gistfile1.txt

library(tidyverse)
#Flip 100 coins, labeled 1 through 100. Alice checks the coins in order (1, 2, 3, …) while Bob checks the odd-labeled coins, #then the even-labeled ones (so 1, 3, 5, …, 99, 2, 4, 6, …). Who is more likely to see two heads *first*?

library(tidyverse)



flip_coin <- function(){
    
flip_coin_tbl <- tibble(
    coin=1:100
    ) |> 
    rowwise() |> 
    mutate(
        face=sample(c(1,0),1)
    ) |> 
    ungroup()
    
method_1 <- flip_coin_tbl |>     
    filter(
        face==1
    ) |> 
    mutate(
        method1=duplicated(face)
    ) |> 
    filter(
        method1==TRUE
    ) |> 
    pull(coin) |> min()


method_2 <- flip_coin_tbl |> 
    mutate(
        even_indicator=coin%%2
    ) |> 
    arrange(
        -even_indicator,coin
    ) |> 
    filter(
        face==1
    ) |> 
    mutate(
        method2=duplicated(face)
    ) |> 
    filter(
        method2==TRUE
    ) |>
    pull(coin) |> head(1)

out <- list()
out$method_1 <- method_1
out$method_2 <- method_2
out$flips <- flip_coin_tbl


if(method_1>method_2){
    out$res <- tibble(
        winner="method_2"
    )
    return(out)
    
}else if(method_1<method_2){
    
    out$res <- tibble(
        winner="method_1"
    )
    
return(out)
    
} else {
    
    out$res <- tibble(
        winner="tie"
    )
    return(out)
    }
}

out <- flip_coin()

out

res <- map(1:1000,\(x) flip_coin() |> pluck("res")) |> 
    purrr::list_rbind()

res |> 
    count(winner) |> 
    ggplot(aes(x=winner,y=n))+
    geom_col()+
    theme_classic()