What good is multiple choice?

open question:
what is the expected percentage of examinees to answer a multiple choice question correctly, accounting for random guessing?

thoughts:
if a question has five multiple choice answers, a student has 20% chance to blind guess the correct answer. If the number of examinees to answer the question right is significantly lower than 20%, does that suggest that the question is unfair, intentionally misleading, or incorrect?

for example question 87 on GRE Physics 9677 had 6%! of students answering correctly. They'd have done better not studying ANY physics and blindly picking ABCD or E! Why did this question make more students answer INCORRECTLY than one could reasonably expect for a multiple choice answer!?

I think it shows a certain intelligence that the majority of students put similar thoughts to avoid the correct answer. Like when Muhammad Ali purposefully chose wrong answers on his IQ test to get out of the army, and the testers concluded that to answer that many answers wrong, far more than one would expect from just random guessing, he must be aware of the right answer and purposefully avoiding it. Here of course, the physics students have no reason to avoid answering correctly for a low score, but I believe that they are onto the right idea, but getting tricked by the question.

But were the 6% who answered correctly truly more expert in their knowledge, or were they 'worse thinkers' for not arriving at the same conclusions as their peers!? Or did they simply get lucky with a guess?

What value does a test have when over half the questions are expected to be answered incorrectly by the average test taker, and the majority of questions have a correct answer rate no better than guessing, and some significantly worse!??

OH I forgot there is a 1/4 point penalty for guessing. So that means a hard problem will have fewer people answering. And the percent answering correctly is out of all test takers, including those that didn't answer the question at all. So maybe 6% answered the question and 6% got it right with 0% answering the problem incorrectly, not necessarily that 100% answered and 94% got the question wrong.

I pick (E) Not enough information provided to arrive at a conclusion.

---

But even then, a multiple choice test is not a valid reflection of real life problem solving. You get better at these tests by practicing shortcuts to eliminate wrong answers, then quickly selecting the better choice of two or three candidates.

Solving worthwhile problems isn't like picking the most attractive bachelor on a TV dating show. You don't just take what has already been done. You have to create an answer nobody has found before.