I am planning several probability problems on outcomes of combat in the game of risk. In order to solve these problems you will need the combat resolution rules. There are several good web sites the explains combat resolution in the game of risk.
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Defenders use up to two white dice to defend against up to three attacking red dice. Attackers declare up to three troops to use on their attack with each troop represented by a die. Defenders use two dice if they have two or more troops, but only one die if they have a single troop. Attackers roll first, defenders roll second. The two highest die in both rolls are used, with the highest of each roll being matched against the highest of the other roll. Ties go to the defender with each losing roll defeating 1 troop. Rounds continue until all defenders are defeated, the attacker runs out of troops they can attack with, or the attacker decides to withdraw.
Attacker rolls 3, 2, 5 Defender Rolls 2, 5 Result = 5 against 5 goes to the defender. 2 Against 3 goes to the attacker. Each player loses 1 troop.
Attacker rolls 4, 6, 5 Defender Rolls 5, 4 = 5 goes against 6 goes to attacker. 4 against 5 goes to attacker. Defender loses two troops.
Attacker rolls 3, 3, 5, Defender rolls 6, 3 = 6 goes against 5 goes to attacker. 3 goes against 3 tie goes to defender. Attacker loses two troops.
At the end of your turn you may reinforce one territory that you own from another adjacent territory that you own. You may make this move once per turn, and you may move as many troops as you want as long as you leave at least one behind.