A look at the most popular games at Brainking shows that games with a random element are quite popular.
1.  Ludo  2.  Backgammon  4.  Hyper Backgammon  5.  Triple Dice Poker  6.  Backgammon Race  7.  Fevga 8.  Dice Chess 10x10  9. Dice Poker  and 10. Nackgammon
All but one of the top ten games have a random element.
Looking through  D. B. Pritchard's book I came across a variant called "Mine Chess," which is identical to
regular Chess except that each player picks two squares on own side of board that are mined.  If the mined squares were randomly chosen instead a randomized element would be introduced into the game. It is true that Backgammon games make up half of the top ten games but it is also evident a significant proportion of the players at Brainking also indulge in Chess, the number three game. When an enemy piece moves to a mined square the player controlling the mine may choose to make the mine explode.  Players can wait for a more valuable piece to go to the square
Judging by the list of most popular games at Brainking this may be a Chess variant that would be popular.  Mined squares clearly would have an impact on endgame play which was one of the motivating factors for its creation. 
Talen314