Reject the first 37% ?

rej-sim.R

## I came across a Chinese science blog which discusses an interesting stuff that girls should reject 
## the first 37% (for 1/e = 36.79%) pursuers in her life. A little R simulation as outlined in the 
## gist is shown below just for fun. In the snippet, m is the total number of boys you can choose. 
## In other words, they are potential husband for you. Larger number means high "quality" but these 
## numbers are randomly sampled, i.e., you don’t know whether the one who just walks into your life 
## is your Mr. Right or not. You reject the first m/e people (probably without any reason...), where 
## e is the Euler’s number, and choose from the rest of the m people. If you find any one of the 
## remaning boys better than the best boy you saw earlier in the first m/e ones, then you choose that 
## guy; otherwise, you have to make do with the last guy for the rest of your life...

## Well, girls basically don’t behave like what stated above...but one thing seems interesting and 
## probably makes sense: it’s too early to laugh when you meet a nearly-perfect boy very early 
## (<37% for sure). If your Mr. Right shows up just after 37%, I would say you are lucky enough :)

m = 30; sim = 10000
cut = round(m/exp(1))
v1 = (1:cut); v2 = (cut+1):m
mat = matrix(0, nr = m, nc = sim)
love = as.numeric(sim)
for (j in 1:sim){
    mat[ ,j] = sample(seq(1,m),replace=FALSE)
}
for (j in 1:sim){
  if(any(mat[v2,j] > max(mat[v1,j])))
    love[j] = mat[v2,j][which(mat[v2,j] > max(mat[v1,j]))[1]]
  else
    love[j] = mat[m,j]
}
hist(love)
sum(love == m)/sim