Yep, the gambler's fallacy is quite well known. The "heuristics and biases" field of psychology thinks it's caused by the representativeness heuristic.
Minor quibble: if a coin fell heads 29 times in a row, my credence for it falling heads a 30th time is higher than 0.5 because I now have reason to believe the coin is biased. How much higher depends on how many biased coins there are, as yummyfajitas said.
I'll quibble with your link as well. Did Yvain actually test to see whether his guessing increased his score over the semester? Or did he just 'prove' it?
Like the presumption of a fair coin in this page, his presumption is that the questions are fair. If they were trick questions, such that the seemingly improbable answer is correct more often than not, guessing based on partial knowledge may not be a benefit.
I think he's right, but I'd trust his results more than his abstract reasoning.
Yes, guessing based on partial knowledge might make you worse off. But as Yvain's footnote 1 says, replacing 30 "I don't know" answers with 30 purely random coin-flip guesses has a 98% chance of improving your score. (I'd like to go on record saying emphatically that this statement doesn't need to be "tested". Recalculated, at most.) So if you have a coin in your pocket, it's pretty hard to rationalize answering "I don't know" to many questions instead of flipping the coin.
I appreciate your response and voted it up. But I disagree that there is no benefit to actually testing his hypothesis. The mathematics don't need to be 'tested', but perhaps the priors do? For example, how certain are you of the assumption that the questions that we need to flip the coin for are evenly distributed between true and false?
It seems plausible that a test might have a bias whereby the harder questions are predominately one answer or the other. How large would this effect have to be to overwhelm the 2% probability? Would you trust your grade on the presumption that this effect can be ignored? What about your life?
For the record, I agree with Yvain's advice. I did just fine on the SAT's, partly because I followed the mathematically correct advice that one should guess if one can eliminate at least one of the 4 choices. But I wouldn't proclaim that this strategy needs no testing just because the mathematics are correct.
On some tests you get a zero score for not answering and a negative score for answering wrong. Balanced in such a way that uniform randomness gives you the same expected score as not answering.
http://en.wikipedia.org/wiki/Gamblers_fallacy
http://en.wikipedia.org/wiki/Representativeness_heuristic
Minor quibble: if a coin fell heads 29 times in a row, my credence for it falling heads a 30th time is higher than 0.5 because I now have reason to believe the coin is biased. How much higher depends on how many biased coins there are, as yummyfajitas said.
Here's another epic example of people failing to use basic probability theory: http://lesswrong.com/lw/13i/shut_up_and_guess/