library(pracma)  #for fzero

N_loops <- 100000

N_trials <- 25

xz <- numeric()
# set.seed(1)

for (k in 3:30){

     store <- numeric()

     for (i in 1:N_loops){

          y <- runif(n = k)

          best_idx <- which(y==max(y),arr.ind=TRUE)

          do_keep <- FALSE
          my_keep <- 0
          for (j in 1:k){

               #draw one
               yi <- y[j]

               #find in rank
               all_ranks <- rank(y[1:j])
               this_rank <- tail(all_ranks,1)

               #compare with acceptance value
               if (j/exp(1) <1){
                    can_keep = FALSE
               } else {
                    can_keep = TRUE
               }


               #do you keep
               if (can_keep ==TRUE & do_keep == FALSE){
                    if (this_rank >3){
                         do_keep <- TRUE
                         my_keep <- yi
                    }
               }

          }
          store[i] <- my_keep

     }

     store <<- store

     myfit <- function(phi){
          if (phi > 1){
               phi <- 1
          } else if (phi < 0){
               phi <- 0
          }

          err <- quantile(x = store,probs = phi)-0.5
          return(err)
     }

     temp <- fzero(myfit,0.1)
     xz[k] <- unlist(temp)
     print(xz[k])
}