Cost-weighted finite search game ($v=(c^2+{\sum }_i{c}_i^2)/(2c)$)

In a hide-and-search zero-sum game with positive inspection costs $c_i$ and $c={\sum }_i{c}_i$, hiding with probabilities $c_i/c$ gives the same expected search cost for every complete search order. For three locations, beginning at $i$ with probability $c_i/c$ and randomizing the remaining two orders also equalizes every hiding location. The common value is the displayed quantity.