Over-success when holding in Diplomacy
A unit holding that has more or equal valid support to hold than its attacker stays put (wins).  Here are some examples:

Example 0: Greater Valid Support To Hold


Army Gascony -> Paris
Army Brest supports Gascony -> Paris
Army Paris Holds
Army Belgium supports Paris
Army Ruhr supports Pairs


Paris's support plus itself is 3 strong, and Gascony's support plus itself is 2 strong, so the defense is greater and Paris holds

Example 1: Equal Valid Support To Hold


Army Gascony -> Paris
Army Brest supports Gascony -> Paris
Army Paris Holds
Army Belgium supports Paris


Paris's support plus itself is 2 strong, and Gascony's support plus itself is 2 strong and the tie does to the defender so Paris holds

Example 2: An invalid support


Army Gascony -> Paris
Army Brest supports Gascony -> Paris
Army Paris Holds
Fleet Belgium supports Paris (* invalid -- you can only support where you can move *)


Paris's support from Belgium was invalid, so it doesn't exist.  Paris is at one strong, and Gascony's support plus itself is 2 strong and so Gascony wins and Paris is dislodged.

Example 3: A support of a move instead of a hold


Army Gascony -> Paris
Army Brest supports Gascony -> Paris
Army Paris Holds
Army Belgium supports Paris -> Brest (* invalid -- Paris isn't trying to move to Brest *)


Paris's support from Belgium wasn't to hold, so it doesn't help.  Paris is at one strong, and Gascony's support plus itself is 2 strong and so Gascony wins and Paris is dislodged.