There are few things in the world as useless as a nuclear weapon nobody else knows you have. All of the game theory, and that is where the advantage comes from,

There are few things in the world as useless as a nuclear weapon nobody else knows you have. All of the game theory, and that is where the advantage comes from, derives from the fact people will go to extremes to keep themselves from getting nuked even once. Keeping a Doomsday Device a secret defeats the whole point.