Considering a board game which has 20 positions only. There are 2 fair dice that can be rolled and the player moves in a clockwise position over the board positions. Considering that the dice are fair and player moves around the board as per the dice roll, how can I compute the steady state probability of being in the starting location (GO i.e. the bottom right position)?
I am thinking that since the average dice roll sum is 7, so the steady state probability of being in any position on the board is $\frac{1}{7}$. Therefore it would be the same for the starting location as well. However, I am not sure. Any help would be appreciated. Thank you.
The probability of being on any square at all is the sum of the probabilities of being on the particular squares. Thus, if your result $\frac17$ were correct, the probability of being on any square at all would have to be $\frac{20}7$. It is in fact $1$, so the probability of being on any particular square is ...?
Note that this probability has nothing to do with how many dice you roll or their average; it depends only on the number of squares.