I did a Networking exam yesterday. It had a True/False section with 60 T/F questions, with a twist: wrong answers take away half the points of a correct answer.

This is a very common practice in my country, not sure if it's done anywhere else.

As an example, let's say you have 2 T/F questions, each worth 1 point. If you:
- answer both questions right you'll have 2 pts (+1 + 1)
- answer 1 question correctly and leave the other blank you'll have 1 pt (1 + 0)
- answer both questions and get 1 right and 1 wrong, you'll have 0.5 pts (+ 1 - 0.5)
- leave both questions blank you'll have (0 pts)
- answer both questions and get both wrong you'll have -1 pts (-0.5 + (-0.5)). Some universities allow negative points, some just clamp it at 0 pts.

In the beginning of the exam sheet, there was a warning: "If you are unsure of the correct answer LEAVE IT BLANK, as wrong answers take away half of a right answer's points".
At first I was following this advice and only answering questions when I was sure the answer was correct.

But then I gave it some thought: in the long run, doesn't it still payoff to guess randomly, instead of not answering?
If I do, I have a 50% chance of + 1 pt, and a 50% chance of -0.5 pts. This means the average expected gain over a large enough number of questions is +0.5 pts.
If I don't answer the question at all, I'll get +0 pts in the long run.

So it is better to answer randomly, than to leave them blank. Is my reasoning correct?

When the exam ended, I exposed this reasoning to the supervising professor. He dismissed it as unimportant :c. However, I think this is important because, if I am correct, the exam sheet is misinforming the students and advising them to take a suboptimal strategy.
The expected value of random guessing is 0.5\*1 + 0.5\*(-0.5) = 0.25. The expected value of leaving the question blank is 0. So in the long run, you should guess.

As an example: Imaging that you don't know 30 questions and you decide to guess randomly. On average, you'd gain +7.5 points. The probability that your total is negative (i.e. you lose points) is very low, just a bit more than 2%.
If it’s a multiple choice style there would be 1 correct and 3 incorrect options for each question, reducing the probability to be correct when guessing randomly.
Guess for sure. Also you could use the percentage of questions with “true” as the answer in the questions you know to inform how you should guess. For example, if you were confident on 45 of the 60 and 30 of the 45 had the answer “true”, it might be reasonable to suspect the professor favors “true” answered questions, so I’d fill the remaining 15 with “true” in that case.
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