When rolling an ability check against a player or NPC, you roll:

Attacker: Base Attack Bonus + Attribute Bonus + 3d6
Defender: Base Defense Bonus + Attribute Bonus + 3d6

Ties go to the attacker

Since calculating stats for every combination of bonuses would be prohibitive, the stats below assume you and your opponent have equal bonuses

Note: These statistics are simulated with 20,000 iterations, and are therefore approximate