library( ggplot2 )
res <- c( )
flips <- c( )
diffs <- c( )
for ( i in 1:1000 ){
  num_of_flips <- i*10
  trial <- stats::rbinom( n = num_of_flips, size = 1, prob = 0.5 )
  Sn <- abs( sum( trial ) - length( trial ) )
  diff <- Sn - ( num_of_flips / 2 )
  percent <- round( Sn / num_of_flips * 100, 4 )
  res <- c( res, percent )
  diffs <-c( diffs, diff )
  flips <- c( flips, num_of_flips )
}

data <- data.frame( flips, res, diffs )