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<blockquote data-quote="N0Man" data-source="post: 4850174" data-attributes="member: 64066">You're missing the point.&nbsp; I said multiple times that the closer to a 45 degree angle, the less accurate 4E becomes, so in the literal 'corner case', it is off noticeably.&nbsp; I'm not arguing that 4E is more mathematical, but rather than it's not mathematically inferior to such a degree that it matters much in the majority of the cases.Both are simplifications.&nbsp; Both have places where they are stronger at.&nbsp; Should I create a PDF in response to show this too?You can spin that 3E is equally accurate, equally wrong, or superior in the majority of the cases, and it's true.I could also spin that 3E only is superior in 3 out of the 6 scenarios, and it's also true.You could argue that the worst offender is 4E being off by 2 squares, which is 1 more square in error than 3E ever has, which is also true.I could respond that in the diagonal examples, that the average size of error for 4E was only 0.5 greater than that of 3E, which is also true (0.5 vs 1.0).See, I understand how all of this work.&nbsp; You don't have to draw me a picture, or explain the math on it.&nbsp; I understand.&nbsp; As difficult as it is for some to believe, I can be proficient in math and still be ok with choosing one flawed arbitrary approximation over another slightly less flawed arbitrary approximation for the reason of simplicity.And again, if your group decides they want to play 3E style, that's fine.&nbsp; But the point remains is that over the course of many diagonals of varying angles, on average, it's just not that great of a benefit to bother with 1-2-1.&nbsp; Just don't make the classic DM mistake of &quot;my houserules that introduce complexity are more realistic&quot; at the expense of the fun of your players or future players down the road.If 45 degree angles occur so commonly in your world that you want to houserule the old 3E rule back in, you might want to consider rotating your entire world 45 degrees.&nbsp; Doing this would make all your angles closer in 4E again. <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f609.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=";)" title="Wink&nbsp; &nbsp; ;)"&nbsp; data-smilie="2"data-shortname=";)" /></blockquote>

[QUOTE="N0Man, post: 4850174, member: 64066"] You're missing the point. I said multiple times that the closer to a 45 degree angle, the less accurate 4E becomes, so in the literal 'corner case', it is off noticeably. I'm not arguing that 4E is more mathematical, but rather than it's not mathematically inferior to such a degree that it matters much in the majority of the cases. Both are simplifications. Both have places where they are stronger at. Should I create a PDF in response to show this too? You can spin that 3E is equally accurate, equally wrong, or superior in the majority of the cases, and it's true. I could also spin that 3E only is superior in 3 out of the 6 scenarios, and it's also true. You could argue that the worst offender is 4E being off by 2 squares, which is 1 more square in error than 3E ever has, which is also true. I could respond that in the diagonal examples, that the average size of error for 4E was only 0.5 greater than that of 3E, which is also true (0.5 vs 1.0). See, I understand how all of this work. You don't have to draw me a picture, or explain the math on it. I understand. As difficult as it is for some to believe, I can be proficient in math and still be ok with choosing one flawed arbitrary approximation over another slightly less flawed arbitrary approximation for the reason of simplicity. And again, if your group decides they want to play 3E style, that's fine. But the point remains is that over the course of many diagonals of varying angles, on average, it's just not that great of a benefit to bother with 1-2-1. Just don't make the classic DM mistake of "my houserules that introduce complexity are more realistic" at the expense of the fun of your players or future players down the road. If 45 degree angles occur so commonly in your world that you want to houserule the old 3E rule back in, you might want to consider rotating your entire world 45 degrees. Doing this would make all your angles closer in 4E again. ;) [/QUOTE]

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