I'm bad at probability and statistics, please understand. Suppose we are writing a multiple choice test, with say 100 questions. Now each question have 4 options to choose from, out of which only 1 is correct. Now we guess on each question, a complete guess. I mean we don't even read the question or look at any of its answers. What is the best way to go, mark the same option for each question (all A's for example) or randomly pick each option?
If the distribution of answers (A, B, C & D) is uniform (which is generally the case in tests), then both options (marking the same, or randomly) will give the same result :
for each question, you have a probabilty of 0.25 to find the correct answer. Thus you will have 25 overall points in average to the test.