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Note that a few of them use dice only for indication and not for randomness. (Most of them do use throwing the dice for random, though.) Also note that a few of them have only a very minor randomness (and that I consider a coin toss to be a "d2" dice roll).
(I don't mind either way; I think good games can be made in both ways.)
GM Vukevich would say Chess may evolve rigorous rules-randomization, just as the beginning had dice for four-player. Http://www.chessvariants.org/index/displaycomment.php?commentid=18729. Http://www.chessvariants.org/index/displaycomment.php?commentid=18909. Only still getting familiar with what has been done, here's a three-player: http://www.chessvariants.org/large.dir/contest84/orwellchess.html. A lot of viewers have just registered ''okay a dice chess,'' not yet discriminating more serious ideas.
Yesterday evening a news story made me think about Chess with dice. The treasurer of UKIP¹ was railing against attempts to get more women on company boards. His argument was that women are less competitive than men, and he cites as an example the shortage of women in competitive activities - not just physical sports² but also more cerebral pastimes like Chess and Bridge. It occurred to me that Chess is not that good an analogy for running a business anyway, but that adding a random element with dice would increase the similiarity to managing employees without the unquestioning obedience of Chessmen. Not that I would suggest that even a randomised variant would be a good test for business leadership, but it does add to realism in terms of the civilian world alongside the familiar fog-of-war arguments³. Of course what would really be needed would be something to represent differences in powers of persuasion, but how that could be achieved short of having an extra person participating for each piece, I cannot imagine.
¹a British political party routinely embarrassed by racist and/or sexist comments by its activists
²in which he claims women are inherently disadvantaged, as many with his attitudes do
³as also used by servicemen who have just shot an obnoxious superior in their own regiment
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