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DiamondIceNS t1_j6oc7ja wrote

As others have stated, if the exam has its answers distributed truly randomly (or at least sufficiently randomly, i.e. by a computer), and if all of the answers had their choice selection decided independently, then your guesses will not matter at all. You gain no statistical advantage by any strategy. You are simply rolling an X-sided die Y number of times, where X is how many choices each question has and Y is how many questions the exam has.

The adage that you should select the same letter multiple times in a row to get an edge stems from two things, one of which is completely unrelated (and may not apply) and the other only holds if the assumptions we made aren't true.

The first is about speed. If you mark every question with something, you are statistically expected to get at least a score of 1/X on all those questions you marked. So if you anticipate the possibility that you might not even finish your exam, if you have them all pre-marked (switching answers to the correct ones as you read your way through the exam for real), then you might get some extra scoring for your guesses on questions you may have otherwise marked blank. This only works, of course, if the exam you are taking doesn't penalize incorrect answers. An exam that marks non-answers and wrong answers the same benefits from guesses; an exam that subtracts points for wrong answers and does nothing for non-answers punishes guesses.

The second is that there is some evidence that in multiple-choice exams with answer keys arranged by humans one letter is statistically more likely to be the answer for any given question. In the common four-choice arrangement with A, B, C, and D, that letter tends to be C. So, provided your exam was written by a human, and the exam doesn't penalize guessing, answering all questions with C has a statistical advantage over random guessing.

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Stellar_Panda OP t1_j6oh8mo wrote

Words are getting a bit too big for five year old. Lol Thank you for your response. But still I ask: Is there no marginable percentage increase if I do, say B and C for my answers and go through and randomly select a few B's along side majority C's? Given you have reasonable expectation that the correct answers won't be a straight line of ALL C's. Would this not give any slight increase in score? Given answers are distributed randomly.

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DiamondIceNS t1_j6oy6v3 wrote

Let me ask a counter question:

You are playing a game where someone rolls a 6-sided die over and over, and each time you have to guess which number it lands on before it is rolled. If you guess correctly, you win.

You happen to know that the die is loaded. It's not a 1/6 chance for each number to show up. The side numbered "4" is slightly more likely to occur than all of the others.

Knowing that, why would you ever guess anything other than "4"? You're not going to win every time, but it's always your best shot.

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Stellar_Panda OP t1_j6pe0pe wrote

Okay, why is selecting a straight line of 'C's better than filling in with no rhyme or reason (like the test probably would have looked like if you actually took it?) I think this is what my question boils down to.

If everything is 1/4 why would always choosing the same answer increase your chances? (Ignoring the whole 'C' is actually a better guess findings.) It doesn't right?-

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DiamondIceNS t1_j6pf6rj wrote

If the test is written by a person, C is most likely. Because the answers are (probably) not 1/4 each.

If the test was shuffled by a machine, and the answers are perfect 1/4 chance, then no strategy is better than any other. Picking straight C is just as effective as picking C most of the time and picking B sometimes, and just as effective as picking with no pattern at all.

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Stellar_Panda OP t1_j6pfl2l wrote

If machine wouldn't having a pattern hurt you? If random, try to be random. Would this not offer some kind of marginal benefit? Because very low probability of answer always being C, etc? I guess not..?

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