Does anyone know how the numbers (1-20) on dartboards came to be arranged the way they are?
http://www.igtfy.com/?q=The+Dartboard+Sequence
“Oddly enough, no one seems to know how this particular arrangement was
selected. It evidently dates back over 100 years…”
The reason for putting smallest numbers next to biggest is to reward accuracy. You might not need to bother aiming well if 20 were adjacent to 18 and 19.
Finding such a dartboard arrangement (or stating criterion rigorously) is sometimes seen as a math or programming exercise. When so pursued, the standard arrangement is found to be “good” but not “optimal.”
Googling for the actual invention, I find “no one knows” but also a link that credits 1896 invention to English carpenter Brian Gamlin.
Sweet. Thanks for the links. For some reason I hadn’t thought to use “sequence” as a search term, which yields a lot more. I grokked the small-by-high reasoning, and yet it is still not averaged optimally as mentioned. If playing a point game, when starting out I’m going to shoot 16-7-19 area over 4-13-6. But then cricket is only 20-15 so I could somewhat see why the sequence is weighted the way it is.
I feel slightly better knowing that no one knows for sure, which almost offsets feeling stupid for the mathematical analysis being slightly over my head. 
So, what would be the optimal arrangement?
Monty- I guess part of the problem is defining what you are optimizing. You could maximize the difference between adjacent numbers, but then you have to consider their adjacent numbers, and consider the overall distribution (totals in this fourth of the board, or this half, top/bottom, left/right), do you want to keep odds/evens mixed, etc. Plus there are so many variants of dart games…ones where you only shoot at certain numbers (Cricket, 20-15 and bulls), ones where you want max points up to limit, then you have to hit exact balance to go “out” (501/301 countdown, “outs” variants), and there are games wher you have to shoot specific numbers in sequence (Round the Clock), so…
Too many variables for me to grasp the math, but if you’re a numbers guy that first search result off **Jamicat’s **link discusses optimization, as do some of the others. Apparently even trying to establish what optimization means is a mathematical exercise in and of itself.