gistfile1.txt

# https://gilkalai.wordpress.com/2009/07/08/test-your-intuition-7/

#Consider the following game: you have a box that contains one white ball and one black ball.
#You choose a ball at random and then return it to the box. 
#If you chose a white ball then a white ball is added to the box, and if you chose a black ball then a black ball is added to the box. 
#Played over time, what is the probability that more than 80 percents of the chosen balls are white?

library(tidyverse)

## make simulation functions -- I couldhave done it one go but just made it more modular

pick_ball <- function(n){
 
    res <- tibble(x=sample(c(1,0),n,replace=TRUE)) |> mean()
    
}

stimulate_pick_balls <- function(n){
 
    res <- tibble(x=replicate(100000,pick_ball(n)))
    
    
    prop_tbl <- res |> table() |> prop.table()
    
    value_vec <- prop_tbl["0.8"] |> unname()
    
    
    out <- tibble(x=value_vec,y=n)
    
    return(out)  
    
}

## sequence values to vary the "over time" piece


n_vec <- seq(10,50,5)


## do iterations

res <- map(
    n_vec
    ,.f=\(x) stimulate_pick_balls(x)
)


## plot resutls
res |> 
    purrr::list_rbind() |> 
    ggplot(
        aes(x=x,y=y)
    )+
    geom_point()+
    geom_line()+
    scale_y_reverse()+
    scale_x_continuous(labels = scales::label_percent())+
    theme_classic()