[yiotri]

This adds HEX0N as a Python game, python_hex0n.

HEX0N is a two-player abstract placement game on an N×N board (5×5 by default). Players place squares, circles and triangles. A triangle that touches a circle and a square removes all three, and the same player then places a permanent, scoring hex on one of the cleared cells. Squares are a limited supply. When a triangle touches several eligible circle+square pairs, one is removed at random, which is modelled as an explicit chance node with up to 16 equally likely outcomes. Most hexes wins, with an optional tie-break on the largest connected hex group.

It is a placement game with stochastic outcomes and a depletable resource, which makes it a compact testbed for placement+conversion+chance.

Polished version & Benchmarks: https://github.com/yiotri/hextriad

Game type

SEQUENTIAL, EXPLICIT_STOCHASTIC, PERFECT_INFORMATION, ZERO_SUM, TERMINAL rewards.

Parameter	Default	Effect
size	5	Board width and height. 101 distinct actions on 5×5, 197 on 7×7.
tie_break	true	On equal hexes, the larger connected hex group wins; otherwise a draw.
opponent_pieces	true	A triad may use the opponent's circle or square (at least one must be the mover's); if false, both must be the mover's.

Actions are kind * N² + cell (square, circle, triangle, hex) plus one pass action, legal only when no placement is.

Changes

• open_spiel/python/games/hex0n.py: the game.
• open_spiel/python/games/hex0n_test.py: 15 tests. They cover random simulation with serialization on 4×4, 5×5 (all variants) and 7×7, a triad with and without a chance node, the 16-outcome maximum, pass legality, tie-break returns, etc.
• open_spiel/integration_tests/playthroughs/python_hex0n.txt, generated with generate_new_playthrough.sh.
• Registration in games/__init__.py, python/CMakeLists.txt, tests/pyspiel_test.py, plus a row in docs/games.md.

Verification

• hex0n_test.py: 15/15 pass. api_test.py and playthrough_test.py pass for python_hex0n.