Many of us have a habit of walking on the right. Imagine you're about the ascend a staircase as fast as possible, following the norm of staying on your right, when some other person will turn the corner and descend. Let p be the probability (between 0 and 1) the descender also follows the same "on the right side" norm so (1 p) is the probability they do the opposite and you collide. Using p, a (a positive number representing the benefit of successfully ascending without collision), and b (a negative number representing the pain of collision) we can think of the expected value of our trip up the stairs using the right side as

right = pa + (1 p)b

and the left side as

left = a(1 p)+pb

Graph the two equations with on the vertical axis and p on the horizontal axis, and find the value of p that sets the value on the right (right) with the left (left).