Skimming through A. V. Murali’s book Chess Variants & Games, I’m finding lots of intriguing board geometries, some of them deft and some outrageous. Tiling the plane with alternating squares and octagons? Murali’s got you covered. But he seems not very interested in exploring actual game-play.

He proposes a number of three-player variants — on boards of hexagons or triangles, for example. But here’s the thing: Three-player chess flat-out doesn’t work. It’s not a playable game.

A game of two-player chess advances from the opening through the middle game and into the endgame primarily through the process of piece exchange. The board is gradually cleared as bishop is traded for bishop, pawn for pawn, or rook for rook. If you can, you try to get the advantage in an exchange — capturing a knight but losing only a pawn, for example. If you can win a couple of exchanges and otherwise trade pieces of equal value, when the endgame is reached you’re pretty sure to win, because you’ll have significantly more material than your opponent.

In three-player chess, this dynamic process fails. At any point where players A and B exchange pieces, player C comes out ahead. Thus there’s a profound disincentive to exchanging pieces. Nobody is ever going to want to capture anything (other than a piece that’s unprotected, and how likely is that?). The game can’t unfold tactically or strategically, because capturing pieces is a bad idea.

Three-player games such as Chinese checkers, in which material is not exchanged, work well. As far as I can see, a three-player chess variant would work only if shogi-style drop capture was included. Player A, let’s say, captures player B’s rook, and the best player B can get in exchange is player A’s bishop. Player C then gets one move in which he has an advantage, but on their next moves players A and B drop the captured pieces back into play. Player A is now shy of a bishop but has an extra rook, player B having an extra bishop but being short of a rook.

In this situation, player A gains from the exchange relative to player C. Whether a drop should be allowed followed by a move in the same turn, or whether a drop should require an entire turn, is a question that would have to be answered by play-testing.

But what if players A and B each capture one of player C’s pieces in the same turn? Player C has been ganged up on. He can only make one exchange when it’s his turn. What’s worse, if player C has, let’s say, a rook that’s protected only by his bishop, player A could capture the bishop, leaving the rook unprotected, and player B could then capture the rook, in the same turn. The prospect of being ganged up on by your two opponents is clearly a reason not to want to play a three-player variant.

But possibly there’s a way around it. A rule could be added stating that if you have had two pieces captured since your last turn, you get two moves in a single turn, in order to compensate. These two moves might be with a single piece, allowing you to capture one opponent’s king. That would be a powerful disincentive to player B to make the second capture — unless player B thinks (hopes) player C will use his double move to kill player A’s king.

Over-the-board talk and bargaining are also a problem in a three-player variant. I’ll leave you to worry about how best to handle that.

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