The equal-odds rule is simply wrong. A few examples: Andrew Wiles, Charles Darwin, John Forbes Nash. These people produced a small amount of work, but they shook the earth. Some people are geniuses, and some are not. It appears rather that some geniuses are prolific while others are not. Examples of some prolific ones: Einstein, Serge Lang.
Edit: A commenter pointed out that Charles Darwin goes in the second list.
I think it is difficult to actually assess the veracity of the equal-odds hypothesis. You don't know how much Darwin or Einstein threw away, or how much of their stuff was irrelevant and forgotten.
I should add however, that the equal-odds thing is the way that i learned to be a better photographer. Shoot as much as you can, figure out what you did to take the good ones (I guess it's like the monte carlo method for artistic improvement).
I agree - there is a vagueness issue with the rule, and it is not obviously falsifiable. But as stated, the rule does not discuss unpublished works - it is a statement about published work, and the statement is that each scientist is throwing the dice when they publish, and there is nothing the scientist can do to increase his chances.
Not sure I disagree overall, but Darwin isn't a very good example. He produced quite a lot of writing throughout a long career, and his most famous book, On the Origin of Species, came somewhat late (he was 50, and it was something like his tenth or eleventh published book).
There will always be outliers in any population. Assuming you are a genius so you only need write once or twice to be universally read is a good way to never be read. Assuming you are subject to the equal-odds rule means you will publish more and have a much higher chance of being read.
Edit: A commenter pointed out that Charles Darwin goes in the second list.