Game AI & search

Minimax that skips branches which cannot change the result; with iterative deepening, PVS and aspiration windows it is the core of classical adversarial search.

Grows a search tree one simulation at a time, picking visits by a bandit rule (UCT or PUCT) and backing up averages; the search behind AlphaZero.

A fixed-size, lossy hash table of search results keyed by a state hash; gives ordering and cutoffs for repeated states, shared lock-free between threads.

The heuristics that make alpha-beta and branch-and-bound fast: try likely-best candidates first (TT, captures, killers, history) and skip or reduce the rest (null move, LMR, futility).

Efficiently updatable neural network: a huge sparse first layer whose output (the accumulator) is patched per move, then tiny int8 layers; fast neural eval.

Feed an accelerator from tree search driven by a learned evaluator: virtual loss gathers leaves within a tree, parallel searches fill batches, an async queue overlaps CPU and GPU.

One 64-bit word per set of up to 64 items, so set algebra becomes shifts, ANDs and table lookups; magic bitboards give ray queries in one multiply.

A state's hash is the XOR of one random 64-bit key per (item, slot) fact that holds in it, updated in a few XORs per change.

Pack a state of a sparse grid into a few fixed bytes (24 for chess: occupancy bitmap plus nibbles) for training data and dedupe, with canonical symmetric forms.