Mordecai and Rigby are hunting for a Turducken. They both start at x=0 and see a Turducken 1 meter away. Mordecai and Rigby start walking at the same rate towards x=1. They each have only one bullet in their guns and they can take it out and shoot at any point along the walk. Given that they are at position x, Mordecai has probability m(x)=x of hitting the Turducken with his shot. Rigby has probability r(x)=x2 of hitting the Turducken. If they shoot at the same time and both miss or hit the Turducken, then they just start again with a new Turducken. If exactly one of them hits the Turducken, then that person gets to keep it for Thanksgiving dinner. They don't neccesarily need to shoot at the same time. Assuming both Mordecai and Rigby apply an optimal strategy, what is Mordecai's chance of keeping the Turducken? The answer is in the form ca−b for integers a,b,c>0 that are pairwise relatively prime. Find a+b+c. Note that Mordecai and Rigby both know m(x) and r(x).
