From A Song of Ice and Fire : TMG Wiki

Numerous effects might allow for dice to be re-rolled. When re-rolling dice, the following rules apply:

  • A die may only ever be re-rolled once by each player.
  • The previous result from a re-rolled die is discarded and has no effect on gameplay, being replaced by the new result entirely.
  • If both players have an effect that would cause a die to be re-rolled, the active player's re-roll happens first, then their opponent's.
  • If both players have optional effects that would allow dice to be re-rolled, then follow the rules outlined under Simultaneous Actions.