optimal bluffing with risk of facing the nuts

625 days ago by Alix

X, n, V = var('X, n, V') 
       
def b(X, n, V): r = V / (1 - V) * X / (1+X) return r 
       
def ev(X, n, V): r = b(X, n, V)* (1 - n) - n * X 
       
diff(b(X, n, V) - n * X, X) 
        
-n - V/((X + 1)*(V - 1)) + V*X/((X + 1)^2*(V - 1))
-n - V/((X + 1)*(V - 1)) + V*X/((X + 1)^2*(V - 1))
solve([-n - V/((X + 1)*(V - 1)) + V*X/((X + 1)^2*(V - 1)) == 0], X) 
        
[X == -(V*n - n + sqrt(-V^2*n + V*n))/(V*n - n), X == -(V*n - n -
sqrt(-V^2*n + V*n))/(V*n - n)]
[X == -(V*n - n + sqrt(-V^2*n + V*n))/(V*n - n), X == -(V*n - n - sqrt(-V^2*n + V*n))/(V*n - n)]