###################################################################### # # In the game Trouble the goal is to move a bunch of markers from a # starting point all the way to the ending point. Ignoring some # subtleties of the game, the basic move is very simple: # # - You roll a standard 6-sided die. # - You move your marker the number of spaces equal to the value # on the die. # - If you rolled a six, you roll and move again. You keep doing # this as a long as you roll sixes. # # For example, if you roll a 3, then you move 3 spaces. If you roll # a 6 followed by a 3, then you move 6 + 3 = 9 spaces. If you roll a # 6, another 6, and then a 3, then you move 6 + 6 + 3 = 15 spaces. # ###################################################################### ##### Simulating Trouble ##### # Prite some code that simulates a move in the game Trouble. # Print the number of spaces moved. ##### What is the average length of a move? ##### ##### What happens if you change the roll-again value? ##### # For example, f you change the rules so that you roll again after rolling # a 1, what is the average length of a move? ##### How does the roll-again value affect the chance of winning? ##### # Suppose you are playing a head-to-head game with another person. # You use the "go again on 6" rule, and the other person uses the "go # again on 1" rule. You both roll your die to complete a move. # The winner is who ever has a the larger move. # (If there is a tie, repeat until there is a winner.) # Is this a fair game, in the sense that both players have an equal probability of winning? # If not, who has the advantage, and what is the corresponding probability?