Random chance in an Age of Corporations game is handled through the Degree of Success System. Every action requiring skill and chance has a designated Target Number, or TN. To succeed at an action, you must roll two six-sided dice (2d6) and achieve a number under your action's TN.
The difference between the TN and the number you roll is your DoS - the Degree of Success of your action. A higher DoS means that your success is more complete. A high DoS means a spectacular success. Sometimes a particular DoS is required to fully finish a task.
The base TN of a complex action by an unskilled person is 6. Easier tasks may have a bonus to TN, harder tasks may have a penalty.
Generally, a task will have a penalty if any success is difficult to achieve, and will require a higher DoS if full success is challenging but partial success is possiible.
In the case of a contested roll, Degrees of Success are subtracted from one another to represent the final DoS of the winner. The higher DoS minus the lower DoS is the final DoS.
In a typical combat roll, the defender's DoS is subtracted from the attacker's DoS. If the result is less than zero, the attack fails. If the result is greater than zero, the final DoS squared equals the successful attack's damage bonus.
Special note: For actions that can be improved through focus or effort, a player may spend 10 energy points to increase a target number by 1 or 20 EP to increase it by 2. One additional +1 bonus can be obtained with a projectile weapon by spending a round aiming.
Equations:
Simple Roll:
TN - 2d6 (+/- penalty) = DoS
Contested Roll:
Winning DoS - Losing DoS = Winner's Final DoS
The ugly-ass combat roll that is simpler than it looks, honest:
(Attacker DoS - Defender DoS)^2 + Attack Base Damage - Armor = TOTAL DAMAGE