#include <stdlib.h>
#include <vector>

const int NTries = 1000000;
vector<char> rolls;

char roll() {
  return rand()%6 + 1;
}

char check() {
  const int N = rolls.size();
  const char r1 = rolls[N-3];
  const char r2 = rolls[N-2];
  const char r3 = rolls[N-1];
  if(r1 == r2 || r2 == r3 || r3 == r1) return 0;
  if(r1 < r2 && r2 < r3) return 1;
  if(r1 < r3 && r3 < r2) return 2;
  if(r2 < r1 && r1 < r3) return 3;
  if(r2 < r3 && r3 < r1) return 4;
  if(r3 < r1 && r1 < r2) return 5;
  if(r3 < r2 && r2 < r1) return 6;
}

int main(){
  double avg = 0;
  double prob[7] = {0};

  for ( int nTries = 1; nTries <= NTries; nTries++) {
    rolls.clear();
    rolls.push_back( roll() );
    rolls.push_back( roll() );
    char ch = 0;
    while (ch == 0) {
      rolls.push_back( roll() );
      ch = check();
    }
    avg = (avg*(nTries-1) + rolls.size())/nTries;
    prob[ch]++;
  }


  cout << "Avg = " << avg << endl;
  for(int i = 1; i <= 6; i++) {
    prob[i] /= NTries;
    cout << "prob[" << i << "] = " << prob[i] << endl;
  }
  return 1;
}

Avg = 4.00243
prob[1] = 0.166725
prob[2] = 0.166508
prob[3] = 0.166607
prob[4] = 0.166534
prob[5] = 0.166988
prob[6] = 0.166638