Die Throw Assignment

In the game of Risk, armies battle via dice throws. Suppose, a defender's position is so weak that only one 6-sided die can be thrown. The attacker on the other hand has sufficient armies to justify up to three dice if desired. In a battle, the defending die is compared with the attacking dice. If any of the attacking dice strictly exceed the defending die, the attacker wins. Simulate the probability that the attacker wins when choosing to roll [a] 1 die, [b] 2 dice, or [c] 3 dice. The answer is accessible with conditional probability, but let's simulate it here.

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