Simulate frequency of lottery quick picks

quickPick.R

library(checkpoint)
checkpoint("2018-01-01")
library(magrittr)
library(tidyverse)
library(parallel)
library(doParallel)

s <- 1e6  # Number of lottery tickets

cores <- detectCores()
cl <- makeCluster(cores)
registerDoParallel(cl)

quickPicks <- foreach (i = 1:s, .combine = rbind) %dopar% {
  sample(1:49, 6)
}

stopCluster(cl)

M <- 
  0 %>% 
  rep(s * 49) %>% 
  as.integer() %>% 
  matrix(nrow = s, ncol = 49)
for (i in 1:s) {
  M[i, quickPicks[i, ]] <- 1
}

df <-
  M %>% 
  data.frame() %>% 
  gather() %>% 
  mutate(number = as.integer(gsub("X", "", key))) %>% 
  rename(picked = value) %>% 
  select(-key) %>% 
  group_by(number) %>% 
  summarize(numberTickets = n(),
            countPicked = sum(picked),
            propPicked = sum(picked) / n(),
            seProp = sqrt((sum(picked) / n()) * (1 - (sum(picked) / n()))/ n())) %>% 
  mutate(lower = propPicked - seProp,
         upper = propPicked + seProp)
df %>% 
  ggplot() +
  aes(x = number, y = propPicked) +
  # geom_linerange(aes(ymin = lower, ymax = upper), color = "grey") +
  geom_line() +
  geom_point() +
  geom_abline(intercept = mean(df$propPicked), slope = 0, color = "blue", size = 2, alpha = 1/2) +
  scale_x_continuous("Number") +
  scale_y_continuous(sprintf("Proportion of %s tickets", 
                             format(s, big.mark = ",", scientific = FALSE))) +
  theme_bw()