Calculating The Chances for Catching Perfect IV Pokemon in Pokemon GO using Brute Force Simulations of Catching and Purification of Shadow Pokemonn

simulations.md

nruns <- 1000000 # one million runs

probability of getting a perfect wild pokemon without weather boosting

minIV <- 0
maxIV <- 15

perfects <- 0
for(i in 1:nruns){
    pokemon <- sample(x = minIV:maxIV, size = 3, replace = TRUE)
    if(all(pokemon == c(15, 15, 15))){
        perfects <- perfects + 1
        }
    }
perfects/nruns

## [1] 0.00024

probability of getting a perfect wild pokemon with weather boosting

minIV <- 4
maxIV <- 15

perfects <- 0
for(i in 1:nruns){
    pokemon <- sample(x = minIV:maxIV, size = 3, replace = TRUE)
    if(all(pokemon == c(15, 15, 15))){
        perfects <- perfects + 1
        }
    }
perfects/nruns

## [1] 0.000535

probability of getting a perfect purified former-shadow pokemon (no weather boosting)

minIV <- 1
maxIV <- 15

purify <- function(x){
    min(x+2, 15)
    }

perfects <- 0
for(i in 1:nruns){
    shadowPokemon <- sample(x = minIV:maxIV, size = 3, replace = TRUE)
    pokemon <- purify(shadowPokemon)
    if(all(pokemon == c(15, 15, 15))){
        perfects <- perfects + 1
        }
    }
perfects/nruns

## [1] 0.007866

probability of getting a perfect purified former-shadow pokemon (Weather boosted)

minIV <- 4
maxIV <- 15

purify <- function(x){
    min(x+2, 15)
    }

perfects <- 0
for(i in 1:nruns){
    shadowPokemon <- sample(x = minIV:maxIV, size = 3, replace = TRUE)
    pokemon <- purify(shadowPokemon)
    if(all(pokemon == c(15, 15, 15))){
        perfects <- perfects + 1
        }
    }
perfects/nruns

## [1] 0.015625

probability of getting a perfect from a lucky trade

minIV <- 12
maxIV <- 15

perfects <- 0
for(i in 1:nruns){
    pokemon <- sample(x = minIV:maxIV, size = 3, replace = TRUE)
    if(all(pokemon == c(15, 15, 15))){
        perfects <- perfects + 1
        }
    }
perfects/nruns

## [1] 0.015623