4-Player Chess In Four Charts

In 4-Player Chess, each player commands their own pieces, but share a single board as they compete for points.¹ Back in the day, my friends and I could squander hours on a single game, often spending more time negotiating deals and betraying armistices than actually moving the pieces.

Despite owning a 4-player board for nearly a decade, I just recently discovered the variant is also available on chess.com. Although it's less charming, playing online does have one advantage: the website archives every game played, immortalizing these games' scores and moves for future analysis.

These records can be leveraged to settle debates my friends and I have had about the game for years. For example, in 2-player chess, controlling the center of the board is often critical to victory. In 4-player chess, by contrast, the center feels like an awfully dangerous place for your pieces to be hanging around. So with a board of 160 tiles, where should you send your pieces, if not the center?

There are plenty of questions we can use the chess.com database to answer: at what point in a game do players earn the most points? Is risk-taking or risk-avoiding the better strategy? Is pawn-pushing actually worth it? Because most games vary wildly, I've opted to analyze a small sample of individual games, rather than trying to answer these questions holistically (this also saves me from a possible ban from chess.com, as excessively running my web scraping scripts could strain their servers).

So, what can we say about this game?

Points & Score

Capturing Pieces

Moving Pieces

Methodology

All data come from web scraping chess.com using Python and Selenium. I opted to collect data only from the ‘Free For All’ gamemode, although chess.com also offers ‘Solo’ and ‘Teams’ as additional modes of 4-player chess. Moreover, I did not collect data from any of my personal games. Other than those two caveats, I handpicked the small sample of games pseudorandomly.

In chess, a player’s “material” refers to their pieces while “Material Strength” refers to how strong their pieces as a collective are. I measured Material Strength using the piece point values: each queen worth 9, each bishop and rook worth 5, each knight worth 3, and each pawn worth 1. Although pawns promote to queens worth 1 point for capturing, I still consider them to be equal as a 9-point queens when measuring Material Strength. I ignored kings in the measurement because they are always present and aren’t typically used in tactical aggression.

All metrics were measured at every game move. Game moves as a unit of analysis is preferable over game rounds, because most of the metrics can change multiple times within a round. For example, if three players all capture a fourth players’ pieces in immediate succession, then that fourth player's Material Strength would drop three moves in a row - a finding collecting data at the round level would obscure.

Footnotes

[1] There are of course other differences between standard and multi-player chess. The move order of 4-Player Chess is: red first, followed by blue, yellow, then green. Although players can be eliminated from play via checkmates or running out of time, the game objective is to finish the game with the most amount of points; therefore it is possible to win even without being the last player remaining. Points are awarded by capturing enemy pieces: 9 points for queens, 5 points for bishops and rooks, 3 for knights, 1 for pawns, and 1 for pawns which promote to queens. Checkmating an enemy king awards 20 points. Finally, delivering a check to multiple kings at once awards 1 point if the check is delivered using a queen, 5 points if delivered by any other piece.