It makes no difference if they do it one at a time or all at the same time. Picture it this way. If they all lined up in front of a card but instead of flipping it at the same time, they flipped the card in front of them one at a time. Everyone would still have a 1/6 chance. Now instead of doing that everyone stands back and walks up to the card that would have been in front of them anyway if they all lined up. The odds stay the same. That last scenario is essentially what they are doing. When they flip the card that would have been in front of them, where they stand and when they do it doesn't change the odds.
