In a hypothetical dungeons and dragons scenario, suppose that your character have a strength modifier of +5. You have an opponent, a wimpy peasant with a strength modifier of +1.
you both get into a fight (aka contest). when this happens, you both each roll a 1d20 then add modifiers. whoever gets the higher roll plus modifiers wins the contest. In case of tie, there will be a re-roll until someone wins
How do I calculate the probability that your character wins the contest?
EDIT: in this situation, modifiers are immediately added after the roll