Single-heap Nim from 5 stones, last take wins. The winning strategy leaves a multiple of four; greedy always takes three (or the rest); take-one is the slowest legal policy.
Enabling structure of the arena (each move drawn once). Hover a move for its role. Enabling.
Leave a multiple of four stones.
Trace against auto. (stuck — Ω)
P-view
Unfolding against every legal Opponent continuation, up to the page bound. O branches fan out; P is a single reply. Click a reply count to expand folded Opponent options.
Always take three, or the remainder.
Trace against auto. (stuck — Ω)
P-view
Unfolding against every legal Opponent continuation, up to the page bound. O branches fan out; P is a single reply. Click a reply count to expand folded Opponent options.
Always take a single stone.
Trace against auto. (stuck — Ω)
P-view
Unfolding against every legal Opponent continuation, up to the page bound. O branches fan out; P is a single reply. Click a reply count to expand folded Opponent options.
The empty strategy Ω: Proponent never moves.
Trace against auto. (stuck — Ω)
P-view
Unfolding against every legal Opponent continuation, up to the page bound. O branches fan out; P is a single reply. Click a reply count to expand folded Opponent options.