smc

We will let the moves be complex numbers $a$, $b$, and $c$, each of magnitude one. The starts on the origin. It is relatively easy to show that exactly one element in the set $$\{|a+b+c|,|a+b-c|,|a-b+c|,|a-b-c|\}$$ has magnitude less than or equal to $1$. (Can you show how?) Hence, the probability is $\boxed{\frac{1}{4}}$.