What if on the first round of a sequential game it is freestyle. This way people could get in the right pattern. For example:
For person 'a' it is noon.
For person 'b' it is 3:00 pm (because of time zones)
For person 'c' it is midnight
For person 'd' is it is 2:00 am
In this case you would not want the order to be: a, d, b, c because b would have to wait forever for d to play