eii/connect4

Strong Connect Four WDL tables

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.

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

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.

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.

Validation

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.