Brilliant Positions with Minimal Pieces

The Saavedra Study

Games with Simple Rules

As a minimalist, I value simplicity in games. As an engineer, I also value efficiency. I'm fascinated when simple game rules generate a vast richness of complex positions and interactions. If you enjoy such elegant games, I can recommend two: Hex and Go.

Hex was independently invented by Piet Hein (a Danish mathematician) in 1942 and later by John Nash (a mathematician and economist known from "A Beautiful Mind").

Hex puzzle

Here's how it works: Red and Blue players take turns placing stones on a diamond-shaped board made of hexagonal tiles. The goal is to form an uninterrupted connection between your two opposite sides of the board (red sides for Red player, blue sides for Blue player). Simple as that — connect your sides to win!

An example of winning connection for Black player:

The game cannot end in a draw. When one player connects their sides, it becomes physically impossible for the other player to connect theirs. Interestingly, Nash proved that when the board is completely filled with stones, there must always be a winning connection for one of the players.

Despite these straightforward rules, Hex offers remarkable strategic depth (especially on larger 13×13 or 17×17 boards typically used for play). You can play it online (on LittleGolem or BoardGameArena), study from strategy books, or compete in Mind Sports Olympiad tournaments. I've dedicated months to studying its patterns, solving puzzles, and playing competitive matches.

Go's rules are simple but more complex than Hex's. While I won't delve into Go here, it became widely known after DeepMind's AlphaGo and AlphaZero breakthroughs, it's a fascinating game with even greater depth than Hex.

Minimalistic Chess Positions

So how does this relate to chess, and specifically the Saavedra position?

Unlike Hex or Go, chess has more complex rules: different piece types and special rules like castling, en passant, and stalemate. To find similar minimalistic brilliance in chess, we need to look at endgames. With just a few pieces remaining on the board, these positions can still generate fascinating gameplay and demonstrate beautiful ideas.

What's the smallest amount of chess pieces that can create interesting gameplay? Searching through HHDBVI (Endgame Studies database), I found 80 studies (out of ~90,000) that use just two Kings and a single pawn.

When we add one more pawn, making it pawn versus pawn, the number jumps to 426 studies. This includes the famous Reti position, where White achieves a miraculous draw despite their King being far behind Black's passed pawn, and Black's King being perfectly positioned to stop White's pawn:

Reti: White to play and draw!

The Saavedra Position

As a next step, we can replace one of the pawns with a piece and get to even richer 4-piece positions. Finally, we reach the main topic of this post: I wanted to show you the famous Saavedra position. It is famous indeed, so many of you probably know it already, but it's so beautiful that I still want to share it with the ones who don't.

Here's the position: White to play and win. Created by Saavedra/Barbier in 1895. Take some time to solve it yourself, or read on for the solution:

Saavedra: Starting Position

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The first challenge here is to understand Black's defensive idea. As White, we play 1.c7 to advance the pawn one step closer to promotion. Playing anything else allows Black to attack the pawn and draw, for example, 1. Ka6? Rd6 2. Kb7 Rxc6 =

How should Black react? You might consider 1…Rd2, planning to check White's King from a2 and b2 to try winning the new Queen. However, when White's King reaches c3, the checks end with no follow-up. Black would face a rook vs. queen endgame, which is a clear loss for the rook side.

We need to refine this idea further. What about 1…Rd6+?

This is promising: if the King goes to the seventh rank, we pin the pawn with Rd7 and draw. If the King goes to a6 or a5, we simply play Rc6 and attack the pawn from behind. If the King goes to c5, we play Rd1! Then we either win the new Queen with a Rc1+ skewer, or if the King moves away, we still play Rc1 to control the promotion square. Therefore, the only viable move for White is 2. Kb5!

After this, we give another check with 2…Rd5+. Following similar logic, the King must go to b4 (going back to b6 only leads to move repetition). The checks continue down the board: 3. Kb4 Rd4+ 4. Kb3 Rd3+. Here you can see this sequence of moves:

But now White can play 5. Rc2, so White’s Rd1 skewering idea no longer works:

So is this the end? Not really, Black has another idea in mind: 5…Rd4!

Now if we promote 6. c8=Q? Rc4+! 7. Qxc4 is a stalemate. And if the Queen doesn’t take the rook, we just capture the Queen:

This is where Saavedra's contribution comes into play. Fernando Saavedra, a Spanish priest and amateur chess player living in Scotland in the late 19th century, made a nice discovery. The study was originally published by G.E. Barbier in the "Glasgow Weekly Citizen" as a draw for Black, showing the moves we've just examined. However, Saavedra spotted something new: by under-promoting to a Rook, White could achieve an instant win!

Here is a position after rook promotion: 6. c8=R!

Now the stalemate trick no longer works: after 6…Rc4+, White simply captures the rook with no stalemate. Though rook versus rook typically leads to a draw, this position is winning for White because of the immediate checkmate threat Ra8#. Black's only defence is to play 6…Ra4 preemptively, but this walks into a double attack: 7. Kb3! — attacking the rook while threatening checkmate from the other side, on c1:

Black is lost. Here is the whole solution for you to enjoy:

This study is truly beautiful. It's inspiring that Saavedra, despite being a weak amateur player, is now remembered throughout the chess world for his under-promotion move. His insight changed the entire evaluation of the position while adding an elegant combination of under-promotion, double-attack and checkmate threat to an already impressive sequence. The study has inspired numerous follow-ups and elaborations, particularly an amazing study by Mark Liburkin that additionally features a bishop under-promotion.

If someone tells you that endgames are boring, just show them the Saavedra position!