Should you guess when there is negative marking?

“Never guess.” “Always guess.” “Guess if you can cut it to two.” Each of these is right for some exam and wrong for another, because the answer depends on two numbers printed in the exam's own notice: what a right answer earns and what a wrong one costs. Put those into one line of probability and the question answers itself.

What do the marking rules say?

Each exam states its rule in its notice or bulletin. These are the rules for the papers sitting in the next few months, from the latest official documents:

For JEE Main, the amounts in the table are from the JEE Main 2024 bulletin: four marks for a right answer, minus one for a wrong one. For 2027, the National Testing Agency's notice of 24 October 2026 confirms “negative marking for incorrect answers in both Section A and Section B”; check the amounts in the 2027 bulletin's marking scheme when you download it. UPSC and ESE also count a question with more than one answer marked as wrong.

What is a guess worth on average?

On average, a guess is worth its expected value: what it would earn per question if you made the same kind of guess many times. Call the number of options \( n \), the marks for a right answer \( a \), and the marks lost for a wrong one \( p \). A blind guess is right one time in \( n \), so

$$ E = \frac{1}{n}\,a \;-\; \frac{n-1}{n}\,p $$

In words: the chance of being right times what a right answer earns, minus the chance of being wrong times what a wrong answer costs. \( E \) is what one guess adds to your score on average.

For a JEE Main question, with four options, \( a = 4 \) and \( p = 1 \):

$$ E = \frac{1}{4}\times 4 \;-\; \frac{3}{4}\times 1 = 1 - 0.75 = +0.25 $$

In words: a blind guess earns a quarter of a mark on average. Twenty of them earn about five marks.

For a 2-mark UPSC question, \( a = 2 \) and \( p \) is a third of that:

$$ E = \frac{1}{4}\times 2 \;-\; \frac{3}{4}\times \frac{2}{3} = 0.5 - 0.5 = 0 $$

In words: on average a blind guess earns nothing. What it wins one time in four, it loses over the other three.

That zero is not an accident. A blind guess is worth exactly nothing when the penalty equals the marks divided by the number of wrong options:

$$ E = 0 \quad\text{when}\quad p = \frac{a}{n-1} $$

In words: with four options there are three wrong ones, so a penalty of a third of the marks cancels the gain exactly. JEE Main's penalty is a quarter of the marks (one out of four), less than a third, so a blind guess comes out ahead.

What happens when you rule out an option?

The guess turns positive under every rule here. With one option struck off, \( n = 3 \):

$$ E_{\text{JEE}} = \frac{1}{3}\times 4 - \frac{2}{3}\times 1 = +\frac{2}{3} \qquad E_{\text{UPSC}} = \frac{1}{3}\times 2 - \frac{2}{3}\times\frac{2}{3} = +\frac{2}{9} $$

In words: two-thirds of a mark per JEE guess, and two-ninths of a mark (about 0.22) per 2-mark UPSC guess. The UPSC guess has gone from worth nothing to worth something, because the right answer now turns up one time in three, not one in four.

One condition: the option you strike off has to be wrong. Rule out the right answer by mistake and every guess among the rest is wrong; you lose the full penalty.

What does the average hide?

The spread. An average of +0.25 a guess does not mean every guess, or every paper, comes out ahead. Take twenty blind guesses in JEE Main. If \( k \) of them are right, each right one earns 4 and each wrong one loses 1:

$$ \text{net marks} = 4k - (20 - k) = 5k - 20 $$

In words: you end below zero whenever three or fewer of the twenty are right.

The chance that exactly \( k \) of twenty blind guesses are right is

$$ P(k) = \binom{20}{k} \left(\tfrac14\right)^{k} \left(\tfrac34\right)^{20-k} $$

In words: the number of ways to choose which \( k \) guesses are right, times the chance of any one such pattern: right \( k \) times at \( \tfrac14 \) each, wrong the other \( 20-k \) times at \( \tfrac34 \) each.

Ruling out one option in each of those twenty questions changes both numbers at once: the average rises to about +13.3 marks and the chance of ending below zero falls to about 6%. Under the one-third rule the contrast is starker. Twenty blind 2-mark guesses average zero, but they cost marks 41.5% of the time, break even 20.2% of the time and gain 38.3% of the time. A blind guess under the one-third rule buys risk and nothing else.

What about questions with no penalty?

In GATE's multiple-select and numerical-answer questions a wrong answer costs nothing, so an answer can only add marks. The cost is time. The brochure gives no partial marks, so a multiple-select guess must pick exactly the right set to score, and a guessed number in a numerical question is almost never right. Worth entering if you have a worked estimate; not worth minutes taken from a question you can solve.

What should you do in the exam?

• JEE Main: a blind guess is worth +0.25 marks on average, and one option ruled out makes it +0.67. Guess where you can rule something out; keep blind guesses for the last minutes, when there is nothing left to solve.
• UPSC Prelims, ESE Prelims, GATE multiple choice: a blind guess is worth nothing on average and adds risk. Guess only when you can rule out at least one option with confidence.
• Never mark two answers on a UPSC or ESE paper: it counts as wrong.
• Qualifying papers: UPSC's GS Paper II only has to reach 33%. If you are sure you are clear of it, a guess adds risk and no rank. If you are short of it, guesses with an option ruled out are the marks left to find.