Wednesday, October 02, 2013
Spotting the Enemy
I touched a little bit on this issue in my Surfing Bird post. Was no one looking down that street when the first VC ran through? Did they look, but only too late to raise their rifles and shoot?
Spotting falls beyond the simple die roll that dictates success or failure. Sure, your character spots the enemy, but when? In time to react or not? The sniper sees the enemy dash through the street. Does he catch him in time to aim and shoot? Or did his sweep of the area come too late and allowed the runner to make it to the other side before the round goes off? When will the patrol that does routine walks through the area come around again?
These can be answered by giving odds of occurring every so many seconds or minutes and then roll until the patrol comes around or the sniper spots its target. The issue with this is that the odds are not always the same minute after minute or second after second. If a patrol comes around every 60 minutes it would be very improbable that it comes back ten minutes after it passed. So rolling every ten minutes with a 15% chance of occurrence is wrong. Same thing occurs for a spotter. He can't have eyes everywhere so at some point a character is safe to raise his head to look for enemy positions. The odds of the spotter looking back into the area is slim. But the question is for how long?
Lets look back at the runner example. It takes him 7 seconds to run across a street. A sniper is scoping the area. At what point in the run does the sniper spot the runner? In the beginning, in the end or halfway through. And how does this affect the response time of the sniper. He still needs to estimate range and lead the runner. If the runner is spotted at second 5 it may be too late to get a clear shot. If the runner is spotted at second 1 he's most surely dead.
Instead of looking at an initiative roll will a flat probability curve and have it determine when an event happens or have a long succession of d100 rolls to see if it happens at a given hour, minute or second, I'm looking for a single roll that says : "the patrol will return in 22 minutes" Such probability curves exist, one such example is the Poission Distribution (pronounced [pwasɔ̃]). It helps answer questions like given a rate of occurrence of an event, what are the odds of one, two, three, four, etc. events occurring in the same period of time.
So instead of rolling every minute to see if the patrol returns I can determine how many times the patrol will come around in one hour by simply using the Poission distribution. On the next post I'll dive into how to do this without having to solve this: