Let’s try a short modified version of Risk where A starts with 3 armies and B starts with 2 armies.
They both roll a 6-sided die at each turn: A will roll the number of dice equal to their number of armies
minus 1 (so they will roll 2 dice when they have 3 armies, 1 if they have 2, and can not attack with 1 army);
while B always rolls one.
They will each continue to roll dice until either A has one army or B has none (in which case A wins).
For a roll, if the maximum of A’s rolls is bigger than B’s roll then B loses an army; if the max for A is lower
they lose an army; if the max for A is the same as the roll for B, no army is lost.
a) (5 pts) Set up the transition matrix for this.
b) (4 pts) Find the probability that A wins.
c) (2 pts) Find the mean number of steps until they stop