This is more of a statistical question versus a programming question, however as I'd like an answer for programming an addon feature, it's both a statistical and programming question. I would like to know the probability of a feature generating through world generation with some scatter chance as a function of distance. Scatter chance is the supposed chance of a feature generating for some XxYxZ volume. Typically, this XxYxZ is represented as a chunk for spans X:0-15, Y:-64-380, and Z:0-15, however I restrict those spans below. Knowing the probability/chunk is not very useful, however knowing the probability of standing still in some chunk and turning 360 degrees seeing 20 chunks for each cardinal direction (a total of ~80+1 chunks) is more useful. So the question is, what is the scatter chance (or probability, or rather the formula to compute this) that I would need to set for a structure to (approximately) generate once in a 81 chunk circumference (i.e., I spin around in a 360)?
Using X=0, Y=62-66, and Z=0, I'm computing the probability of a structure for 81 chunks to be scatter chance * XYZ points/chunk * 81 chunks or 100/2650 * (1*5*1) * 81 = ~15%. This would suggest a 15% or almost 1/7 chance in seeing the structure generated when standing in one spot looking around 360 degrees at a total of 81 chunks. This should be somewhat rare, however the generation is placing ~10 of these features in a 81 chunk circumference when standing in any one spot. I could understand statistically 2-3 features spawning by chance, however I cannot understand how by chance 10 features could spawn.
I know of real life risk probabilities computed similarly for standing in any one spot for a 360 degree distance you can see (~10-20 kilometers), however I cannot find how they compute these probabilities.
Does anyone know how to compute this probability in terms of scatter chance by distance?