Even Odds Chess (not technically a chess variant, but a chess opening)

Currently even at the top levels of FIDE chess, the player with the White pieces is known to have a significant advantage over the player with the Black pieces. Even the top chess engines show this advantage for White when they analyse the opening chess position with White to move first. This built-in advantage can present problems with pairings, especially for a tournament with an odd number of rounds.

I have devised a simple way to even the odds of any single chess game, at least according to initial projections. These initial projections are based on Stockfish 10 analysis, and have yet to be reinforced by many thousands of actual game results.

I call it "Even Odds Chess" and a second advantage it has is that like chess960, it pretty much elminates opening chess theory as a factor in games, although maybe it should be said that in any Even Odds Chess game between two players of equal talent, but Player 1 has a much better standard chess opening knowledge than Player 2, there might still be an opening advantage to Player 1.

The method is simple: start every game with the standard chess opening position, then have each player make these 2 moves:

1.Nf3 a6 2.Ng1 h6

Or, of course, you could just set up the chess opening position but with Black's a-Pawn on a6 and h-Pawn on h6; I only give the above opening moves to make it compatible with all chess engines without having to set up a position.

White technically still has first-move, but has given apparently away the advantage. I say "apparently" based on these analyses from Stockfish 10, and particular note the miniscule advantage given to White, less than a 10th of a Pawn in the best line, whereas without these opening moves, Stockfish 10 would give White more than half-a-Pawn point advantage in the best line:

Stockfish 10 Analysis of Standard Chess Opening Position:

1 (33 ply search depth) +0.53
      1.Nf3 c5 2.e4 e6 3.c3 d5 4.exd5 exd5 5.d4 Nf6 6.Bb5+ Bd7 7.Bxd7+ Nbxd7 8.O-O Be7
      9.dxc5 Nxc5 10.Qc2 O-O 11.Be3 Bd6 12.Nbd2 Re8 13.Rfe1 Rc8 14.h3 a5 15.Bd4 Nfe4
      16.Nxe4 Nxe4 17.Rad1 Qd7 18.Qd3 Bc5 19.Bxc5 Rxc5

Stockfish 10 Analysis after 1.Nf3 a6 2.Ng1 h6 (Even Odds Dhess):

1 (33 ply search depth) +0.09
      3.d4 d5 4.Nf3 Nf6 5.e3 Bf5 6.Bd3 Bxd3 7.cxd3 e6 8.b3 c5 9.Bb2 cxd4 10.Nxd4 Bc5
      11.O-O O-O 12.Nd2 Re8 13.Rc1 Bxd4 14.Bxd4 e5 15.Bb2 Nc6 16.Nf3 Nd7 17.h3 Rc8
      18.d4 e4 19.Ne5 Qe7 20.Qd2 Nf6 21.Rfe1 Qd6

Now, here's something else to notice: the range of openings playable by White as determined by their Stockfish 10 analysis scored to a 26 ply search depth (less than above because it takes longer to calculate each line with top 20 lines specified versus top 1 line):

1 26 +0.10
      3.e4 c5 4.c4 e6 5.Nc3 Nc6 6.Nf3 Nd4 7.b3 Ne7 8.Bb2 Nec6 9.Bd3 Be7 10.O-O O-O
      11.Nxd4 cxd4 12.Na4 d6 13.f4 Bd7 14.Ba3 Re8 15.f5 exf5 16.exf5
2 26 -0.02
      3.d4 d5 4.Nf3 c5 5.e3 Nc6 6.dxc5 e6 7.a3 Bxc5 8.c4 Bb6 9.b4 dxc4 10.Qxd8+ Bxd8
      11.Bxc4 b5 12.Be2 Bf6 13.Ra2 Nge7 14.O-O O-O 15.Bb2 Bxb2 16.Rxb2 Rd8 17.Nc3 Bb7
3 26 -0.06
      3.Nf3 d5 4.d4 Nf6 5.e3 Bf5 6.Bd3 Bxd3 7.cxd3 e6 8.O-O c5 9.Bd2 Nc6 10.Bc3 Bd6
      11.dxc5 Bxc5 12.Nbd2 O-O 13.Re1 Rc8 14.Rc1 Bd6 15.h3 e5 16.Nb3 Kh8 17.a3 Bc7
4 26 -0.09
      3.e3 e5 4.d4 exd4 5.exd4 d5 6.Nf3 Nf6 7.Bd3 Bd6 8.Qe2+ Be7 9.O-O O-O 10.Be3 Re8
      11.Qd1 Nc6 12.a3 Bd6 13.Nbd2 Ng4 14.Re1 Qf6 15.c4 Nxe3 16.fxe3 Bf5 17.Bxf5 Qxf5
      18.Rc1 dxc4 19.Rxc4
5 26 -0.10
      3.g3 d5 4.Nf3 c5 5.Bg2 Nf6 6.O-O e6 7.e3 Be7 8.b3 O-O 9.d4 b5 10.dxc5 Bxc5
      11.a4 b4 12.c4 bxc3 13.Nxc3 Nbd7 14.Bb2 Bb7 15.Ne2 Ne4 16.Nd2 Rc8
6 26 -0.12
      3.c4 e5 4.Nc3 Nf6 5.e3 Bb4 6.Nge2 O-O 7.a3 Be7 8.d4 exd4 9.Nxd4 d5 10.b4 dxc4
      11.Bxc4 Nc6 12.O-O Nxd4 13.Qxd4 Re8 14.Bb3 Qxd4 15.exd4 Bf5 16.Be3 Rad8
      17.Rfc1 Be6 18.Bxe6 fxe6
7 26 -0.16
      3.f4 d5 4.Nf3 e6 5.g3 Bd6 6.Bg2 Ne7 7.O-O O-O 8.d3 b5 9.Nbd2 Nd7 10.e4 Bc5+
      11.d4 Bb6 12.c3 c5 13.dxc5 Nxc5 14.Nd4 b4 15.exd5 bxc3 16.Nc4 Nxd5 17.Bxd5 exd5
8 26 -0.21
      3.Nc3 d5 4.d4 Nf6 5.Bf4 c5 6.e3 cxd4 7.exd4 Nc6 8.Nf3 Bg4 9.Be2 e6 10.O-O Bd6
      11.Ne5 Bxe2 12.Nxe2 O-O 13.Nxc6 bxc6 14.c3 Rb8 15.Rb1 a5 16.Re1 Bxf4 17.Nxf4 Qd6
9 26 -0.29
      3.a3 e5 4.e4 Nf6 5.d3 Nc6 6.Be2 Bc5 7.Nf3 O-O 8.b4 Ba7 9.c4 d6 10.O-O Nd4
      11.Nc3 Be6 12.Nxd4 Bxd4 13.Qc2 c6 14.Be3 b5 15.Bxd4 exd4
10 26 -0.36
      3.c3 e5 4.d4 e4 5.c4 Nf6 6.Nc3 b5 7.e3 c6 8.d5 Bd6 9.Nge2 O-O 10.Ng3 Re8
      11.Nf5 Bf8 12.d6 Qb6 13.b4 a5 14.c5 Qd8 15.Bb2 axb4 16.Ne2 Na6
11 26 -0.37
      3.h3 c5 4.e3 Nc6 5.d4 d5 6.Nf3 Nf6 7.c4 cxd4 8.exd4 Bf5 9.Nc3 e6 10.c5 b6
      11.Qa4 b5 12.Qb3 Qc7 13.Be3 Be7 14.Be2 O-O 15.O-O Rab8 16.a3 Rfc8 17.Qd1 Ne4
      18.Rc1 Bg6 19.Bd3
12 26 -0.46
      3.d3 d5 4.Nf3 c5 5.e4 e6 6.Bf4 Nc6 7.c3 Nf6 8.Nbd2 Nh5 9.Be5 Be7 10.h3 Nxe5
      11.Nxe5 Nf6 12.Be2 O-O 13.O-O Qb6 14.Qc2 Qc7 15.f4 Bd6 16.Rae1 Bxe5 17.fxe5 Qxe5
      18.Nf3 Qc7
13 26 -0.46
      3.b3 e5 4.Bb2 Nc6 5.e3 d5 6.Nf3 e4 7.Ne5 Nxe5 8.Bxe5 Ne7 9.d3 Nc6 10.Bg3 exd3
      11.Bxd3 h5 12.h3 g5 13.c3 Qe7 14.Be2 Bg7 15.Qxd5 h4 16.Bh2
14 26 -0.55
      3.b4 e5 4.Bb2 Bxb4 5.Bxe5 Nf6 6.Nc3 c6 7.Rb1 a5 8.Bxf6 Qxf6 9.Ne4 Qe6
      10.Ng3 Qxa2 11.e3 b5 12.c3 Bd6 13.Nf3 Bxg3 14.hxg3 d5 15.Bd3 Na6
15 26 -0.67
      3.a4 d5 4.Nf3 c5 5.d3 Nc6 6.e4 e6 7.Be2 Bd6 8.Nbd2 Nf6 9.b3 O-O 10.O-O d4
      11.Ba3 e5 12.Nc4 b6 13.Nxd6 Qxd6 14.Nd2 Be6 15.h3 Qc7 16.Bb2 Rfd8 17.Re1 b5
      18.Rc1
16 26 -0.84
      3.Nh3 d5 4.d4 Nf6 5.Nf4 c5 6.e3 Nc6 7.Nc3 e6 8.dxc5 Bxc5 9.g3 Qc7 10.Bg2 O-O
      11.O-O Rd8 12.Nd3 Bd6 13.e4 d4 14.Ne2 e5 15.f4 Qb6 16.fxe5 Nxe5 17.Bxh6 Nfg4
      18.Bg5 Ne3 19.Qd2 Bd7 20.Bxd8 Rxd8 21.Nxe5 Bxe5

Notice that the same standard opening moves as in regular chess all give about an even score, if we assume that as much as a 1/5th Pawn advantage (i.e. +0.20 to -0.20 range) is in the range of error and basically denotes an even score. Only when you get to moves like 3.a3, or 3.c3 or 3.h3, does the score start getting significant in favor of Black.

Thus if White plays any one of the "usual" White opening moves as in regular chess,
3.e4
3.d4
3.Nf3
3.g3
3.c4
3.e3
3.f4
3.Nc3

the result should be an even-odds game, ignoring the ratings of the two players involved.

This game can be used on all the current chess platforms that are offering online chess, players only have to agree to play the first 2 moves as given above. Then the game played will be virtually free of opening memorization influence, but again, the primary purpose is to remove the advantage of opening color in tournaments with odd number of rounds.