How many armies does it take to conquer a territory?
Again, it depends what version of the rules you’re using. The following analysis assumes that (a) the defender must choose how many dice to roll without first seeing the attacker’s roll, and (b) the defender is allowed to (and therefore should) roll 2 dice if he has exactly 2 armies remaining. If the attacker has enough armies that he will always be able to roll 3 dice (and is willing to do so), then the number of armies he expects to lose before conquering a single territory is, on average: 0.8534144 N – 0.2213413 (1 – (-0.525359)^N) where N is the number of armies initially in the target territory. This is only an average; any particular battle of course depends on how the dice may fall! Still, this formula has a few interesting corollaries. The increase in defensive value obtained by adding a second army to a territory that had only one army is far greater than that obtained by adding that army anywhere else. In eliminating a one-army territory, an attacker expects to lose about 1/2
