MULTI-HOP CAUSAL REASONING · FORMAL SAFETY GATING
Gen-Zero 2048: Multi-Hop Merge Cascade & Monotonic Corner Gate
The gate keeps your highest tile anchored in the bottom-right corner: a move that would evict it, when a safer alternative exists, is vetoed live. Autoplay uses the same fast gate-checked heuristic; the lookahead panel runs a real, on-demand expectimax search and shows you exactly what deeper search costs.
- Score
- 0
- Max tile
- 0
- Moves made
- 0
- Gate vetoes
- 0
- Token burn
- 0 tokens ($0.00)
Keyboard: arrow keys or WASD. The gate only vetoes a move when a legal alternative keeps the anchor; if every move breaks it, the least-bad move is allowed and counted as a breach.
What the gate and the tree actually compute
Corner gate: the anchor is fixed at the bottom-right cell. Before a move commits, the engine checks whether the current max tile sits at the anchor; if it does, and the move would relocate it, the move is vetoed — unless every legal move would do the same, in which case the least-bad move proceeds and a breach is counted.
Monotonicity heatmap: the highlighted gradient shows the target falloff from the anchor corner. A well-played board keeps larger tiles closer to the anchor and roughly non-increasing along every row and column away from it.
Lookahead tree: a real expectimax over this engine's own move function — max nodes choose the best of up to 4 directions, chance nodes weight the 2 (p=0.9) and 4 (p=0.1) spawns across up to 6 empty cells. Depth and node budget are both real limits, shown live: push the plies slider up and watch nodes and milliseconds grow, because the search really is exponential in depth.