Domains: Clerics get 2 domains. Contemplative can give another domain or two. Those are the two most commonly used sources.
- Competition Domain: +1 bonus on all opposed checks.
- Luck Domain: Gives a reroll of anything 1/day.
- Travel Domain: Free and automatic freedom of movement effect. Automatically wins you the opposed grapple check to escape or avoid a grapple.
Skill Mastery: Lets you take 10 on a number of skills. Rogues can pick it up at 10th. Swashbucklers get it from a few skills, too. Exemplar is another biggie. See the math section for the details of when and why taking 10 is good for you.
If you can take 10, it's like your opponent is making a fixed DC check, except that you can still have an advantage on a tie (thus forcing him to beat the "fixed DC" rather than just meet it). You only need a +10 modifier instead of +19 to assure victory this way. Worse than rolling if your relative modifier is +3 or less. Better than rolling if your modifier is +5 or better. Breaks even at a +4 relative modifier (70% success either way). However, taking 10 may prevent you from rerolling, which is a bad thing, especially in reroll wars when taking 10 would only give you a small advantage compared to rolling.
The Savvy Rogue feat lets you "take 12". Actually, it gives you a +2 bonus when you take 10, which is even better if you've otherwise got a relative modifier between -2 and +0 since it improves your tiebreaking. This makes "taking 12" better than rolling with a relative modifier all the way down to -7 (before including the +2 taking 10 bonus). The difference isn't huge down there, but it's amazing the difference in range of usefulness.
Mantles: Mantles are the "domains" of psionics, most give small bonuses. Available by default to Ardents, and with ACFs to almost everyone else.
- Fate Mantle: Add your level in the class that granted you mantles to any d20 roll 1/day. Big bonuses are even more necessary here to ensure victory than against a fixed DC.
- Time Mantle: +2 initiative never hurts.
Auras: Marshal auras can give large bonuses to a variety of things.
- Art of War: Adds your Charisma bonus to everyone's disarm, trip, bull rush, and sunder attempts. That's opposed attack rolls, Str checks, Str checks, and attack rolls, respectively.
- Motivate Dexterity: King of the motivate series of minor auras unless you're going for something specific. Adds your Charisma bonus to everyone's Dexterity checks, Dexterity-based skill checks, and initiative. Everyone rolls initiative, and while it isn't technically an opposed check, the mechanics are very similar.
- Motivate Strength/Dexterity/Constitution/Intelligence/Wisdom/Charisma: Adds your Charisma bonus to everyone's checks and skills for the designated ability score. There are six of these auras, one for each ability score, so it's unlikely you'll have them all, and you can still only use one at a time. Motivate Dexterity is a standout due to influencing initiative (see above).
Battle Skill: Starting at 11th level, Warblades get to add their Intelligence bonus as an insight bonus to oppose bull rush, disarm, feint, overrun, sunder, and trip attempts. This only boosts their ability to defend against them, not to attack with them, unfortunately.
