Funny thing is the weights they assigned didn't discourage random guessing at all; they merely made your expected gain from guessing equal with the expected gain from not answering (i.e. zero).
So even if you had the very slightest idea, you should absolutely guess. If you took the test multiple times, then probabilistically you'd be better off if you always guessed even when you had no clue: some of your scores would be higher and some would be lower than if you hadn't guessed, and usually only your highest score is considered. Most guides overemphasized the penalty.
That said, it can screw you of course too if you happen to be unlucky in your guessing. This is what Terry's scheme overcomes.
I remember in high school having no shortage of teachers who recommended not guessing if you didn't know, to avoid the wrong answer penalty. I tried to argue with them initially, then settled for simply trying to re-educate my friends. It's pretty astounding how few people understand probability.
Indeed, if a wrong guess has value -1, and a correct guess has value 1, then the expected value 2p - 1, which is indeed positive if p is greater than 0.5. Random guessing has p = 0.5, and so gives you a base-line expectation of zero. Thus guessing is not actually punished, as such, and guessing can still be used if you have p > 0.5 for any reason.
What this simple scheme eliminates is credit awarded for random guessing. If correct answers are given weight 1, and all else is zero, then if the student knows 0% of the material, he or she nevertheless falsely obtains about 50% credit.
With guessing punished by -1 weights, someone who knows nothing an expect a result clustered around zero.
As an aside: I’ve seen “defiantly” as an autocorrect error for “definitely” (via *definately) so much now that I almost always assume “defiantly” is an error.
In the case of an exam, students are under stress and pressure that will often lead them to underestimate themselves, especially knowing that if they're wrong that 100% probability will net them a -infinity score for the exam, even if they get everything else right.
This also means questions have to be very carefully worded. I recall a number of exam questions (over many years of school, not one class in particular) where the "wrong" answers were arguably right depending on how the sentence was parsed just based on poor use of punctuation or other ambiguous wording.
If one were to actually use this scheme for a class, I think it'd make sense to compute both the classical grade and the probabilistic grade and isolate students whose classical and probabilistic grades differed greatly (as in your example of someone who answers everything correctly, but with low confidence). The professor could then exercise manual judgment to assign the appropriate grade and also probably discuss the discrepancy with the student (i.e., they might find it interesting that they consistently underestimated their knowledge of the subject; on the other hand, a student who was overly confident but did poorly might find it interesting that they were consistently overestimating their knowledge).
Or even more to the point: it punishes those who are geniuses at the subject matter, but not so great at probability. Especially under stress, where the system could be seen as akin to gambling.
So even if you had the very slightest idea, you should absolutely guess. If you took the test multiple times, then probabilistically you'd be better off if you always guessed even when you had no clue: some of your scores would be higher and some would be lower than if you hadn't guessed, and usually only your highest score is considered. Most guides overemphasized the penalty.
That said, it can screw you of course too if you happen to be unlucky in your guessing. This is what Terry's scheme overcomes.