Calculate your real score in an exam with negative marking, see your accuracy, and find out whether guessing helps or hurts.
“Never guess when there’s negative marking” is common advice, and often wrong. Whether a guess helps depends on the penalty, the number of options and how many you can rule out. A little probability gives you a clear rule.
Expected value of a guess
If a question has k options and you pick one at random from the ones still in play:
EV = P(correct) × marks − P(wrong) × penalty
A positive EV means guessing gains marks on average over many questions; a negative EV means it costs marks.
Blind guessing (no options eliminated)
With 4 options and +1 for correct, P(correct) = ¼ and P(wrong) = ¾:
| Penalty per wrong | EV per blind guess | Verdict |
|---|---|---|
| 0 | +0.250 | Always guess |
| −0.25 (¼) | +0.0625 | Slightly positive |
| −0.33 (⅓) | 0.000 | Neutral |
| −0.50 (½) | −0.125 | Don’t guess blindly |
| −1.00 | −0.500 | Never guess blindly |
For the +4 / −1 scheme (4 options): EV = 4 × ¼ − 1 × ¾ = +0.25 marks per blind guess, which is mildly positive.
Eliminate one option and everything changes
Rule out just one wrong option and you’re choosing from 3, so P(correct) = ⅓:
| Penalty | EV (1 eliminated) | EV (2 eliminated, 50/50) |
|---|---|---|
| −0.25 | +0.167 | +0.375 |
| −0.33 | +0.111 | +0.333 |
| −0.50 | 0.000 | +0.250 |
| −1.00 | −0.333 | 0.000 |
For a typical ¼ or ⅓ scheme, once you’ve eliminated even one option, guessing clearly pays. Down to two options, it pays under almost every common scheme.
A simple decision rule
Guessing pays on average when:
Remaining options − 1 < marks per correct ÷ penalty per wrong
| Scheme | Ratio (marks ÷ penalty) | Guess when remaining options are… |
|---|---|---|
| +1 / −0.25 | 4 | 4 or fewer (always, with 4-option MCQs) |
| +1 / −0.33 | 3 | 3 or fewer (eliminate at least 1) |
| +1 / −0.5 | 2 | 2 or fewer (down to 50/50) |
| +4 / −1 | 4 | 4 or fewer |
| +1 / −1 | 1 | Never, unless certain |
Expected value isn’t everything
EV is an average. On any single question, a guess either gains or loses. Consider:
- Variance. Many guesses make your score less predictable. If you only need to clear a cutoff comfortably, lowering risk can be sensible.
- Tie-breakers. Some exams rank tied candidates by fewer wrong answers or higher accuracy.
- Partial knowledge. Your “guesses” are rarely random. If you lean toward an option for a reason, your real odds are better than 1/k.
- Time. A guess takes seconds; agonising over it costs time for questions you can answer.
Check your own pattern
After a mock test, use the negative marks calculator to compare your score with and without negative marking, and look at your accuracy. If you lose more than about 10% of your gained marks to penalties, review which questions you guessed and whether you’d really eliminated anything.
For the mechanics of scoring, see How Negative Marking Works in MCQ Exams (With Examples). For broader test tactics, read MCQ Exam Strategy: How to Maximise Your Score With Negative Marking.
Calculate your real score in an exam with negative marking, see your accuracy, and find out whether guessing helps or hurts.