The odds are against you:
If all four million 17-year-olds all took the SAT, and they all guessed randomly, it’s a statistical certainty that there would be no perfect scores on any of the three sections.
Update from a former Kaplan SAT prep instructor:
XKCD was making the point that it was highly, highly statistically improbable to get a perfect score by guessing. That doesn't mean you shouldn't guess. The SAT is scored in a way to make guessing neutral. Every correct answer is 1 point, every incorrect answer is minus 1/4 point. Since you have 1/5 chance of guessing correctly, guessing five times breaks even: 1 – 1/4 – 1/4 – 1/4 – 1/4 = 0. So there's no harm in guessing, and if you can eliminate one or more of the five choices, the odds bend in your favor.
Another reader expands on that point:
It's actually not quite true to say you shouldn't guess on the SAT. It's true that students are advised not to take a totally wild guess, but normally if you can eliminate one or more of the available answers, then guessing is +EV.
The reason for this is that unlike many other standardized tests, the SAT penalizes incorrect responses. Most of the multiple choice questions have 5 potential responses. For such questions, a correct answer is worth one point, and an incorrect answer deducts 0.25 points. So the Expected Value of randomly selecting from five responses is: 1/5*(1) + 4/5*(-0.25) = 0. While the neutral EV here still represents better odds than you get in any casino game, students are normally advised to be risk-averse and take the guaranteed zero (by leaving the answer blank) rather than risk the 80% chance of losing a quarter point.
However, if you can eliminate one of the 5 answers as being definitively incorrect, the equation becomes EV positive: 1/4*(1) + 3/4*(-0.25) = +0.0625. Since in the long run you're expected to improve your score by guessing in these circumstances, students are normally advised to embrace the variance and take the guess. Obviously, your odds continue to improve as you narrow the possible responses down further.
Even for someone not taking the SAT, it's a worthwhile concept to fully grasp, because it gets at the sort of quantitative intuition of probability and risk that a lot of people lack, and that poker players and bank traders possess in excess.
(As an aside, it's also worth pointing out that the argument posed by the article you've sited, about the fact that everyone guessing would result in no perfect scores, is totally meaningless. Say I offered you a bet where I would pay you $10 every time a coin lands on heads, and you pay me $5 every time it comes up tails. The argument in this "What If" article would appear to suggest that you shouldn't take that bet because you pretty much can never expect to win a few hundred times in a row.)
The Dish 