Hello, Cut or Tap readers! I’m Jake Gearhart, and if you’ve read anything from me in the past— whether on Twitter, or in any articles I’ve written elsewhere— you’ll know that I love talking about a different side of Pokémon from what most people tend to spend time on. Sometimes that’s critiquing game-design, or poking holes in the game’s most complicated rulings, but the topic I’ll be writing on today involves statistics!
Before the reverberation of painful school memories pushes you away from continuing, rest assured that I’ll be explaining everything as simply as I can, though it does get a bit complicated. Even if you don’t like math, I encourage you to persevere, because the knowledge you’ll gain from this article should be well worth any minor headache. Today, I’ll be attempting to answer the titular foundational question that everyone’s asked themselves before:
How likely am I to win a tournament?
This is, unsurprisingly, quite a complex question to answer. To make things simple to start with, let’s imagine a single-elimination, Best-of-1 coinflip tournament with 512 players. It’s just as simple as it sounds— Each round, one player calls heads or tails, and the other flips a fair coin. The winner of the flip wins the round, and the other player is eliminated from the tournament. With 512 players, you need nine rounds of single-elimination to get down to 1 player, so in order for you to win the tournament, you’d need to win 9 coinflips in a row. So how do we calculate the probability of that happening?
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