Monte Carlo Simulation of http://mathoverflow.net/questions/9037/how-is-it-that-you-can-guess-if-one-of-a-pair-of-random-numbers-is-larger-with

guessing.c

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>

int main(int argc, char *argv[])
{
  srand(time(0));
  
  // successes is the number of times the "smart"
  // method correctly guesses >/<. dumb_successes is the
  // number of times the trivial 50-50 method is correct
  int i, successes = 0, dumb_successes = 0, total_trials=100000;
  
  for (i=0; i<total_trials; i++)
  {
    // generate first and second random numbers
    int first = rand(), second = rand();
    
    // generate third random number
    int x = rand();
    
    // if third random number > first random number
    if (x > first)
    {
        // then our guess is that the second number is also greater
        if (second > first)
        {
          successes++;
        }
    }
    // if third random number < first random number
    if (x < first)
    {
      // then our guess is that hte second number is also less
      if (second < first)
      {
        successes++;
      }
    }
    
    // now for the dumb method: arbitrarily chose greater than or less than
    // To chose this, I just use x%2. odd means guess "greater", even means
    // guess "less than"
    
    // greater than
    if (x%2 == 1)
    {
      // if correct, increment dumb successes
      if (second > first)
      {
        dumb_successes++;
      }
    }
    
    // less than
    if (x%2 == 0)
    {
      if (second < first)
      {
        dumb_successes++;
      }
    }
  }
  
  printf("Smart method: %f\n", ((double) successes)/total_trials);
  printf("Dumb method: %f\n", ((double) dumb_successes)/total_trials);
  
  return 0;
}