High or Higher

I've been tinkering more with the idea of exploiting the mechanics-neutral table mercilessly for actual dice rolls and simply specifying everything as "high roll or better means things change", which greatly simplifies rules (only mechanics choices are whether to use different dice for different subsystems and what modifiers are relevant.) It does make a couple descriptions tricky, but I've found a way for each of the major components:

• Attack Roll: High or better vs. armor and shield means a potentially fatal blow; no protection gives an advantage to the attacker, full plate metal protection gives an advantage to the defender; shields provide 1/3rd of the protection (either a follow-up roll for 1d6 combat or a 1-point protection value for shields in a 1d20/3d6 combat system, vs. 2 points for better armor than normal.)
• Saving Throw: High or better vs. extreme natural attacks or rays of light with unnatural effects; Extremely High or better vs. pure magic or powerful effects like dragon's breath; characters with classes get to modify the roll based on hit dice, and some classes modify saves against specific effects.
• Surprise Roll: High or better to surprise an opponent; rules mostly dwell on when not to roll surprise, or potential modifiers to surprise.
• Risks or Accidents Roll (drop hand-held item when surprised, spike slips): High or better means things change and the accident happens; can be modified by ability scores or preparations, of course.
  
• Hear Noise, Spot Hidden Enemy, etc.: Merged with the Surprise rules; no longer "skills", but allows characters to be forwarned (escape surprise.) Similarly, Open Doors is a roll to see if you force a door open with one swift kick, surprising any opponent; failure just means it takes longer and you negate surprise.
• Secret Door Roll: Merged with the Surprise rules; adventurers are considered "surprised" by the door and unable to notice it; if a monster uses the door to suddenly attack, the adventurers are automatically surprised; searching attempts to change that surprised state (High or better.)

A few things get noted as Very High or Extremely High, but there are only a few of these exceptions (Very High chance to avoid wandering monsters or getting lost, for example.) The main complication comes from bonuses and penalties. Since sometimes the players want things to change and sometimes they don't, a +1 on the roll is sometimes a good thing (Attack Roll, Surprise Roll) and sometimes not (Save, Accidents.) I'm thinking of expressing it as:

Adding a modifier to the roll makes change more likely; adding it to the target number for a High result makes change less likely. If you have an advantage in a situation, you may add a bonus of +1 or more to either the die roll or the target number, whichever you choose, depending on whether you want things to change or not.

Thoughts?