Risk Variants

Variant One

I. Army Deployment

1. Each player recieves a predefined amount of armies. Anywhere from 10 to 30 is a good starting point. The less armies, the more 'neutral' territory there will be at the beginning of the game. These armies must be placed in the players 'inactive' pile.
2. Every player roll a die, the one with the highest roll is the 'dealer'. The dealer will shuffle the territory cards and place them face up into six piles as follows:

   Pile #	Amount of Cards(original)	Amount of Cards(new)	Income/Cost to buy
   1	1	2	5
   2	2	4	4
   3	4	6	3
   4	8	10	2
   5	16	14	1
   6	11	6	0

   These territories are 'unpurchased'. In the next phase, players will get income and purchase these territories.
3. Starting with the player to the left of the dealer, each person takes the following actions:
   1. Move one army from your 'inactive' pile to your 'active' pile.
   2. If desired, the player may elect to purchase any number of unowned territories by moving a number of armies equal to the 'cost to buy' from his active pile to that territory. The player then transfers the card for that territory from the 'unpurchased' pile into his own pile, ensuring that he keeps track of the income generated by that territory.
   3. Players continue in this fashion until all armies have been placed on the board. If there are no more territories to 'buy', a player may place his armies on one of his existing territories.
4. After all players armies have been placed, the remaining unpurchased territories will be populated by neutral armies. Place a number of neutral armies equal to that territories' income on that territory (minimum 1)

II. The Turn

1. Income and army placement

   All players must determine their income and place their armies on their territories as follows.

   For each income generating territory a player possesses, he will receive the number of armies for that territory. These armies are placed in that territory. For example, if player A possesses brazil which has an income of 3, in the income phase, 3 armies will be placed in brazil. Each player will continue in this fashion until all armies have been placed.

   Any complete continents owned by a player will generate additional income as per the normal rules. These armies must be placed in the continent in which they were generated. They may be placed anywhere in the continent. For these armies, deployment will occur one army at a time, starting with the person to the left of the dealer.

   For each neutral territory, place a number of armies equal to the income generation of that territory on that territory. If a neutral territory has an income of 0, then assume it has an income of 1 while it is neutral ONLY.

2. Actions

   Starting with the person to the left of the dealer, each player may do ONE of the following:

   1. Make ONE attack from any one territory into one other. This attack will continue until the attacker takes the attacked territory, the attacker has one army left in the attacking territory, or the attacker decides to call off the attack.

      Defender responses

      In response to a declaration of attack, the defending player may declare a response as follows:

      1. Hold - this is the default response, the defender fights until all his armies have been destroyed or until the attacker calls off the attack (or runs out of armies to attack with). If the defender later wants to retreat, he may do so, but loses one additional army.
      2. Retreat - the defender may retreat into an adjacent friendly territory in response to an attack declaration. No battle is fought and no armies are lost by either side
      3. (optional rule) Retreat and salt - As for retreat, except the territory is 'salted' (see below).
   2. Move any number of armies from one territory into one adjacent friendly territory.
   3. Salt a territory - this permanently reduces the income of a specified territory by one. The minimum income of a territory is 0. NOTE: it would be interesting to have NEGATIVE incomes, now wouldn't it?
   4. Improve a territory. To do this, the player must spend a number of armies from that territory equal to the current income of the territory+1. After 'spending' these armies, the income generation of the territory permanently goes up by one, up to a maximum of 6. For example, if a territory has an income of two, then to raise it to three, three armies from that territory must be sacrificed.
   After all players have had a chance to perform an action, one 'action round' has been completed. Continue in this fashion performing action rounds until all players have passed and decided they want to perform no other actions.
3. End Turn

   After all players are finished with their actions, the turn is ended and the next turn's income phase is started.

III. Appendix

Attacker: one die; Defender: one die:

	Attacker wins 15 out of 36 (41.67 %)
	Defender wins 21 out of 36 (58.33 %)


Attacker: two dice; Defender: one die:

	Attacker wins 125 out of 216 (57.87 %)
	Defender wins 91 out of 216 (42.13 %)


Attacker: three dice; Defender: one die:

	Attacker wins 855 out of 1296 (65.97 %)
	Defender wins 441 out of 1296 (34.03 %)


Attacker: one die; Defender: two dice:

	Attacker wins 55 out of 216 (25.46 %)
	Defender wins 161 out of 216 (74.54 %)


Attacker: two dice; Defender: two dice:

	Attacker wins both: 295 out of 1296 (22.76 %)
	Defender wins both: 581 out of 1296 (44.83 %)
	Both win one: 420 out of 1296 (32.41 %)


Attacker: three dice; Defender: two dice:

	Attacker wins both: 2890 out of 7776 (37.17 %)
	Defender wins both: 2275 out of 7776 (29.26 %)
	Both win one: 2611 out of 7776 (33.58 %)