3x3 Chess

Introduction

This page is about the game of chess on 3x3 board. This game is now 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 due to the reduced board size there is no castling and no double first move of pawn (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 this 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

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 this page.

Problems

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

Analysis board

For your convenience, there is an online analysis board available. First, let's look at the example position: an empty board and two kings in the corners: w..k...K... As you see, script "3x3can.cgi" is called when you open the link. Position is specified after the question mark by a 10-character description, somewhat similar to FEN (Forsythe-Edwards Notation). The first character is 'w' or 'b', it tells which is the side to move. Other characters describe 9 squares of the board, in this order: a3 b3 c3 a2 b2 c2 a1 b1 c1. Empty square is '.' (dot), pieces are written as: K, Q, R, B, N, P for King, Queen, Rook, Bishop, Knight and Pawn. White pieces use capital characters, black pieces - small characters. Another example: wK.k..NqRn. Just open an example position and try to type your own position in the address bar.

Statistics

There are 304'545'552 legal positions in 3x3 chess. Out of them 104'863'672 are checkmates, more than 1/3 of all positions. 3'685'330 positions are stalemates, 1.2% of all positions. So, there remain 195'996'550 normal 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 48'582'710, which is 24.8% of all not game-over positions.

Out of 195'996'550 not game-over 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%).

Thanks

My thanks go to all people, who made this study much easier:

• Takuma Yamada for being always active in discussion and producing a lot of strange ideas.
• Eugene Roshal and Igor Russkih for creating the best development environment (FAR+Colorer).
• Chessbase, Germany, for providing a colorful chess graphics.

Feedback

Please, let me know your opinion about this study. Any questions, comments or suggestions are welcome. Please, contact me by email: kkryukov@lab.nig.ac.jp (in Russian or English). Or, leave a message in the guestbook.