Silent Duelsвђ”constructing The Solution Part 2 Вђ“ Math В€© Programming Online

f(x)=A′(x)A(x)3f of x equals the fraction with numerator cap A prime open paren x close paren and denominator cap A open paren x close paren cubed end-fraction

: In the actual game loop, sample from this distribution to decide the exact frame of the "Silent" shot. f(x)=A′(x)A(x)3f of x equals the fraction with numerator

The goal is to make the opponent's payoff constant regardless of when they shoot. This leads to an integral equation where the payoff f(x)=A′(x)A(x)3f of x equals the fraction with numerator

is the accuracy function, the "value" of the game is determined by finding a threshold (the earliest possible shot) and a density function for all times f(x)=A′(x)A(x)3f of x equals the fraction with numerator