Roll

Roll is a mechanic used to determine outcomes of many events in Terra Invicta. Rolling is random, and it is weighted by difference between offence and defense modifiers. The exact formula is as follows:

diff = offense-defense

if diff >=0
  chance = 1-0.5*0.775^abs(diff)

else 
  chance = 0.5*0.775^abs(diff)

For example, councilor with 10 expionage trying to assasinate another councilor with 7 security needs to do a roll with diff = 10 - 7, and will be 76.7% likely to succeed.

Below table is just to ilustrate results of the above formula - Chance meaning chance to success of the offense.

Success chance

Off - Def	Chance	Off - Def	Chance
0	50.0%	0	50.0%
-1	38.8%	1	61.3%
-2	30.0%	2	70.0%
-3	23.3%	3	76.7%
-4	18.0%	4	82.0%
-5	14.0%	5	86.0%
-6	10.8%	6	89.2%
-7	8.4%	7	91.6%
-8	6.5%	8	93.5%
-9	5.0%	9	95.0%
-10	3.9%	10	96.1%
-15	1.1%	15	98.9%
-20	0.3%	20	99.7%

Critical success and Critical Failure

Critical success chance is 10 times lower than chance to success.

   e.g. for Off - Def = 5, it is 8.6% (86% / 10)

Critical failure chance is is 10 times lower than (1 - chance to success).

   e.g. for Off - Def = 5, it is 1.4% ((1 - 86%) / 10)

Related achievements

Solomon's Curse - Fail a mission with where you have greater than 99% chance of success

Source

Detection mechanics revealed - how spotting a councilor works