I'm wondering what probablity can tell me about dice rolling strategies in the game Risk. When a player attacks another player, they can roll up to 3 dice. The defending player can choose to roll either 1 or 2 dice in defence. They must choose how many dice they are going to roll before the attacking player rolls.
The highest valued dice by each player is compared, and if the defending player's dice has a higher or equal value then the attacking player loses a soldier, otherwise the defender does. If the defender has chosen to roll a second dice, then the second highest roll by each player is compared with the same comparison.
My question is, over time will the defending player be better off rolling 1 or 2 dice in defence?