Power heuristic in multiple importance sampling Both Mitsuba and Tungsten use the power heuristic to do multiple importance sampling (MIS).

Mitsuba:

inline Float miWeight(Float pdfA, Float pdfB) const {
    pdfA *= pdfA;
    pdfB *= pdfB;
    return pdfA / (pdfA + pdfB);
}


Tungsten:

static inline float powerHeuristic(float pdf0, float pdf1)
{
    return (pdf0*pdf0)/(pdf0*pdf0 + pdf1*pdf1);
}


Advanced Global Illumination gives the balance heuristic:
$$F=\cfrac1N\sum_{i=1}^n\sum_{j=1}^{n_i}\cfrac{f(X_{i,j})}{{\sum\limits_{k=1}^n}\frac{c_k}Np_k(X_{i,j})}$$

The power heuristic may be like this:
$$F=\cfrac1N\sum_{i=1}^n\sum_{j=1}^{n_i}\cfrac{f(X_{i,j})p_i(X_{i,j})}{{\sum\limits_{k=1}^n}\frac{n_k}Np_k^2(X_{i,j})}$$

I know they are all valid estimators.

What's the motivation to use the power heuristic?

What about the cube heuristic?
$$F=\cfrac1N\sum_{i=1}^n\sum_{j=1}^{n_i}\cfrac{f(X_{i,j})p_i^2(X_{i,j})}{{\sum\limits_{k=1}^n}\frac{n_k}Np_k^3(X_{i,j})}$$
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Veach determined it empirically.