10-day contract contains 10 days, regardless of the number of games team plays. You should choose the right day to sign the player. After 2 consecutive 10-day deals, you have to either sign him for the remainder of the season or waive.
Darius Miles' situation was a typical example of 10-day players. Such as:
2009/01/10: Grizzlies sign Darius Miles to 10-day contract
2009/01/20: Grizzlies sign Darius Miles to second 10-day contract
2009/01/30: Grizzlies sign Darius Miles for the remainder of the season
During the first 10-day period, he played 3 games, during second, he played 5. Neither players nor teams have nothing to do with the schedule.
Hopefully, I've been clear enough.