is symmetric. Through some heavy lifting in calculus, we find that the optimal density is proportional to:
When constructing the solution programmatically, two hurdles often arise: If your accuracy function starts at zero, the term explodes. We must enforce a lower bound to ensure the strategy is valid. is symmetric
Should we look at the for solving the threshold when the accuracy function is complex? is symmetric
: In the actual game loop, sample from this distribution to decide the exact frame of the "Silent" shot. is symmetric
The goal is to make the opponent's payoff constant regardless of when they shoot. This leads to an integral equation where the payoff