The Russian roulette with proportional probability is the same as the efficiencyoptimized Russian roulette except that the user specifies the value for which to divide the path throughput (importance) by instead of having this value calculated from the previous n rays cast.
I have the Russian roulette turn on after the ray depth is greater than 3 since for the first several bounces it is really likely that a light source is hit and it would be a shame to terminate a ray after just one bounce.
I modified the Cornell box scene slightly so that the far bottom left corner is covered from above and partly from the side (the box is hiding the side cover). The slope of the covers makes it even harder for light to escape. I did this so that the area in the corner would be more heavily shadowed and thus better show the differences between the methods (if there is little shadowed area, the images would all look roughly the same since most pixel contributions would come from depths of less than 4 and all the methods, in my code, handle paths of less than 4 the same way).
To compare the images, look at the resulting image diffs. You'll notice that the fixed depth images, unless you use a vary large depth, will have more error in the shadowed areas since rays were terminated before they had a chance to hit the light. The "speckles" in the Russian roulette images are from the increased variance that results from Russian roulette, since each time you let a ray bounce, you need to increase the value of that ray (so a ray that bounces 10 times in the 50% kill Russian roulette would be 2^10 times brighter than a ray that hit the light source from the start). Finally, note how the efficiency optimized Russian roulette has no bias, the amount of variance compares roughly (or possibly better) with the fixed depth of 100 image, and is faster than the fixed depth 7 and 30% kill Russian roulette. All the images however show some error compared to the reference image since I didn't have time to take enough samples. Alas...
If you want to learn about efficiencyoptimized Russian roulette, look at chapter 10 of Veach's thesis.
I used this bash script to generate the difference image.
The following images were made using 5,000 rays per pixel.
Rendered Image  contrast enhanced diff with Reference Image  dark areas enhanced diff with Reference Image  Details 
Reference image around 45 hours Since I want something that looks perfect (or close to it)this uses 10,000spp 

Fixed Maximum depth (100). 134 minutes. fixed max ray depth of 100. ray depth of 100 should make this pretty much optimal 

Fixed Maximum depth (10). 33.9 minutes 

Fixed Maximum depth (7). 27.7 minutes 

Fixed Maximum depth (5). 23.1 minutes 

Fixed Maximum depth (3). 17.4 minutes 

EfficiencyOptimized Russian Roulette. 24.8 minutes 

Proportional to 0.004 (actually 1/255) Russian Roulette. 24.2 minutes 

Proportional to 0.01 Russian Roulette. 23.5 minutes 

Russian roulette with 30% kill probability. 27.6 minutes note the noise that comes from the increased variance. 

Russian roulette with 50% kill probability. 24.8 minutes While this is around the same speed as fixed depth of 5 and the bias is much lower (there is actually none), the increased variance, in my opinion, ruins the image. 
Side by Side comparisons of the "good" choices.
0.004 Proportional Russian Roulette  EfficiencyOptimized Russian Roulette  Fixed Maximum depth(100)  Fixed Maximum depth(10)  
Images  
contrast enhanced diffs  
dark area enhanced diffs 
Here's a zoomed in version of the modified cornell scene:
Rendered Image  contrast enhanced diff with Reference Image  dark areas enhanced diff with Reference Image  Details 
Reference image  100,000spp with proportional to .04 and min depth
before Russian roulette turns on at 100. (many hours)


Fixed Maximum depth (10) at 10,000spp 89.1 minutes 

Proportional to 0.004 (actually 1/255) Russian Roulette at 30,000spp
67.7 minutes 

EfficiencyOptimized Russian Roulette at 30,000spp 76.9 minutes 
Rendered Image  Details 
entire scene 10.5 minutes EfficiencyOptimized Russian roulette 

Zoomed in Fixed Max depth of 10. 10.6 minutes note how after 10 bounces nothing is drawn.


Zoomed in Fixed Max depth of 100. 53.2 minutes note how this is still incomplete even after 100 bounces.


Zoomed in Efficencyoptimized Russian roulette. 28.8 minutes note how things are drawn until the very end (at least it looks that way). Also interesting is how the the render time has gone up compared to the entire scene render above, which also used efficencyoptimized Russian roulette, but it's still faster and more complete than the 100 depth render. This shows how this method will go faster on the easy sections and slower on the harder sections.


Zoomed in Russian roulette with probability proportional to pathThroughput/0.01 32.6 minutes This is a bit slower than the efficencyoptimized Russian roulette, but quality is about the same.


Zoomed in Russian roulette with probability proportional to pathThroughput/0.1 31.3 minutes This is still a bit slower than the efficencyoptimized Russian roulette and now the quality is not as good (much more noisy).


Zoomed in Russian roulette with probability proportional to pathThroughput/0.5 27.8 minutes This is finally a bit faster than the efficencyoptimized Russian roulette, but now the quality is rather bad due to the high noise.


Zoomed in 30% kill Russian roulette. This clearly looks horrible. Those few pixels that got drawn in the middle were actually extremely bright before they were clamped; that's why there is no bias introduced (but clearly the variance is HUGE).
