You randomize it at the Nash equilibrium. The more obvious the place, the less probability you give to hiding it there.
The Nash equilibrium is based on the idea that your opponent will know your strategy, and fight specifically against it, and it will still be the best strategy. In this case, if you hide it using that probability distribution, no matter how you look for the coin later, you’ll be exactly as likely to find it.
You randomize it at the Nash equilibrium. The more obvious the place, the less probability you give to hiding it there.
The Nash equilibrium is based on the idea that your opponent will know your strategy, and fight specifically against it, and it will still be the best strategy. In this case, if you hide it using that probability distribution, no matter how you look for the coin later, you’ll be exactly as likely to find it.