How to use the guessing expected value calculator
With the clock running out, a few blank answer bubbles force a decision. On a test with no penalty for wrong answers the math is easy, but a penalty rule, or a question where you have already ruled out some choices, is hard to work out in your head. Enter how many questions you plan to guess on, the number of choices, the choices you have ruled out, the points at stake and the penalty, and this page reports the expected value, the spread and the chance of at least one hit.
The math follows straight from the definition of probability. With r choices left, picking at random hits with probability 1 ÷ r, and the expected value per question is hit chance × points - miss chance × penalty. The total expected value multiplies that by the number of questions. Treating the questions as independent, the variance per question is added up across the questions and square-rooted for the standard deviation, while the chance of at least one hit is one minus the chance of missing every one.
Two limits are worth keeping in mind. The math assumes every remaining choice is equally likely to be correct, which stops being true when a test writes tempting distractors or falls into patterns. And this page reports the expected value and the spread only; it does not tell you whether guessing is worth it. Penalty rules differ from test to test, so enter the figure printed in your own test instructions, and note that questions carrying partial credit do not fit this model.
Frequently Asked Questions
The hit chance is one divided by the number of choices left. On a five-choice question with two choices ruled out you are picking one of three, so the chance is one third, about 33.33%.
It means that over endless repeats under the same rules the points gained and the points lost average out. This page reports the expected value and the spread only; it does not judge whether guessing is worth it.
The expected value is only an average, and any single sitting can land well away from it. The standard deviation puts that spread in points, so you can see how far the real total may drift even when the average stays the same.