Hi,

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.

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?

Thanks, Matt