Armageddon POP

September

Tuesday

2024

2024 09 03

Bad moves

It is widely believed, but not yet proven, that chess is a draw with best play. This belief stems from the extensive analysis of chess positions and games by both human experts and computer engines, which often conclude that optimal play by both sides leads to a draw. However, proving this mathematically is an entirely different challenge.

Current Status:

Human and Computer Analysis: For decades, grandmasters and advanced chess engines have analyzed countless games and positions. In most cases, they have found that with perfect play, neither side gains a decisive advantage, often resulting in a draw. However, these analyses are not exhaustive and cover only a fraction of all possible positions in chess.

Endgame Tablebases: Endgame tablebases have been generated for positions with up to seven pieces on the board, and these tables prove that many of these positions are draws with perfect play. However, these tablebases do not cover the full complexity of chess because the number of pieces is limited.

Computational Limits: The total number of possible chess positions is astronomically large (estimated to be around 10⁴⁰), making it impossible with current technology and algorithms to map out the outcome of every possible position comprehensively. Therefore, no complete proof exists.

Why a Proof is Difficult:

Complexity of Chess: Chess is an immensely complex game with a vast number of potential positions and sequences of moves. A proof that chess is a draw with best play would require either analyzing all positions or finding a general mathematical approach that demonstrates perfect play inevitably leads to a draw.

Game-Theoretical Approach: In theory, game theory suggests that deterministic games with perfect information (like chess) have a definitive result (win, lose, or draw) given perfect play by both sides. However, determining which of these outcomes applies to chess through game theory is infeasible without exhaustive analysis or an overarching mathematical breakthrough.

Summary:

It is not proven that chess is a draw with best play, but the consensus based on available evidence suggests it is likely. A formal proof would require either an enormous computational effort far beyond current capabilities or a new theoretical approach to understanding the game at a fundamental level.

Bad vs. Good Chess Moves:

Yes, there are significantly more "bad" chess moves than "good" ones in any given position. This imbalance is due to the fact that only a small subset of all possible moves leads to advantageous or at least neutral positions, while the majority of moves either worsen the player's situation or lead directly to a losing position.

Reasons Why There Are More "Bad" Moves:

Limited Good Moves: In most positions, the number of moves that maintain or improve a player's position is relatively small. Good moves are those that achieve objectives such as maintaining material balance, gaining a positional advantage, or creating threats against the opponent.
Abundance of Blunders and Weak Moves: There are many ways to make mistakes in chess, from obvious blunders (like losing a piece for no compensation) to subtle positional errors that gradually worsen the player's situation.
Complexity and Decision-Making: The complexity of chess means that in any given position, there are typically many legal moves, but only a few align with the strategic goals of the game.
Role of Calculation and Strategy: Good moves often require precise calculation and an understanding of both immediate and long-term strategic implications.

Practical Example:

In an average chess position, a player might have 20 to 40 possible moves. However, only 1-3 of those moves might be the best or optimal, keeping the position balanced or advantageous. The rest of the moves can range from slightly weakening (bad) to outright losing (very bad).