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Lawless: Six would definitely take the randomness out! However I am just trying to desribe a commercial variant that I played a long time ago in the 1980s. I never owned it and my memory may be a bit foggy. However foggy or not, with dice chess one still has to balance randomness with skill. With too many dice you might as well just play chess, and with too few there is no skill. One die seems too random for me, and those 4-move games published below must not have been that much fun to play for either side.
grenv: Yes the game I played allowed you to choose between the two die roll choices as well. It reduced the possibility of not being able to move anything.
mangue: I am curious why not two dice instead of one? A second die would allow a distribution of faces more equivalent with the number of pieces. I haven't played "Vegas Fun Chess" in a while but it seems on two dice there were 4 faces for pawns, 2 each for Knight, Bishop and Rook and 1 for the King and Queen. There also might have been a "variant with 3 faces for pawns and a wild card that allowed you to move anything. Vegas Fun chess, I think also allowed the king to move freely out of check. The checking player also had a free move to continue his attack after a check. Perhaps the last rule might be difficult to program in?
I guess anything is possible, although Fischer always has been real careful about his privacy and I don't think he would be that overt in letting his real identity be known.
Those Internet Chess Games were always speculation as to whether Fischer played them or not. Something like an urban legend among chess players.