I agree the authors should have used the improved odds calculation you mention. However, doing so would only explain the missing 10% if two photons hitting a si

I agree the authors should have used the improved odds calculation you mention. However, doing so would only explain the missing 10% if two photons hitting a single rod led to 100% correct response rate, and it seems unlikely for the response to be so nonlinear. Anyway with such an experiment, we don't know why the subjects are above chance, and can only make inferences. As I point out above, you really need single photon emission to know for sure. I went back to the original paper [1] and the authors' conclusions are much more measured than précis we are all discussing. From page 838: ... the range of 54 to 148 quanta at the cornea becomes an upper limit of 5 to 14 quanta actually absorbed by the retinal rods. [ed: I presume this is where the figure of 9 comes from] 3. This small number of quanta, in comparison to the number of rods (500) involved, precludes any significant two quantum absorptions per rod [ed: oops], and means that in order to produce a visual effect, one quantum must be absorbed by each of 5 to 14 rods in the retina. 4. Because this number of individual events is so small, it may be derived from an independent statistical study of the relation between the intensity of a light flash and the frequency with which it is seen. Such experiments give values of 5 to 8 for the number of critical events involved at the threshold of vision. 1. http://www.cns.nyu.edu/~david/courses/perceptionGrad/Readings/HechtShlaerPirenne-JGeneralPhysiol1942.pdf http://www.cns.nyu.edu/~david/courses/perceptionGrad/Reading...