3x3 Chess

Introduction

This page is about the game of chess on a 3x3 board. This game is now strongly solved. It means that the database of all positions is constructed, and the best move is known in every position. It is not clear how to define a starting position on 3x3 board, so all possible positions were included. Rules are same with chess, except that there is no castling and no double pawn move (and no en passant). Pawns promote when they reach the last rank - third for white and first for black.

Does it look too simple for you? Read these pages, try to solve problems, then follow the correct line with the analysis board. Then tell me if 3x3 chess is still too simple or not. I hope you will enjoy this beautiful chess variant as much as I do.

The Answer

"Alright," said Deep Thought. "The Answer to the Great Question ..."
"Yes ...!"
"Of Life, the Universe and Everything ..." said Deep Thought.
"Yes ...!"
"Is ..." said Deep Thought, and paused.
"Yes ...!"
"Is ..."
"Yes ...!!!...?"
"Forty-two," said Deep Thought, with infinite majesty and calm.

- Douglas Adams, The Hitch Hiker's Guide to the Galaxy

The question is, of course, how long is the longest checkmate. We don't know which variant Deep Thought was solving (perhaps this or this one). But we already have the Answer for 3x3 chess: 16 moves! More details, including mate in 16 and other interesting positions, are on the Positions page.

Problems

Test your tactical thinking by solving problems on a 3x3 board. The position will be selected for you randomly. When you choose your move, the best defence of computer will immediately follow. If the problem is too hard, use the 'Analysis board' link at the bottom.

Analysis board

Here you can input any 3x3 chess position for analysis:

A position is defined by a 10-character string. First, a 'w' or 'b' indicating the side to move. The next 9 characters describe the board squares, in the order: a3, b3, c3, a2, b2, c2, a1, b1, c1. Each square can contain one of the pieces: K = King, Q = Queen, R = Rook, B = Bishop, N = Knight, P = Pawn. White pieces use capital characters, black pieces - small characters. A dot (.) encodes an empty square.

For example, w..k...K.. has just the two kings in the opposite corners (white on a1, and black on c3). Another example position: wK.k..NqRn. More examples are on the Positions page.

The analysis board is hosted on another server. Please let me know if it does not respond, or you notice any other issues with it.

Statistics

There are 304'545'552 legal positions in 3x3 chess (counting separately all left/right symmetric and white/black to move positions). Out of them 104'863'672 are checkmates, more than 1/3 of all positions. 3'576'856 positions are stalemates, 1.2% of all positions. So, there remain 196'105'024 in-game (non game-over) positions, where some moves are possible.

Number of drawn positions, including stalemates, is 52'268'040, or 17.2% of all legal positions. Number of drawn positions, which are not stalemates, is 48'691'184, which is 24.8% of all in-game (non game-over) positions.

Out of 195'996'550 in-game positions there are 78'022'680 positions where side to move wins (39.8%) and 69'391'160 positions where side to move loses (35.4%).

Here is the detailed statistics:

Note that these numbers are based on the indexing scheme used in the solver. They can provide a general idea about the size of the position space, but are not very useful for comparing with other chess variants. A more sound method of counting considers only unique legal positions, as described on the NULP website. The total number of unique legal positions (NULP) in 3x3 chess is 54,687,564, computed in 2012 (source forum post).

History

I started to think about 3x3 chess after solving one small board shogi variant in March 2003. In November of 2003 I constructed my first 3x3 chess database. The website and a fully functional online analysis board was first first opened on February 16, 2004.

In 2024 my paid dynamic DNS provider stopped propagating DNS updates, and repeated attempts to reach their support were unsuccessful. Therefore, after 20 years of service, the original domain could no longer be maintained. I moved the pages to the current address, and configured a separate node for analysis board.

Source code

The original source code of the solver:

https://kirill-kryukov.com/chess/3x3-chess/Kirr's%203x3%20Chess%20Solver%201.0.0%20-%20source.7z

I originally shared it in a forum post in 2011: https://kirill-kryukov.com/chess/discussion-board/viewtopic.php?p=63657#p63657.

Thanks

I would like to thank following people:

Takuma Yamada for ideas and discussion.
Chessbase, for allowing to use their graphics.

Contact

Please email any comments to kkryukov@gmail.com. Alternatively, you can try chess forums such as EGTB Forum and TalkChess.

Other studies of 3x3 chess

Aloril has also solved 3x3 chess, see his website. These two studies are totally independent, in fact we were not aware of each other existance until we both solved the game and made our websites. He completed his solution earlier than me - his webpage sais his first tablebase is dated 2001-05-02. However I believe 2004-02-16 is the day, when 3x3 chess analysis was first made open to the public, on these pages.

There is a slight difference between the game rules we used. Aloril's solution does not include positions where there is a white pawn on the 1-st rank, or black pawn on the last rank. This restriction makes perfect sense from the full-size chess point of view. However such positions are included into my study, for several reasons:

3x3 board is already tiny. It seems too limiting to allow pawns on second rank only.
On the small size board heavy pieces are too powerful. I wanted to see more pawns for some balance.
If that positions are excluded, a pawn can never take another pawn, or even just move without promotion.
Since there is no defined starting position in 3x3 chess, the definition of a position being legal if it is reachable from the starting position does not apply.
No pawn chains if that positions are excluded. :-)