Testing Exploding Dice Expected Value

set.seed(123)

N    = 6           #set sides of dice
Nsim = 10000000    #set number of simulations
vals = rep(0,Nsim) #initialize simulation vector

for(i in 1:Nsim){

  draw = sample(1:N,1) #draw value
  val  = draw          #set value

  #start recursive loop
  #if draw == N, draw again and add to val
  #keep doing while draw == N

  while(draw == N){
    draw = sample(1:N,1)
    val  = val + draw
  }
  vals[i] = val
}

mean(vals)          #simulated expected value
(N/2)*((N+1)/(N-1)) #theoretical expected value