Category: SAT Math


In this post, I explain why blind guessing on the SAT is a bad idea. Now we will talk about why guessing is a bad idea even if you have eliminated one answer. Technically, you should have a slight mathematical advantage by then – and yet, almost every student who applies this finds themselves still losing points. There are a few key reasons why this happens.

1. The calculations are based on ignoring the rounding effect. They treat getting 1 right and 3 wrong as a quarter point gain. In reality, an outcome of 1 right and 3 wrong is NOT a gain of a quarter point because your score will be rounded down. This is another situation where your most likely outcome (at about 42%) is no harm and your next most likely outcome (at about 31%) is getting all 4 wrong and harming your score.

2. If you can only eliminate one, that probably means the question is very hard for you. Which means the possibility that you will eliminate the correct answer just went up (since obviously that’s more likely to occur on a difficult question). Once that has happened, you have 0% chance of getting the question right, 100% guarantee of a lost quarter point, and any additional time spent on that question is wasted.

3. Even if you correctly eliminate one wrong answer, you don’t have a true 1 in 4 chance of guessing the right answer. To understand this part, consider the street game 3 Card Monty (we will modify it slightly to fit our scenario of guessing with 4 answers left). A dealer shows you four cards, one of which is a Joker and 3 of which are pip cards (numbered cards). They offer to bet with you. If you can select the Joker card after they place all 4 face down and shuffle them briefly, you will win a fantastic payoff worth far more than your wager! You rub your hands together greedily, knowing the payoff is worth more than you are betting, and confident that with a 1 in 4 chance you can win enough to make this game worthwhile. The dealer shuffles, you watch the cards and pick, confident you saw where that Joker landed. WHAT?!? You stare in amazement; the card you picked is NOT the Joker. You demand to see the cards turned over, sure that the dealer must have slipped the Joker off the table or into a sleeve. But no, it’s right there on the table, just not where you thought it was. Hmm, well that payoff is still good, good enough to risk another bet and you are going to pay *real* close attention this time. The dealer shuffles… and sure enough, you lose again. You keep guessing wrong, all the while losing confidence, time and money, while that smug bastard laughs at you.
 

Now let’s look at why you didn’t win 1 in 4 times, or anything close to it. The dealer doesn’t need to cheat – it is his extensive experience at shuffling deceptively, distracting you and knowing how people react to his game that gives him a strong advantage. He makes a living doing this – you are just wandering by. You are, no matter how smart and no matter how well trained, a teenager being sent into a battle of wits in very specific areas with people who have advanced degrees and years of experience in the fine art of making you guess wrong. If you can only eliminate one answer, the chances that one of those trap answers will suck you in rises to a point where your real odds are no longer 1 in 4.

Finally, let’s consider the big picture. Even if you ignore the rounding effect, and feel 100% sure you won’t eliminate the right answer and will guess without being even slightly affected by any of the 3 remaining trap answers, it still won’t work out overall. Think about it realistically – will you really say ‘ok, I got rid of one, I’ll guess now and move on.‘? Of course not. You know eliminating more would improve your odds further, so you will sit there staring at the remaining ones hoping to find a reason to get rid of more. Meanwhile the clock is ticking, other questions never get tried because time ran out and the Joker is just sitting there, grinning at you evilly.

Don’t let him get away with it. Be strong enough and smart enough to refuse to play his game until the odds really are in your favour. Walk away from those harder ones and go knock out some easier questions instead!


     Deciding whether or not to guess when you have 5 answers left is a perfect example of one of the key principles of mastering SAT math – step back. Take a moment to process the problem and be sure your set-up is correct, because if it isn’t, everything else will go wrong.

     There are problems that look hard, but if you step back and process the concepts, you discover they are actually quite easy. And, of course, the other trickster – the problem that looks easier than it actually is. One example of this is the classic problem about traveling 30 mph going to a location and 50 mph on your way home – you are asked for your average speed and there’s a temptation to just say to yourself “Hey, the average of 30 and 50 is 40. It’s 40, I’m done!” But if you step back from the problem and think, you will realise that it must have taken longer to get there (since you were going more slowly) than it took to get home, and that the extra traveling time must have dragged your average speed down. Dangitall, there are going to be extra steps.

     So, let’s now look at guessing at 5. You might run across people who advocate this and their logic is as follows:  Since you gain 1 point for every right answer and lose 1/4 for each wrong answer, you will get 1 right and 4 wrong out of every 5 questions. 1 – 4(1/4) = 0 so they declare that there is in fact ‘no penalty for guessing’ and proceed to try to convince you this is a safe plan. And admittedly, it looks good at first and triggers an eye-widening omg effect as the reader thinks they have stumbled upon some revelation.

     Now there are a lot of potential problems with this approach, but we won’t be going into all of them right now. On its own terms, a crucial mistake has already been made. So what went wrong? The proponents did not step back. Stop and think – does it make any sense that you can be 100% sure of getting exactly 1 right and 4 wrong? Of course not. You might get 0, 2, 3, 4, or 5 right. To properly assess the probability, we need to put it in context. Like a weighted average, we need to factor in the likelihood of every possible outcome for those 5 questions.

     We now redo the math, correctly, and discover that getting 1 right and 4 wrong, far from being a guaranteed starting point, actually only occurs less than half of the time (about 41%). The next most likely scenario (at about 33%)? You guessed it – getting all 5 wrong. 😯 Your odds of getting all 5 wrong are much greater than your odds of getting 2, 3, 4 or 5 combined.