Marsellais Chess is a variant of Chess in which each player makes two moves per turn. A player loses his second move for a given turn if he checks the King on his first move on that turn. A further variant, Balanced Marsellais Chess, gives White only one move on his first turn.
This provides a close balance between the two players, but having two moves per turn results in a game quite a bit different from ordinary Chess.
One way to provide a game with a precise balance between the two sides might be to start with Balanced Marsellais Chess and make a few more changes:
The idea is to both eliminate the large margin of insufficient material which produces draws, but also to precisely equalize the initiative of both players through an initial phase of two moves per turn, but one which can be ended equally well by either player, so that instead of the game remaining, until the end, a game of two moves per turn, different from regular Chess, it is Chess made symmetrical through having only an initial portion of the game differ in that significant respect from regular Chess.
Retaining existing endgame theory, by making stalemate inferior to checkmate, might still be desirable, but rather than the system noted above, where 100 points are given for the game, one that gives more credit for bare King would be appropriate:
rather than even, say, 10/0 for checkmate, 8/2 for stalemate, and 6/4 for bare King, so that instead of bare King being almost a draw, but with slight credit for one side, it is more than half as significant as a checkmate (the point differences between the sides being 10, 8, and 6, rather than 10, 6, and 2).
It may be, however, that the 10/0, 8/2, 6/4 system would also work, if the consequence was that bare King was the usual form of victory, but the extra points for forcing stalemate or forcing checkmate were a valuable bonus given to a player whose attack created a larger advantage.
Also, the condition that the two moves in a turn be made by different pieces is said to slow the game down; this condition was included because rather than regarding it as a bad thing, I regard it as helping to fulfill the goal of keeping the game as much like regular Chess as possible.