Risky Odds

In th game of Risk, one player attacks another player using armies in an adjacent location. Create a game tree showing all of the possible results for a single attack when each side has up to 5 pieces. Hint: You can draw one game tree with every possible combination of results as subtrees within it. (18 points)

Modify your game tree by adding probabilities for each outcome, assuming both sides roll the most dice allowed every time. Using your modified game tree, determine the probability that the end scenario is: (32 points)

• Both sides start with 5 armies and attacker loses every time
• Both sides start with 3 armies and attacker ends up with one army in each location
• Defender starts with 2 armies, attacker starts with 4 armies, and attacker wins with any number of armies
• Both start with the same number of armies, and the defender wins (assume each scenario is equally likely)