You're right, a 0.5 strategy is better than random chance. Unfortunately, the simplest generalization of that strategy yields only 0.5^(n-1), which is not good

You're right, a 0.5 strategy is better than random chance. Unfortunately, the simplest generalization of that strategy yields only 0.5^(n-1), which is not good enough - you need to start with a bigger base case.