: RISK : The game of world domination
: RISK is the popular strategy game of world conquest
in which opponents move armies around the world map in an effort
to defeat their opponents, capture territory, acquire RISK cards
and ultimately rule every territory on the map.
: This task is accomplished primarily through wit, deception,
strategy and luck with the dice. While we could say some things
about the former topics, here we concentrate on the latter. Specifically,
when defending a territory against the invading armies of your
opponents, is it better to roll 1 or 2 dice? How much better?
: Let me lay out the problem parameters and describe
the rules of engagement:
1. An attacker may roll up to a maximum of 3 dice
during an engagement, and must have one more unit in the attacking
country than the number of dice thrown (this is because the attack
must move at least a number of troops into the conquered country
which is equal to the number of dice rolled, yet must leave behind
at least one troop in the attacking country).
2. A defender may defend with up to 2 dice and is not restricted
in any way.
3. Both participants must choose, before throwing their dice,
how many they will use in the engagement.
4. Once the dice are thrown, each participant sorts the dice in
descending order and matches them up by rank (i.e. the two high-dice
are matched up, the two next highest, etc.). The owner of the
lower value then loses one troop unit with the defender winning
: To the answer
: Credit - the image is from iConquer's
(a Mac version of RISK) website.