Re: Stealth and Risk
Posted: Mon Feb 15, 2021 1:45 pm
So for the sake of making this easy, I've made some assumptions here and will explain as I go:
First, I make the assumption that the person searching is rolling the median value within their range each time... I know this is a huge assumption but didn't want to have to work with 2 variable rolls here... so someone with 100 perception skill would have a max roll of 200 and always be rolling 100 for the purpose of this calculation. Next I assume that p(being seen)=1-[p(not being seen based on a single roll)^(1+ absolute value of reroll number)].
The most simplistic situation is the following:
Stealth of hider and perception of searcher are equal (percentage is approximate chance of being seen on one roll):
0 rerolls: 50%
-1 reroll: 75%
-2 rerolls: 88%
-3 rerolls: 94%
-4 rerolls: 98%
-5 rerolls: 99%
0 perception versus 500 stealth:
0 rerolls:9%
-1 rerolls: 16%
-2 rerolls: 23%
-3 rerolls: 29%
-4 rerolls: 35%
-5 rerolls: 41%
300 perception versus 600 stealth:
0 rerolls: 29%
-1 rerolls: 49%
-2 rerolls: 64%
-3 rerolls: 74%
-4 rerolls: 81%
-5 rerolls: 87%
Ok... so again, each of those is the probability of a single median roll on the search end resulting in a stealth character being spotted (or the result of a single stealth check). As a note, in order to get into position to ambush with 0 rerolls against something with like perception, the chance of achieving this is approximately 0.50*0.50*0.50 = 12.5%... so in setting up an attack against someone of equal perception, we're seen 87.5% of the time and induce paranoia. I assume that there is usually more of a gap for mobs though and that wechuge perception, for example, is lower than mine... this would be the result if I was trying to ambush black, however... I would have about a 12.5% chance of not being seen. Pretty low given our skill is approximately equal.
Ok so... risk accumulation. Going to provide a straight progression based on 3 and 5 sec rts... haven't logged in to check the actual rt yet.
3 second rt:
Start of search: 12 risk, 0 seconds elapsed
Search 2: 12 - 3 +12 = 21 risk (-1 reroll), 3 seconds in
Search 3: 21 - 3 +12 = 30 risk (-1 reroll), 6 seconds in
Search 4: 30 - 3 +12 = 39 risk (-1 reroll), 9 seconds in
Search 5: 39 - 3 +12 = 48 risk (-2 rerolls), 12 seconds in
Search 6: 48 - 3 +12 = 57 risk (-2 rerolls), 15 seconds in
Search 7: 57 - 3 + 12 = 66 risk (- 3 rerolls), 18 seconds in
Search 8: 75 risk, (-3 rerolls), 21 seconds
Search 9: 84 risk (-4 rerolls), 24 seconds
Search 10: 93 risk (-4 rerolls), 27 seconds
Search 11: 100 risk (-5 rerolls), 30 seconds
5 second rt:
Start: 12 risk 0 seconds elapsed
Search 2: 12 - 5 + 12 = 19 risk (0 rerolls), 5 sec
Search 3: 26 risk (-1 reroll), 10 sec
Search 4: 33 risk (-1 reroll), 15 sec
Search 5: 40 risk (-2 reroll), 20 sec
Search 6: 47 risk (-2 reroll), 25 sec
Search 7: 54 risk (-2 reroll), 30 sec
Search 8: 61 risk (-3 reroll), 35 sec
Search 9: 68 risk (-3 reroll), 40 sec
Search 10: 75 risk (-3 reroll), 45 sec
Search 11: 82 risk (-4 reroll), 50 sec
Search 12: 89 risk (-4 reroll), 55 sec
Search 13: 96 risk (-4 reroll), 60 sec
Ok... so no one is clearly meant to stand there for close to a minute while someone is searching for them...
But let's now calculate the probably of being caught on each search using the numbers above...
We can start with someone with perception at half of our stealth and a 5 second rt and 0 starting risk and calculate the probability of being seen after X searches.
Search 1: 29%, 0 seconds
Search 2: [1 - (.71*.71)]*100= 50%, 5 seconds in
Search 3: [1 - (.71*.71*.71)]*100= 64%, 10 seconds in
Search 4: [1 - (.71*.71*.71*.51)]×100= 82% 15 seconds in - this is where the reroll kicked in
Search 5: 91% chance of having been seen, 20 seconds in
Search 6: now we have added another reroll - so [1- (.71*.71*.71*.51*.51*.36)]*100 = 97%, 25 seconds in.
This means that even if you have twice the skill of your opponent, you are still near guaranteed to be seen before 6 searches. That means that 600 stealth against 300 perception will essentially allow you to be found within 25 seconds. I will do the math for the other scenarios in a bit... but the point is that even with a massive skill gap, I'm likely to be noticed VERY quickly and nearly guaranteed to be noticed by 5 or 6 searches.
First, I make the assumption that the person searching is rolling the median value within their range each time... I know this is a huge assumption but didn't want to have to work with 2 variable rolls here... so someone with 100 perception skill would have a max roll of 200 and always be rolling 100 for the purpose of this calculation. Next I assume that p(being seen)=1-[p(not being seen based on a single roll)^(1+ absolute value of reroll number)].
The most simplistic situation is the following:
Stealth of hider and perception of searcher are equal (percentage is approximate chance of being seen on one roll):
0 rerolls: 50%
-1 reroll: 75%
-2 rerolls: 88%
-3 rerolls: 94%
-4 rerolls: 98%
-5 rerolls: 99%
0 perception versus 500 stealth:
0 rerolls:9%
-1 rerolls: 16%
-2 rerolls: 23%
-3 rerolls: 29%
-4 rerolls: 35%
-5 rerolls: 41%
300 perception versus 600 stealth:
0 rerolls: 29%
-1 rerolls: 49%
-2 rerolls: 64%
-3 rerolls: 74%
-4 rerolls: 81%
-5 rerolls: 87%
Ok... so again, each of those is the probability of a single median roll on the search end resulting in a stealth character being spotted (or the result of a single stealth check). As a note, in order to get into position to ambush with 0 rerolls against something with like perception, the chance of achieving this is approximately 0.50*0.50*0.50 = 12.5%... so in setting up an attack against someone of equal perception, we're seen 87.5% of the time and induce paranoia. I assume that there is usually more of a gap for mobs though and that wechuge perception, for example, is lower than mine... this would be the result if I was trying to ambush black, however... I would have about a 12.5% chance of not being seen. Pretty low given our skill is approximately equal.
Ok so... risk accumulation. Going to provide a straight progression based on 3 and 5 sec rts... haven't logged in to check the actual rt yet.
3 second rt:
Start of search: 12 risk, 0 seconds elapsed
Search 2: 12 - 3 +12 = 21 risk (-1 reroll), 3 seconds in
Search 3: 21 - 3 +12 = 30 risk (-1 reroll), 6 seconds in
Search 4: 30 - 3 +12 = 39 risk (-1 reroll), 9 seconds in
Search 5: 39 - 3 +12 = 48 risk (-2 rerolls), 12 seconds in
Search 6: 48 - 3 +12 = 57 risk (-2 rerolls), 15 seconds in
Search 7: 57 - 3 + 12 = 66 risk (- 3 rerolls), 18 seconds in
Search 8: 75 risk, (-3 rerolls), 21 seconds
Search 9: 84 risk (-4 rerolls), 24 seconds
Search 10: 93 risk (-4 rerolls), 27 seconds
Search 11: 100 risk (-5 rerolls), 30 seconds
5 second rt:
Start: 12 risk 0 seconds elapsed
Search 2: 12 - 5 + 12 = 19 risk (0 rerolls), 5 sec
Search 3: 26 risk (-1 reroll), 10 sec
Search 4: 33 risk (-1 reroll), 15 sec
Search 5: 40 risk (-2 reroll), 20 sec
Search 6: 47 risk (-2 reroll), 25 sec
Search 7: 54 risk (-2 reroll), 30 sec
Search 8: 61 risk (-3 reroll), 35 sec
Search 9: 68 risk (-3 reroll), 40 sec
Search 10: 75 risk (-3 reroll), 45 sec
Search 11: 82 risk (-4 reroll), 50 sec
Search 12: 89 risk (-4 reroll), 55 sec
Search 13: 96 risk (-4 reroll), 60 sec
Ok... so no one is clearly meant to stand there for close to a minute while someone is searching for them...
But let's now calculate the probably of being caught on each search using the numbers above...
We can start with someone with perception at half of our stealth and a 5 second rt and 0 starting risk and calculate the probability of being seen after X searches.
Search 1: 29%, 0 seconds
Search 2: [1 - (.71*.71)]*100= 50%, 5 seconds in
Search 3: [1 - (.71*.71*.71)]*100= 64%, 10 seconds in
Search 4: [1 - (.71*.71*.71*.51)]×100= 82% 15 seconds in - this is where the reroll kicked in
Search 5: 91% chance of having been seen, 20 seconds in
Search 6: now we have added another reroll - so [1- (.71*.71*.71*.51*.51*.36)]*100 = 97%, 25 seconds in.
This means that even if you have twice the skill of your opponent, you are still near guaranteed to be seen before 6 searches. That means that 600 stealth against 300 perception will essentially allow you to be found within 25 seconds. I will do the math for the other scenarios in a bit... but the point is that even with a massive skill gap, I'm likely to be noticed VERY quickly and nearly guaranteed to be noticed by 5 or 6 searches.