Sailesh Chandra

Think Like An Engine 4

Part 4 of a multi-part series

Positional Sacrifices

Positional sacrifice in chess is a profound concept, where a player voluntarily gives up material – a pawn, an exchange, or even a piece – not for an immediate forced win or mating attack, but to gain significant long-term positional advantages. These advantages can include domination, more active pieces, centralization, advanced pawns, control over open files, or key squares. Tigran Petrosian, the ninth world champion, was renowned for his unique understanding of piece value and his innovative style, making him a leading exponent of the positional exchange sacrifice.

Can an Engine see Petrosian’s positional sacrifice. The answer is yes and no. Yes it will eventually see it, after running for many hours and it may still not see it as the best option.

1. Positional sacrifices require a schematic understanding of Chess, which humans are better at. However, after a lot of plys, the engines see the positional features and rate the positional sacrifice, much better and often an advantage.
2. If you want to play like an engine, you need to have a strong understanding of these positional features. This combined with your “human” understanding of schematic features can make you very strong at positional sacrifice.
3. The psychological impact of a positional sacrifice on your opponent cannot be caught by any evaluation engine. Even if your sacrifice was not completely sound, it is bound to unnerve an opponent to a certain extent.

How Computers Evaluate Positional Sacrifices

For humans, assessing whether a material sacrifice is justified by positional gains is one of the most challenging aspects of chess, often relying on experience and intuition. However, chess engines, such as Lichess's Stockfish, provide an objective evaluation, often expressed in pawn points,even when one side is down material.

As we have seen in the previous think like an engine articles. These points are :

• Employing complex evaluation functions: Unlike human "piece points," which are merely a rule of thumb, engines use sophisticated algorithms that assign numerical values to a multitude of positional factors. These factors include, but are not limited to:
  • Space advantage: The control of more squares on the board.
  • Piece activity and coordination: How well pieces are placed and work together to exert pressure or restrict the opponent.
  • Pawn structure: The quality of the pawn formation, including protected passed pawns, blockades, and weak points.
  • King safety: The vulnerability or security of the king.
  • Lead in development: How quickly and effectively pieces have been brought into play.
  • Control over specific files, ranks, or diagonals: Often gained by clearing lines.
  • Outposts: Strong squares for pieces, particularly knights, that cannot be easily dislodged.
• Calculating deeply and widely: Engines don't just evaluate the current position; they calculate "many (lots of) positions many moves down the line" to determine the long-term implications of a sacrifice. This allows them to "establish the truth" of a position.
• Fine-grained assessment: Computers have a "more fine-grained number for 'space', 'piece activity', etc." compared to human estimations.

In essence, when an engine shows a significant advantage for a side that is materially down, it means that the sum of these positional advantages outweighs the material deficit in its calculations.

Improving Positional Sacrifice Skills with Computer Insights

While humans cannot compute like machines, understanding how engines evaluate positional sacrifices can significantly improve our own strategic thinking:

1. Grasp the Value of Compensation: Instead of focusing solely on material, learn to appreciate the various forms of compensation that justify a sacrifice. An engine's evaluation can highlight which specific positional factors (e.g., a strong knight outpost, an open file, or a weak enemy king) are driving the advantage after a sacrifice.
   • Active Blockades: Learn how to create an "active blockade" by sacrificing a pawn to establish a dominant piece (like a knight on E5 in Geller's game) or to deny the opponent a key square, leading to an attack, as seen in Geller-Pilnick and Penrose-Tal. This differs from a "passive or defensive blockade" used to create a fortress.
   • Clearance Sacrifices: Understand that a pawn or piece can be sacrificed to "clear a square, a file, or a diagonal for one of your other pieces", where the cleared path is more valuable than the material given, as demonstrated by Steinitz.
2. Cultivate Intuition, Then Verify: Grandmasters like Alex Ipatov note that positional sacrifices often stem from intuition when "concrete threats" or forced wins aren't immediately apparent. They have an "intuitive feeling that if we put our pieces on the best squares eventually the tactics will come up". After making such an intuitive sacrifice in your own games or when studying, use engines to verify your intuition and understand the deep underlying reasons for the position's evaluation.
3. Focus on Follow-up and Execution: A positional sacrifice is not an end in itself; it's the beginning of a plan. It's crucial to know "how exactly they're going to proceed from there, how will they grow their advantage or convert it into something tangible". Engines can show optimal follow-up moves and
4. Recognise Human vs. Computer Differences: It's important to remember that engine evaluations, while "true," might not reflect the practical difficulties for a human opponent. As noted in The Exchange Sacrifice according to Tigran Petrosian, sometimes an engine might indicate an advantage, but a human player's position is still perfectly defensible or even difficult for the opponent to navigate. The psychological element, such as causing frustration to an attacker or changing the character of the game, is also a human factor that engines don't directly quantify.

Tigran Petrosian: A Masterclass in Positional Sacrifice

Petrosian's approach to material was revolutionary; he "refused to adhere to strict numerical values", greatly valuing the "mobility and long-term prospects of the pieces". He understood that a rook's conventional value could be less important than an "outpost for attack or defense" for a minor piece. His sacrifices were "unanimously praised in chess literature". Grandmaster Alex Fishbein notes that he had no idea "how many different types of exchange sacrifices Petrosian played".

As a famous proponent of the exchange sacrifice, Petrosian demonstrated this theme throughout his career. His unique style allowed him to explore "new paths that were inconceivable for most masters of his time".

Here are two classic examples from his career that exemplify his approach: (sourced from chessgames.com)

Reshevsky-Petrosian, Zürich 1953

• The Sacrifice: In a seemingly difficult position, Petrosian played 25...Re6!!, sacrificing an exchange (a rook for a minor piece). This "splendid offer" was highlighted by Mikhail Tal as one of the most amazing moves in chess history.
• The Purpose: This sacrifice immediately "break[s] the force of the attack". By giving up the rook, White is forced to give up their "only good minor piece," and Black gains an "unassailable post on d5 for his knight". This knight ties down White's forces and strengthens Black's bishop on the light squares, leading to a "total blockade".
• Computer Context: The book notes that "The engines will all tell you that White has a substantial advantage after 26.Bxe6, but the truth is that he has nothing after either black recapture". This highlights a practical human truth that transcends raw engine scores, demonstrating how Petrosian's deep positional understanding led to a sound, defensible position even when down material.

Tal-Petrosian, Riga 1953

• The Sacrifice: In this game, Petrosian, facing the aggressive Mikhail Tal, found himself in a "lost position" early on. He used an exchange sacrifice, involving the improbable journey of his Ra8 to f4(!). Mikhail Tal himself was impressed by Petrosian's 31...Rf4! sacrifice from their game in Gothenburg 1955.
• The Purpose: While "the exchange offer, albeit correct, should not have worked, as Black’s position simply did not contain enough resources," it crucially caused a "change in the character of the game" and "lure[d] Tal into mistakes". This demonstrates Petrosian's "universal style" and his ability to use psychology in addition to pure chess prowess. Tal, despite his brilliance, "did not like positions which required patience".
• Human vs. Computer: This game powerfully illustrates that even if a sacrifice isn't objectively "winning" according to an engine, its practical effect on a human opponent, especially one who dislikes defensive positions like Tal, can be decisive. As Boris Spassky famously remarked about Petrosian: "Petrosian reminds me of a hedgehog. Just when you think you have caught him, he puts out his quills".

When Sacrifices are Refuted: The Importance of Counterplay and Defence

While masters like Petrosian excelled at making positional sacrifices work, it is equally important to understand that not all such sacrifices are sound, and even thematic ones can be refuted by skillful defence. This demonstrates that even with a strong positional advantage, winning a "won" game can be very difficult.

Korchnoi vs. Petrosian, Moscow-Leningrad 1965:

(source: chessgames.com)

• The Sacrifice: In this game, 38...Rb4 by Petrosian was identified as "one of Petrosian's thematic exchange sacrifices".
• The Refutation: However, the sources note that "Korchnoi's refutation is quite skillful". It is suggested that Black's best option in this position would have been "passive defense" rather than the sacrifice. White's potential counterplay included a breakthrough on the kingside with g4, h4, and g5. This game is seen as Korchnoi beating Petrosian "at his own game".

In conclusion, it is best to understand that in addition to understanding the positional components of chess evaluation, it is important to understand a schematic understanding of the positional sacrifice. Also, while it is good to make the sacrifice and have an advantage, what would happen if the material was returned, and finally do not underestimate the psychological component of the sacrifice which cannot be captured by an evaluation function of a chess engine.