Should I guess on the SAT?

The current SAT has no guessing penalty, so you should always answer every question. Older SAT versions had a 0.25-point penalty.

When is guessing worth it with a penalty?

If you can eliminate even one choice, guessing becomes more favorable. With 4 choices and 1 eliminated, expected gain per guess rises significantly.

A penalty of 1/(choices - 1) makes random guessing have zero expected value. For 4 choices, that is 1/3 or about 0.333.

Calculate the expected score impact of guessing on a multiple-choice test with a wrong-answer penalty.

Number of Guesses

Choices per Question

Penalty per Wrong Answer

Expected Points from Guessing

0.63

Expected Correct Guesses2.5

Expected Wrong Guesses7.5

Expected Points from Guessing vs Number of Guesses

When a test penalizes wrong answers, random guessing has an expected value.

Expected Gain = Guesses x (P(correct) x 1 - P(wrong) x Penalty)

Where P(correct) = 1 / Number of Choices

If the penalty equals 1/(choices-1), guessing has zero expected value.

A student randomly guesses on 10 questions with 4 choices each and a 0.25 penalty.

Calculate raw test score with penalties.

Calculate test accuracy.

Calculate questions needed right.