Creating a Board game and finding the Prob. of Winning

[Carson888]

hey, I'm in a grade 12 probability and statistics class, and I've been assigned to create a board game and calculate the probability of winning. All my ideas get to complicated and I am finding my self confused so I am trying to keep it relatively simple. It is a board game where the first person to the finish will win, which has 50 individual squares to travel through. You roll two die, and move along through each space accordingly. When you land on a spot you flip a coin. If it lands on heads you move forward a square, and if tails, back one. I am suppose to calculate the theoretical probability of winning and the expected value... can anyone offer any help on how to do this? PS. when you reach the end you do not flip a coin and any roll over the amount of spaces you needed to reach the end still counts as a win.

 

[Carson888]

psps i don't want the work done i would just like any ideas to help

 

[bpet]

You could try finding an approximate answer by running some simulations with a random number generator. For example in Excel the formula for a dice roll would be something like ceiling(6*rand()) or randbetween(1,6). It might be tricky to program but once you've set up a single game just get it to repeat many times and count the proportion where player 1 wins.

The probability can also be calculated exactly with the aid of some college-level theory and a computer (about 67%).

Good luck!