We are 7 billion human beings on the Earth. But how many mice are there? How would you estimate such a number?
Mark-recapture is the most frequently used method for small mammals. It's best when combined with uncertainty estimates and population dynamics models (e.g. projection matrix).
The fluctuations of small rodent populations have long fascinated scientists, and various models have been developed. Logistic regression models can be used to estimate likelihood of mice outbreak based on local rainfall data.
Rat population in New York city, for example, was thought to be 1 rat to 15 humans in the mid 40s, 1:36 in the late 40s (Davis ratio), 12:1 in 2002.
The population of mice is often estimated per hectare - 0.25-60/ha in buildings and 1-200 in the field, over 1000/ha during outbreaks. 10^9-10^10 hectares of habitable land means that populations of mice and men are, probably, of the same order of magnitude.