If you haven’t heard of HQ, the free live trivia game show where you compete for real money on your phone, stop reading this and download it now. Sure to be one of the biggest apps of the coming year, when playing it for the first time you may find yourself wondering how anyone knew the answer to the question you got eliminated on. With questions that specific, you might assume other people are just guessing. But if you don’t know the answers to any of the questions, what are the odds you’ll win completely by chance? Alternatively, how many people would you need in one room to try every combination of answers and win every time? Using some simple probability and math, we can answer these questions, and start to better understand the kind of luck that underlies this game of skill.
Each game of HQ is a series of twelve multiple choice questions with three possible answers for each question. A single wrong answer gets you eliminated, so each question needs to be correct independent of the others. You only have ten seconds to answer each question, effectively eliminating the possibility of having Google do the thinking for you. With the wide range of topics and idiosyncratic details (the so-called “nitty-gritty”), many rounds rapidly devolve into a guessing game. Keeping this in mind, how hard is it to win the game by guessing?
The questions in HQ are independent; getting a correct answer at random has no impact on the outcome of the next question. When dealing with independent events, statisticians multiply the probability of one event occurring by the probability of the other event occurring. For example, flipping a coin once gives you a 1/2 chance of the toss landing on heads. Flipping the coin a second time will produce the same probability of getting heads or tails. From this, we can say that the probability of getting heads twice is 1/4. Adding additional coin tosses decreases the probability at a correspondingly increasing rate.
We can use the same logic when discussing HQ. If given a question with options A, B, or C and you have no information to influence your decision, you have a 1/3 chance of getting the question correct if you pick a letter at random. If you were seriously unlucky and had to guess on every single question, your odds of winning with this strategy are a whopping 1 in 531,441.
1 in 531,441
Your odds get even worse on Sunday, when adding three more questions brings the odds to an utterly impossible 1 in 14,348,907. While these odds may make you not want to play, we know this isn’t a fair representation of the game. Most people have at least some inkling of the answer for many questions, and the first two questions are usually deliberately very easy. Assuming you know the first two questions and a handful of others (say, for example, six answers), your odds improve, but are still pretty long. The odds of guessing even six of HQ’s twelve questions are a disheartening 1 in 729.
But what if you want to take guessing out of the equation entirely? And knowledge, for that matter? How many friends do you need to work with to make sure you always win? When we discussed the odds of guessing the combination of correct answers yourself, we saw that there’s only one correct set of winning answers. Conversely, there are 531,440 possible incorrect combinations that you can hit upon. In order to be guaranteed a win, you would need one person to try every one of those 531,441 combinations in order to be certain you would hit the right one. Dividing your group of half a million friends into three groups, each told to try either A, B, or C, and re-dividing the remaining players after each question, you will eventually converge on a single winning combination. After the first question, you would be left with around 177,147 players, and so on until one winner remained. The excitement would be short-lived once you realized you and your half a million friends would have to split the prize into fragments of a cent.
Suffice it to say, your chances of winning HQ are slim if you don’t know the topic being discussed in the question. But that doesn’t make it any less exciting. If the odds haven’t discouraged you, click here for some general advice on how to win HQ.