/**
    A puzzle from Robin Houston:

   Someone posted a really nice mathematical question on work slack.

   We have a population of independent single-called organisms in a dish. At
   each generation, each of them:

   • with probability 0.4, dies
   • otherwise, divides into twon

   Initially the population is 1. What is the probability that the colony eventually becomes extinct?

   https://twitter.com/robinhouston/status/1565622812924121088
*/

trials = million
gens = 15
alive = 0
largestDead = 0

TRIAL:
for count = 1 to trials
{
   largest = 0
   p = 1
   
   GEN:
   for gen = 1 to gens
   {
      if p > largest
         largest = p
      
      if p == 0
      {
         if largest > largestDead
            largestDead = largest
         
         next TRIAL
      }
      
      pnew = 0
      for n = 0 to p-1
      {
         if randomFloat[0,1] > 0.4
            pnew = pnew + 2
      }

//      println["$gen $pnew"]
      p = pnew
   }

   alive = alive + 1
}

println["$alive out of $trials"]
println["Probability of extinction is " + (1 - (alive/trials))]
println["Largest dead is $largestDead"]