The short answer to the question of how probability and statistics impact your life is that they impact it whenever anything happens at all, but that is extremely boring. In fact, so many things are boring! That is why we turn to fun and games for entertainment. Alas, math follows you even into the colorful world of cubing and the fantastical realm of roleplaying games. Let us see how probability and statistics impact the focuses of two clubs at Dublin High School and how you can apply it to your — yes, your — life.
“[S]tatistically speaking, every single scrambled state can be reached within 20 moves,” says Rubik’s Cube Club president Adhi Jeyappragash, but “[s]ome solutions naturally end up shorter than others due to easier algorithms and […] steps already done by sheer luck.” For beginner cubers who just want to solve the puzzle, this may not matter much, but for more advanced cubers trying to get fast times or beat an adversary, probability is everything. The different patterns on a Rubik’s cube vary in difficulty, and the same person might take half or double the time to solve a cube depending on the pattern they are given.
More impactful real-life situations revolve around probabilities as well. Someone solving a Rubik’s cube might get a harder pattern than their competitor and lose the lunchtime competition, and that might not matter to you, but because of those same principles you might get a harder test than your friend and get a lower score. There is nothing you can do to change these probabilities or make them more favorable to you, but if you know that a test has different versions that may be slightly different in difficulty, you can prepare ahead of time and make sure that you are ready for the harder version, and if you end up getting the easier one, well, that just means you can get a higher score than you initially would have.
Chance has plenty of impact on Rubik’s cubes, but a game much more well-known for probability is the beloved tabletop RPG Dungeons and Dragons. One of the core mechanics in this game is that the players must roll “checks” with dice – one of the most recognizable ones being a D20, a die with twenty faces – which determine the outcome of actions they choose to take in-game. Players can also have “modifiers,” which usually represent skill and can add or subtract points to the number they roll; a player with a +2 modifier who rolls a ten for a certain check will have their roll seen as a twelve. This system “tends to be very similar to the real world in how it interacts with luck,” according to Cameron Genest, the president of the Dungeons and Dragons Club on campus.
The checks in Dungeons and Dragons were designed to be similar to chance in real life, so it would be pointless to compare the two already-similar systems, but the way players try to mitigate this element of chance is something we can learn from for real-life application. The same way players seek modifier bonuses to reduce the impacts of low rolls, we can improve our own skills to reduce the chance of failure.
Ultimately, while we cannot control the roll of the die or the chance of getting a harder test, we are not all powerless. The true lesson from these formations of probability is that our focus should be on what we can control. Just as the fastest rubik cube solvers practice algorithms to solve any problem and a great student takes their learning above what is taught in the classroom, we can invest time sharpening our skills and preparing. By building our knowledge and resilience, we prepare ourselves to succeed across a range of possible outcomes, turning the unpredictable nature of probability from a threat to a small obstacle. Chance may seem to control us, but it is our preparation that actually determines the outcome.
Special thanks to Adhi Jeyappragash from the Rubix’s Cube Club and Cameron Genest from the Dungeons and Dragons Club for agreeing to give quotes for this article! We could not have done this without you.