Reference no: EM132858276

In the game Monopoly on each turn you roll a pair of dice and move your marker a number of positions corresponding to the total number of dots on the pair. So you move a total of 2-12 positions. However, if you get "doubles" (e.g. two 1's, two 2's, ..., two 6's) you move your marker the amount shown on the total of the two dice (e.g. 2,4,6,...,12) but you get to roll again in that turn. While in Monopoly if you get three doubles in a row you go to jail, for this problem suppose you can just keep on rolling the pair of dice every time you get doubles and moving your marker corresponding to the total in the roll.

Determine the expected number of positions you move in total in a single turn where you can have multiple rolls because of doubles.