The Arithmetic of Negative Marking and When to Guess
The Arithmetic of Negative Marking and When to Guess
Whether or not to guess is not a question of opinion but of arithmetic. In this system of five options with an option E, the answer comes out clearly, and it is different from what most candidates assume. This topic sets out that arithmetic in full.
The Expected Value of a Guess
Suppose n options remain on a question and you choose one of them. The chance of being right is one in n and the chance of being wrong is n minus one over n.
Expected marks = (1 / n) × 1 − ((n − 1) / n) × (1/3)
| Options left | Expected marks | Decision |
|---|---|---|
| 4 (nothing ruled out) | 0.00 | same as E |
| 3 (one ruled out) | +0.11 | guess |
| 2 (two ruled out) | +0.33 | certainly guess |
| blank bubble | −0.33 | never |
The first row is the surprising one. Marking a bubble blindly and marking option E have the same expected value of zero. So blind guessing brings no average gain at all; it only adds variation.
✗ Guessing always causes a loss | ✓ With four options a guess breaks even at zero; the moment one option is ruled out it becomes profitable
The Rule That Follows
- If even one option can be ruled out — guess, the arithmetic is in your favour.
- If nothing can be ruled out — mark E, since the return is equal but the risk is lower.
- Never leave a bubble blank — it is the one case with a certain loss.
The third rule is the strictest and the most easily broken. A blank bubble is the only situation with a negative expected value; every other choice is zero or better.
Practical Ways to Rule Out an Option
- In grammar, an option that does not agree in gender or number is wrong.
- In an idiom question, the option giving the literal meaning is always wrong.
- In an unseen passage, an option saying something outside the passage is wrong.
- In an antonym question, an option of the wrong word class is wrong.
Each of these four checks removes one option, and by the table above, the moment one option goes, guessing becomes profitable. So treat them as habits to build rather than rules to memorise.
सार एक पंक्ति में: सोचकर लगाया गया अनुमान लाभ देता है, बिना सोचे लगाया तुक्का बराबरी पर रहता है, और खाली गोला निश्चित नुकसान देता है।
TRE pointer: This table is the most useful thing in the paper and, because of the new five-option system, it will not be found in older market material — under four options a guess always lost. Now a single elimination makes guessing profitable, and that one change reverses the whole strategy.
60-Second Recap
- The value of a guess depends on how many options remain.
- With four options a guess is worth zero, the same as option E.
- Ruling out one option makes the expected value positive.
- Ruling out two makes guessing clearly profitable.
- A blank bubble is the only case with a certain loss.
- Literal-meaning and outside-the-passage options are the easiest to eliminate.
Frequently Asked Questions
Should you guess when there is negative marking?
If you can rule out even one option with certainty, yes, because the expected value then turns positive. If nothing can be eliminated, a guess and option E both come to zero, so marking E is the safer of the two.
Why is a four-option guess worth zero?
Because one chance in four of being right earns a mark, which comes to 0.25, and three chances of being wrong cost a third each, which also comes to 0.25. The two cancel, so the net gain is zero.
What is the harm in guessing blindly, then?
There is no average gain, but the variation increases. In a qualifying paper the aim is only to cross thirty percent, so there is no reason to take avoidable risk. Where nothing can be eliminated, marking E and moving on is the better course.
What are the quickest ways to eliminate an option?
In grammar, the option that does not agree in gender or number; in an idiom question, the one giving the literal meaning; in an unseen passage, the one saying something not in the passage; and in an antonym question, the one of the wrong word class. Each check removes one option.