="bookmark" href="https://gnusocial.jp/conversation/3474759#notice-6828661">In conversation</a><time datetime="2024-08-05T01:31:46+09:00" title="Monday, 05-Aug-2024 01:31:46 JST">about 4 months ago</time> <span>from <span><a href="https://dice.camp/@Sophie/112904249720838177" rel="external" title="Sent from dice.camp via ActivityPub">dice.camp</a></span></span><a href="https://dice.camp/@Sophie/112904249720838177">permalink</a><h4>Attachments</h4><ol><li><label><a rel="external" href="https://gnusocial.jp/attachment/3000292">An illustration of 12 icosahedron nets where each face is numbered from one to twenty. The nets are labelled from A to F and R(A) to R(F).Below is the text:
"There are only six number layouts (and their reflections) for a d20 that are optimally fair.The most common layout (where the 20 is surrounded by 2, 14, 8) is not numerically balanced, apart from by opposite-face sum (Which only helps negate bias from a squashed shape).d20 dice with the above layouts should roll the expected value (10.5) on average, even if their shape is squashed (common for very old, cheap, or melted dice), their center of mass is offset (common in dice with inserts, multiple materials, air bubbles), or they are not fully isohedral where faces/edges are slightly different (common for handcrafted gem/glass/metal dice, and dice not evenly tumbled).Key features:
• Opposite-faces always sum 21
(two faces with an average value of 10.5)• Faces around each vertex always sum 53 or 52(five faces with average value of 10.6 or 10.4.)• A face’s three adjacent faces always sum 32 or 31
(three faces with average value of 10.666… or 10.333…)Feel free to use any of the layouts above for your own dice to make them fairer overall!"</a></label><br><a href="https://cdn.masto.host/dicecamp/media_attachments/files/112/904/226/883/338/423/original/12d500e64887d683.png" rel="external">https://cdn.masto.host/dicecamp/media_attachments/files/112/904/226/883/338/423/original/12d500e64887d683.png</a></li><li><article><header><img height="128" width="128" src="https://gnusocial.jp/thumbnail/3000293?w=128&amp;h=128"><h5><a href="https://www.youtube.com/watch?v=Nh2H_4g6evc&amp;feature=youtu.be">Numerically-balanced d20 dice</a></h5><div> from <span>Henry Segerman</span></div></header><div>For more details, see http://thedicelab.com/BalancedStdPoly.htmlThese dice are available from http://www.mathartfun.com/DiceLabDice.html</div><footer></footer></article></li></ol></footer></blockquote>