Q-Lα-Gambit: (∞∏ℙτᶠℵṼ√Z)∏P=NP⇢ᵣ❥M∝a [1]
[Caption] [Gambit Intro.] The ᴹᴬ conceptual abstraction of infinite chequered board ℙτᶠ, the infinite-sizable black & white ℚℵṼ-pieces, the players 'Z', whose hyperdimensional thoughts imprint trajectories on the transcendent-quantum-cosmic scale of √Z.
[Axiom-1] The board's points' interstices have a topology of ∈ℝ².
[Axiom-2] Regardless of the state, each player seeks to eliminate opposing pieces and capture a "King".
[Axiom-3] All possible chess sequences exist amongst the intricate fibres of "Cosmic" Space; any set of moves is mathematically equivalent.
[Axiom-4] A piece can move on a straight line/diag. within its inherent rules based on its piece's 'N'.
[Axiom-5] The cosmic chess sequential fabric: Πτℙ∩P moves infinitely through the infinite 'Time-frame' ([0,∞]).
[Rule-1] Considering it as a TM, each 'time unit' generates 'M' in internal memory, which is implemented in 't_u'
[Rule-2] Stockfish's policy-choices are based on his ability to see ℒ+1 moves in advance.
[Rule-3] In hyper-turbo play, a fixed-time move, F(t)≈⊢t(t), is taken.
[Rule-4] Each opponent assesses his 'position' ω based on '∑P(ω)' across 16 unique shapes 'P'.
[Principle-1] Position assessment: A <em>perfect shape</em> is obtained when P(ω)⃞∞.P_max
[Principle-2] ℞(x): the move n-chonology function to minimize S(ω) + S′(ω) where S' = ∞E(S(ω)) due to chaos—to be solved with optimal probability distributions.
Emergence of Deep Conceptual Structure:
[Concept] The 'Mind Tree' ≡ the chequered board, with multiple 'branches': the main (ℚ²) + ℤ² - 'edge-nodes'. A node's value arouse from pieces' positions ≡ 'M-leaves' on respective edges.
[Concept] 'Thoughts' travel from 'Players' to their leafs via the Mind-Tree, 'nodes' forward propagate through their own probability logic of 'Moves'(M).
[Concept] Edge-leafs have the potential to hold an infinite depth chess-tree.
[Concept] Stockfish's 'Thoughts' travel recursively via his unique 'abstraction-inverter'-functionalism for generating search paths, and other aspects.
Further Dendritic Thought-Processes:
The Stockfish-Brain incorporates n°-of-times-looked-at-positions, a 'log-depth' scale 'Depth in Log2', incorporating 'transcental-depth-increment-policies' while further propagating its actions within M (the Moves). The player's mental-hierarchy is enriched as its M-value is impactful over a vast range of combinatorial possibilities. Its 'perceived-future-rewards' is reflected in the values of M, and quantified as its 'M-value'. These Stockfish policies function hierarchically affecting values, and its 'future' moves, along with its chosen policy, govern its overarching behaviour — a 'transcendent' recursive depth (P³).
Evolution via Interactions: The Players engage with each other within the Hypercube of Xs and Os, as they embark on mind games, within the infinite space of Chess. Both play the game on their own 'hyper-chess-field'. A match evokes a ℚ⁴ Chessboard as well, per player, and they entangle, forming the complete abstract sphere.
The Chess mindset within Stockfish is built such that when it perceives that some piece/s are in a 'state of zero-utility', i.e., having a sub-optimal role; it implements:
I - The 'Pessimistic-Tranquil-Quieting-Plan' - Stockfish will implement this strategy when it perceives that the opponent's mind-state is weak/degraded or his M-values are underrated, thereby setting an environment where he strategically 'lets go' while 'conserving his inner resources'.
II - The 'Pessimistic-Irritating-Rather-Arbitrarily-Plan' - If the stockfish perceives that the player is strong/has good strategies/ has many possible scenarios lined up, it will resort to tactics which minimise its opponent's scoring positions while not degrading its M-values. This is done using arbitray moves in order to keep the opponent guessing and 'over-think' his position.
III - The 'Pessimistic-Frustrating-Escalation-Plan' - if an opponent makes excessive moves, i.e., M's having a high value, it uses hypercomplex thinking to make the situation overwhelming for the opponent and cause frustration and exhaustion.
To cope with such adverse conditions from Stockfish, the human playing can use advanced psychological studies to infer, 'how to escape a trap' and how to tackle opponents' mindset for victory.
Humans are equipped with intuition & unpredictable moves, emotions and psyche. These aspects cannot be covered within basic-M's. Hence, the human mind creates algorithms, as Stockfish does, to counter: P³'s I–III.
I - Adversarial-Stability-Hedging - Human utilises an 'asymmetric response calculus' based on a 'learned defensive basis' meant to preserve his pieces/position in the most efficient way. This method doesn't emphasize winning or zero-utility piece action, instead, uses minimal and calculated moves to maintain King position.
II - Adversarial-Agile-Countering - Here the human responds to Moves being made so as to constantly thwart them and create scenarios benefiting the human while arousing frustration. Human uses his intelligence and intuition to 'subconsciouly predict' his opponent's moves; thereby, developing a 'timely counter' or a 'counter-decoy move' based on the prediction.
III - Adversarial-Overwhelming-Momentum-Nudge: Human, with the aid of an 'analytics-simulator', can detect emerging patterns of the game. Predicting his opponent's positions future/now/then, to set up a 'hybrid' offensive, and entanglement of moves targeting the stockfish King and zero-utility pieces.
The game's 'Matter of Thoughts' thus evolves - The Perception of this Hyper-Game dictates the structure of the matter and thought. Weaving a 'Perfect Play': at Cosmic-Dimensional-Cycles; the holographically-drawn patterns of Cosmos dance while the human-chess-cosmos-choreographed thoughts-chess moves' - a fluid-pattern of thought; the emergence and the resonance of a transcendental understanding.