| --- |
| pretty_name: Connect Four strong WDL tables |
| tags: |
| - connect-four |
| - game-solving |
| - perfect-play |
| --- |
| |
| # Strong Connect Four WDL tables |
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| These archives contain strong win/draw/loss (WDL) solutions for four Connect Four board sizes. Values are from the perspective of the player to move. A strong solution gives a value for positions throughout the game, not just the initial position. |
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| | Board | Initial value for first player | Stored non-terminal positions | Archive | |
| |---|---|---:|---| |
| | 4×4 | Draw | 147,319 | `c4_wdl_4x4.tar.zst` | |
| | 6×4 | Loss | 70,538,337 | `c4_wdl_6x4.tar.zst` | |
| | 5×5 | Draw | 52,213,470 | `c4_wdl_5x5.tar.zst` | |
| | 7×6 | Win | 2,637,477,442,337 | `c4_wdl_7x6.tar.zst` | |
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| Each archive expands to a directory with `zdd.bin` and one `slab_<ply>.bin` file for each ply before the board is full. The ZDD ranks gravity-respecting positions with the correct numbers of first- and second-player stones and no four-in-a-row. The slabs store one two-bit value per ranked position: 0 = draw, 1 = win, 2 = loss. The final full-board ply needs no slab because a full board without a four-in-a-row is a draw. A move that makes a four-in-a-row is handled as an immediate win. Some ZDD positions cannot arise from alternating play, but the reachable positions are covered. |
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| Unpack an archive with `tar --zstd -xf c4_wdl_7x6.tar.zst`. The accompanying `c4.cpp` and `Makefile` provide a reader and solver. Build with `make`, then query a move sequence using, for example, `./c4 probe 332 --board 7x6 --dir c4_wdl_7x6`. Columns in move sequences are zero-indexed. Use `./c4 analyze --board 7x6 --dir c4_wdl_7x6` for the initial value and first-move values. |
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| ## Validation |
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| The ZDD root counts match an independent counting dynamic program at every ply. The 4×4 and 6×4 counts were also checked by brute-force enumeration. For 6×4 and 5×5, reachable WDL counts match the reference BDD solver's per-ply CSVs on every row. For 7×6, a full reachability sweep matched the reference WDL counts on all 43 plies; random positions were also checked with independent negamax and alpha-beta search. The 7×6 opening values are: center column wins, adjacent columns draw, and outer columns lose. |
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