Did predecessors of modern chess use dice to determine which piece to move? According to the Wikipedia article of Magic: The Gathering, creator Dr. Richard Garfield has compared the evolution of the game from luck to skill as being similar to that of chess.


  According to Dr. Garfield, Magic has and would likely continue decreasing its degree of luck as the game matured. The "Mulligan rule", as well as card design, past vs. present, are good examples of this trend. He feels that this is a universal trend for maturing games. Dr. Garfield explained using chess as an example, that unlike modern chess, in predecessors, players would use dice to determine which chess piece to move.


However, the article on Chess doesn't mention dice in its history. Did predecessors to modern chess indeed use dice? And if so, was it removed as part of a maturation of design to emphasize skill over luck, as Dr. Garfield  suggests?
Richard Eales addresses this question in Chess: The History of a Game (p.30):


  On one last matter, whether or not the early Indian chess was played
  with dice, there is simply no evidence on which to base a general
  conclusion. Al-Biruni saw dice being used in the four-handed game
  (throw two to move the chariot, three for the horse, and so on), but
  this is a practice which continually crops up in the history of
  pre-modern chess, particularly when gambling was involved. The
  Chatrang-namak described chatrang as a game of pure skill but the dice were not unknown in Islam, and certainly reappeared more
  frequently in medieval Europe. There is no clue preserved in the
  structure of the game to betray whether the 'original' chess was
  played with dice or not.


So it seems that this question is one on which we should remain agnostic.