tag:blogger.com,1999:blog-1678761812929125529.post5400594128457539941..comments2023-05-27T11:14:02.426-04:00Comments on Some Space to Think: The Stranger, the Twins and the ScalesAnonymoushttp://www.blogger.com/profile/14216103531396452644noreply@blogger.comBlogger10125tag:blogger.com,1999:blog-1678761812929125529.post-83007222502636726892010-06-05T22:34:38.537-04:002010-06-05T22:34:38.537-04:00I also think this is brilliant. I love games that...I also think this is brilliant. I love games that use familiar things in a different way. This is a great way to build a relationship map.I'll be following the development. Please keep up posted. Thanks for sharing.Unknownhttps://www.blogger.com/profile/13605422761452625140noreply@blogger.comtag:blogger.com,1999:blog-1678761812929125529.post-24460740990030397182010-06-04T21:14:04.255-04:002010-06-04T21:14:04.255-04:00It turns out you shouldn't trust me, since I m...It turns out you shouldn't trust me, since I made a bunch of mistakes. This time I actually spent the time to write everything down, draw diagrams, got someone else to check my numbers, etc., so I'm much more confident. You can see the results with explanation and calculators at http://alfedenzia.com/misc/hexbones/hexbones.html<br /><br />The biggest difference is that the probability of getting an askew result is higher than predicted earlier.Mark Sherryhttps://www.blogger.com/profile/03375042954626453877noreply@blogger.comtag:blogger.com,1999:blog-1678761812929125529.post-24425640472187464962010-06-04T15:40:24.049-04:002010-06-04T15:40:24.049-04:00@mds I am 100% willing to trust your numbers. And...@mds I am 100% willing to trust your numbers. And ~40/40/20 is a pretty good ratio, to my mind - I like askew to be a little rare.<br /><br />Thanks again!Anonymoushttps://www.blogger.com/profile/14216103531396452644noreply@blogger.comtag:blogger.com,1999:blog-1678761812929125529.post-53659760788398782882010-06-04T15:25:54.910-04:002010-06-04T15:25:54.910-04:00Assuming I did my math correctly, requiring at lea...Assuming I did my math correctly, requiring at least two corners be in separate squares from the others gives about 41.5% inside, 41.5% outside and 17% askew. This is with no margins. Margins would just decrease the askew percentage even more.<br /><br />Unlike the previous case, where the die landing with sides parallel to the squares had the minimum probability of being askew, when you require two corners to be outside of the square, you get a 45 degree rotated die being askew only when it's sitting in the corner with the corners in different squares. <br /><br />(P(sitting right on the edge at exactly 45 degrees) = 0, but then again, P(angle is exactly 45 degrees) = 0 too.)<br /><br />Formula available upon request, but it involves a bunch of trig functions and integrals. I've been using Maple to actually evaluate it.Mark Sherryhttps://www.blogger.com/profile/03375042954626453877noreply@blogger.comtag:blogger.com,1999:blog-1678761812929125529.post-2029555979383265392010-06-04T14:30:31.356-04:002010-06-04T14:30:31.356-04:00@mds that said, Math is awesome! Thank you.@mds that said, Math is awesome! Thank you.Anonymoushttps://www.blogger.com/profile/14216103531396452644noreply@blogger.comtag:blogger.com,1999:blog-1678761812929125529.post-60448368782144456102010-06-04T14:23:59.859-04:002010-06-04T14:23:59.859-04:00@mds That is actually one of the big things that n...@mds That is actually one of the big things that needs revision. I didn't have the math, but my gut was suggesting that there's be too many askew results. Odds are good the final version will have one page as a printable rolling surface that uses bigger solid sections. That said, I wonder if it might be a good stopgap on a chessboard to say askew happens when two corners of the die are in a different color than the others (with roller discretion if you happen to get a perfect 45 degree angle on the dividing line).Anonymoushttps://www.blogger.com/profile/14216103531396452644noreply@blogger.comtag:blogger.com,1999:blog-1678761812929125529.post-24251056155714124862010-06-04T14:10:23.621-04:002010-06-04T14:10:23.621-04:00A less math-centric post, I really like the ideas ...A less math-centric post, I really like the ideas in this post. It's the kind of thing that can be easily automated by a program, but gains so much more from being done by hand, and the cards give it a Tarot feel.Mark Sherryhttps://www.blogger.com/profile/03375042954626453877noreply@blogger.comtag:blogger.com,1999:blog-1678761812929125529.post-68866391090479515002010-06-04T13:55:42.887-04:002010-06-04T13:55:42.887-04:00If you're using standard 5/8" dice on a 2...If you're using standard 5/8" dice on a 2" square board and count anything touching or crossing a side as "askew", the odds of not getting an askew result is about 42%, split evenly between "Inward" and "Outward". If you allow a 1/8" margin (i.e. the die is allowed to cross at most 1/8" into neighbouring squares), then you get a 72% chance of something other than askew. That gives you odds of 36% inside, 36% outside, and 28% askew. Not quite as evenly distributed as you might like, but the 1/8" margin is a considerable fudge factor, as you're unlikely to be carefully measuring things to get precise results. (3/32" gives 66%, but good luck eyeballing that.)<br /><br />All this assumes that tosses are one-at-a-time or otherwise independent. If they're likely to be bumping into each other, the above will act as a rough guideline only.Mark Sherryhttps://www.blogger.com/profile/03375042954626453877noreply@blogger.comtag:blogger.com,1999:blog-1678761812929125529.post-71865779743032815352010-06-04T10:27:18.769-04:002010-06-04T10:27:18.769-04:00There's a draft of the original pdf here but I...There's a draft of the original pdf <a href="http://logrus.com/~moose/page1/files/hexbones.pdf" rel="nofollow">here</a> but I don't wave it around much because it is hugely in need of a rewrite, but yes, the basic idea is to roll a few d6's to generate relationship maps (basically using the configurations of the dots as the model for each facing). The one thing I don't mention here is that you roll on a two-color surface (like a checkerboard) to determine inward, outward or askew.Anonymoushttps://www.blogger.com/profile/14216103531396452644noreply@blogger.comtag:blogger.com,1999:blog-1678761812929125529.post-25287018491175847782010-06-04T10:21:14.754-04:002010-06-04T10:21:14.754-04:00Dammit, Rob, if I understand what's happening ...Dammit, Rob, if I understand what's happening here, it's fucking brilliant. (If I don't, then you may have just inspired something that I don't have time to implement.)Will Hindmarchhttp://www.gameplaywright.netnoreply@blogger.com