On a surface, Russian Roulette determines whether a photon is absorbed or reflected.

The photon power is not scaled.

Reflection or Absorption:

a: [0, 1] is a random variable

p: probability of reflection

phi: the power of incoming photon

if( a < p ) reflect photon at power phi

else photon is absorbed

Specular or Diffuse Reflection:

a: [0, 1] is a random variable

p_d: probability of diffuse reflection

p_s: probability of specular reflection

where ( p_d + p_s < 1 )

Diffuse Reflection: a: [0, p_d]

Specular Reflection: a: [p_d, p_d + p_s]

Absorption: a: [p_d + p_s, 1]

In participating media, Russian Roulette determines whether a photon is absorbed or scattered.

The probability of a photon being scattered is given by the scattering albedo ( rho / (rho + alpha) ) [Jensen 1998], where rho and alpha are the scatter and absorption coefficients.

Scattering or Absorption:

a: [0, 1] is a random variable

p: probability of scattering

phi: the power of incoming photon

if( a < p ) scatter photon at power phi

else photon is absorbed 

New direction of a photon being scattered from diffuse reflection or participating media:

Sampling techniques. Importance sampling is usually applied.