For instance, the ability to rule out one of four choices on a one-point question where a wrong answer costs a quarter point means that you should guess from the remaining three—the expected point value of this guess is positive. If you can rule out one of four choices and a wrong answer costs half a point, leave it blank.
If you can rule out one of four choices, you’ll get the right answer 1⁄3 of the time, and a wrong answer 2⁄3 of the time, for an expected value of 1(1/3) - (1/2)(2/3) = 0, so it doesn’t matter whether you guess or not.
It was stated that a wrong answer costs a quarter point, so the expected value is 1(1/3) - (1/4)(2/3) = 1⁄6. A cost of 1⁄4 point for a wrong answer is too low though, since in that case the expected value of guessing from all four choices is still 1⁄16. The cost should be 1⁄3 to make that expectation equal 0.
If you can firmly rule out one of the 4 options, it seems pretty unlikely that you are literally indifferent between the other three, so guessing is almost certainly positive expectation.
If you can rule out one of four choices, you’ll get the right answer 1⁄3 of the time, and a wrong answer 2⁄3 of the time, for an expected value of 1(1/3) - (1/2)(2/3) = 0, so it doesn’t matter whether you guess or not.
It was stated that a wrong answer costs a quarter point, so the expected value is 1(1/3) - (1/4)(2/3) = 1⁄6. A cost of 1⁄4 point for a wrong answer is too low though, since in that case the expected value of guessing from all four choices is still 1⁄16. The cost should be 1⁄3 to make that expectation equal 0.
Filling in the bubble costs time.
Inversely, filling in the bubble prevents you from getting one cell off for the following questions.
If you can firmly rule out one of the 4 options, it seems pretty unlikely that you are literally indifferent between the other three, so guessing is almost certainly positive expectation.