\problemdata
{random variable}
{monopoly}
{s01 ps10}

\begin{problem}
In the board game Monopoly, the number of
squares that a player advances in a single turn is determined by up to
three rolls of dice as follows.

\begin{problemparts}
\problempart Initially, the player rolls two dice, sums the results, and
advances that many squares.

\problempart If the same number comes up on both dice---this is called
\emph{rolling a double}---then the player rolls the dice a second time,
sums the results, and advances that many additional squares.

\problempart If the player rolled on double on the second roll, then the player
rolls the dice a third time, sums the results, and advances that many
additional squares.

\problempart However, if third roll was a double, then the player ``goes to
jail''.  We will treat this as though he had to reset his position to
where he was just before the first roll, so the total number of squares
advanced by the player in this case is zero.

\problempart
What is the expected number of squares that a player advances in a single
turn?  Assume that the dice are fair and six-sided and that rolls are
mutually independent.

\end{problemparts}
\end{problem}