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twanvl comments on Multiple Choice - Less Wrong
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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.