Welcome to the first installment of Video Game Probability! You can read the introduction and motivation for this series here along with a list of all posts. This post contains mild spoilers for probability distributions in Stardew Valley. Without further ado, I’m going to jump in!
Stardew Valley is a farming/lifestyle RPG where you grow crops, fish, find love, fight monsters, go on quests, and so much more. I have so much to say about this game and I’m trying so hard to hold in my enthusiasm – I hope you appreciate the sacrifices I make in the name of succinct writing. (But no really I love this game, it’s on Steam, it’s on Switch, it’s even on iOS and Android, so you have no excuse not to play it, please give it a try, it has something for everyone.)
One of your major tasks in Stardew Valley is to fix the Community Center. If you have no soul, you can go corporate and pay a ton of money, but most people go for the Bundle route because they’re not dead inside. A bundle is a set of items (crops, foraged goods, etc) that you donate to the spirits of the forest in exchange for rewards. Once you complete every bundle, you fix the Community Center!
Today, we’re going to talk about the Quality Crops bundle: you must gather 5 golden parsnips, melons, pumpkins, and corn to complete the bundle. The pesky thing about these crops is that parsnips are only grown in spring, melons are only grown in summer, pumpkins are only grown in fall, and corn can be grown in summer or fall. So if you reach the end of spring or summer and didn’t manage to collect the 5 crops for that season, you have to wait a whole year for another chance!
When you harvest a crop, it has a chance of being regular, silver, or gold quality. The game calculates your chances based on your farming level and what fertilizer, if any, was used. (Note: While “luck” is a mechanic in the game that I’d love to explore further, I don’t think your daily luck affects your harvests – correct me if I’m wrong!)
Here’s our big question for this post: How many crops should we plant with what fertilizer in order to guarantee a certain probability of getting at least 5 golden crops?