#include <cstdio>
#include <cmath>
#include <random>
using namespace std;
 
std::mt19937 rnd;
 
double rndf() { 
  return (rnd() - rnd.min() + 0.5) / (rnd.max() + 1.0 - rnd.min());
  }
 
/* Box Muller transform */
double rnorm() {
  double u1 = rndf(), u2 = rndf();
  return sqrt(-2 * log(u1)) * cos(2 * M_PI * u2);
  }
 
bool win(double v) {
  int potions = 10;
  bool ok = true; 
  for(int a=0; a<2000; a++) {
    while(rndf() < 0.4) potions++;
    double x = 2 * rnorm() + 4;
    if(x < v && potions) { potions--; continue; }
    double y = x + rnorm();
    if(y < 0) return false;
    }
  return true;
  }
 
int main() {
  printf("cutoff;wins\n");
  int ngames = 100;
  for(double v=1; v<6; v+=0.1) {
    int good = 0;
    for(int a=0; a<ngames; a++) if(win(v)) good++;
    printf("%6.2f;%f\n", v, good * 1. / ngames);
    }
  return 0;
  }
 

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