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 Espionage trying to Assassinate another councilor with 7 Security needs to do a roll with diff = 10 - 7, and will be 76.7% likely to succeed.

Note: This is not actually true in practice because there are many other Mission Modifiers that affect the Assassinate mission, adding points to the offense or defense.

Below table is just to illustrate 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