#include <iostream>
#include <ostream>
#include <istream>
#include <intrin.h>

const unsigned maxCards = 20;
const unsigned drawnCards = maxCards / 2;
const unsigned allConfigs = 0x1 << maxCards;

int drawSequence(unsigned config)
{
  int numberOfSpells = 0;
  int bitPointer = 0;
  for (int i = 0; i < drawnCards; ++i, ++bitPointer)
  {
    if ((2 * __popcnt(config)) < (maxCards - bitPointer)) ++bitPointer;
    if (config & (0x1 << bitPointer)) ++numberOfSpells;
    config &= ~((0x2 << bitPointer) - 1u);
  }
  return numberOfSpells;
}

int main()
{
  int spellsDrawn = 0;
  for (unsigned i = 0; i < allConfigs; ++i)
  {
    spellsDrawn += drawSequence(i);
  }
  int allCardsDrawn = allConfigs * drawnCards;
  std::cout << "spells drawn:" << spellsDrawn << std::endl;
  std::cout << "cards drawn:" << allCardsDrawn << std::endl;
  std::cout << "relation:" << double(spellsDrawn)/allCardsDrawn << std::endl;
  std::cin.ignore();
}