Embedded Files
INTRODUCTION
A shiny Pokémon is a rare version of a Pokémon that has an alternate color palette. They were first introduced in the Pokémon Gold and Silver games that released in 1999. The probability of encountering one of these alternately colored Pokémon was incredibly slim (1/8192). This rarity made shiny Pokémon fiercely desired and sought after by devoted Pokémon fans. Players started to "shiny hunt" in order to find a shiny version of a specific Pokémon they were interested in. This usually involves saving the progress of the game right before an encounter with a Pokémon, which then allows the player to repeatedly reset the game and re-roll the 1/8192 chance of the Pokémon being shiny.
A shiny hunt is a daunting task since the odds are thoroughly stacked against you. Anyone attempting a shiny hunt likely wants some idea of how many times they will have to reset their game in order to finally get that shiny Pokémon. Towards this end, we can simulate a shiny hunt in R to answer that question!
A normal Pokémon on the left and a shiny version on the right.
METHOD
Here we define a simple function with two parameters. The first parameter "trials" is the number of shiny hunts that we want to simulate. The second parameter "p" is the probability of getting a shiny Pokémon.
For each trial, the function executes a Bernoulli trial using the rbinom() function. Recall that a Bernoulli trial is an experiment with only two possible outcomes, either "success" or "failure". In our case, finding the shiny Pokemon is the successful outcome. The rbinom() function runs this experiment for us with the probability that we specify. Then the function repeats this process until we get a successful outcome (finding the shiny Pokémon). Finally, the function stores how many attempts it took into a vector.
Here is an app I built based on the code above that lets us simulate an individual shiny hunt. Feel free to play around with the probability to see how it affects the number of resets it takes to get a shiny (Just don't set the probability to zero, or the simulation will never finish). Of course, the amount of resets it takes to finish a single shiny hunt does not give us a good idea of how many it will take on average. To get a good answer we need to simulate thousands of hunts and analyze the data.
RESULTS
Here are the results of simulating 100,000 shiny hunts and then visualizing with a histogram and box plot.
The median, or 50th percentile, of our simulation results was 5666 resets. This means that half of the 100,000 simulated shiny hunts were successful before 5666 resets. 95% of the shiny hunts were successful before 24,538 resets. The unluckiest shiny hunt across all simulations ended after 102,917 resets (ouch). This was the maximum value of our dataset. The minimum value of our dataset, AKA the luckiest shiny hunt across all simulations, was 1 reset.
Perhaps unintuitively, a shiny hunt that is successful on the very first reset is actually the most likely outcome. This is because the chance of getting a shiny Pokémon on the first try is 1/8192, where as the chance of getting it on the second try is (8191/8192)*(1/8192). Therefore if we could simulate a very large number of successful shiny hunts, the mode of the data would actually be 1.
The mean number of resets it took to get a Shiny Pokémon was 8137 resets. This value is a fair bit higher than the median. This is typical of a positively skewed data distribution like we have here. The data is positively skewed because we can have extreme values on the high end (i.e. outlier shiny hunts like the one that took over 100,000 resets) but we can't have any extreme values in the other direction since the minimum is hard capped at 1 reset, which is also the most likely value (mode).
CONCLUSION
If you're considering going on the hunt for a rare shiny Pokémon, just know that the odds are against you. If you commit to resetting your game 5666 times then there is only about a 50% chance you will have gotten the shiny Pokémon by then. And if you want to increase your chances to 95%, then you will have to reset your game upwards of 25,000 times!
Page updated
Google Sites
Report abuse