Partial 4131: White to move

All results are relative to White. Black-to-move source positions are rotated 180 degrees and their colors exchanged. Bounds and unknown remain distinct.

Opposite material: White to move

Full count | Special positions | Back to statistics


Full count

All positions

White to move. Captures included. Percentages use this category's legal total.

Win: 1.419.352.550.158 (47.8%)
Draw: 1.231.102.838.348 (41.5%)
Lose: 62.581.813.971 (2.1%)
Loss or draw: 10.744.272.426 (0.4%)
Draw or win: 236.453.052.420 (8.0%)
Unknown: 6.947.169.177 (0.2%)

Exact value: 2.713.037.202.477 (91.4%)
Legal: 2.967.181.696.500

Non capture positions

White to move. White has no capture. Percentages use this category's legal total.

Win: 194.194.620.279 (26.4%)
Draw: 286.813.582.710 (39.0%)
Lose: 609.880.929 (0.1%)
Loss or draw: 10.744.272.426 (1.5%)
Draw or win: 236.453.052.420 (32.1%)
Unknown: 6.947.169.177 (0.9%)

Exact value: 481.618.083.918 (65.5%)
Legal: 735.762.577.941

Fully quiet positions

White to move. Neither side has a capture. Percentages use this category's legal total.

Win: 65.836.160.696 (21.9%)
Draw: 113.092.426.550 (37.6%)
Lose: 67.496.896 (0.0%)
Loss or draw: 7.584.066.972 (2.5%)
Draw or win: 107.959.433.883 (35.9%)
Unknown: 6.085.053.582 (2.0%)

Exact value: 178.996.084.142 (59.5%)
Legal: 300.624.638.579

Saved slices: 1766; mirrored slices: 0. Invalid or unreadable files excluded: 0. Counts cover saved and color-reversed mirrored slices; examples sample saved slices. Header and file length checked; payload checksum and WDL correctness are not verified by this report.

Random validation examples: single-board viewer | JSON (14128 positions; 0 slices with fewer than eight).

Example search: sampled. Examined 999556 of 5246250600000 saved physical-board indexes (366496 legal, 119102 double quiet). Large reports inspect at most 1000000 indexes in evenly spaced windows across saved slices. An absent example does not prove that the category is absent.

Only exact partial WIN/DRAW/LOSS values qualify as example results. Bounds and unknown alternatives remain distinct. DPART002 blocks used for examples have their block checksums checked; full-file checksums and independent WDL correctness are not verified.


Special WDL positions

One example per category. Every starting position is double quiet: neither side has a capture. Results and move outcomes are relative to the player to move in the diagram. Kings have a double ring.

All diagrams and move results are for White to move.

Pip count means remaining rank distance to promotion (kings: zero). Highest pip count puts men nearest their starting ranks; both sides must simultaneously attain their material's maximum.

Only move to win

At least three legal moves; exactly one wins and every alternative draws or loses.

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White to move: Win. Pip count: White 36, Black 27.

W:WK44,47,48,49,50:BK1,2,3,4

MoveResult
44-39Draw
44-33Draw
44-28Draw
44-22Draw
44-17Draw
44-11Draw
44-6Draw
44-40Loss
44-35Draw
47-41Win
48-42Draw
49-43Draw
47-42Draw
48-43Draw
50-45Draw

Only move to draw

At least two legal moves; exactly one draws and every alternative loses.

1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950

White to move: Draw. Pip count: White 36, Black 27.

W:WK3,47,48,49,50:B1,2,4,K25

MoveResult
3-8Loss
3-12Loss
3-17Loss
3-21Loss
3-26Loss
3-9Loss
3-14Loss
3-20Loss
47-41Loss
48-42Loss
49-43Loss
50-44Loss
47-42Loss
48-43Draw
49-44Loss
50-45Loss

Mutual zugzwang

On this same board, White to move loses and Black to move loses.

No qualifying example proved from the available WDL data.

Whoever moves wins

On this same board, White to move wins and Black to move wins.

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White to move: Win. Pip count: White 36, Black 27.

W:WK45,47,48,49,50:B1,2,3,K4

MoveResult
45-40Win
45-34Win
45-29Win
45-23Win
45-18Loss
45-12Loss
45-7Loss
47-41Loss
48-42Loss
49-43Loss
50-44Draw
47-42Loss
48-43Loss
49-44Draw

Unique winning sacrifice

Exactly one of at least two moves wins; every compulsory reply captures the piece offered by that move.

1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950

White to move: Win. Pip count: White 36, Black 27.

W:WK28,47,48,49,50:B1,2,4,K25

MoveResult
28-22Draw
28-17Loss
28-11Draw
28-6Draw
28-23Draw
28-19Draw
28-14Loss
28-10Loss
28-5Draw
28-32Draw
28-37Draw
28-41Draw
28-46Draw
28-33Draw
28-39Win
28-44Draw
47-41Draw
48-42Draw
49-43Draw
50-44Draw
47-42Draw
48-43Draw
49-44Draw
50-45Draw

Promotion trap

A promotion draws or loses, while a non-promoting move wins.

No qualifying example proved from the available WDL data.

Both sides at highest pip count: win

Both sides attain their maximum pip count; the player to move wins.

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White to move: Win. Pip count: White 36, Black 27.

W:WK46,47,48,49,50:B1,2,3,K4

MoveResult
46-41Win
46-37Win
46-32Win
46-28Win
46-23Win
46-19Win
46-14Win
46-10Loss
46-5Win
47-41Draw
48-42Draw
49-43Draw or win
50-44Draw
47-42Draw
48-43Draw
49-44Win
50-45Win

Both sides at highest pip count: loss

Both sides attain their maximum pip count; the player to move loses.

No qualifying example proved from the available WDL data.

White wins with Black on its starting rank; White closest to home

White to move wins, with all Black pieces on squares 1-5. Among the qualifying positions inspected, select the greatest White pip count (men closest to their starting rank).

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White to move: Win. Pip count: White 36, Black 27.

W:WK46,47,48,49,50:B1,2,3,K4

MoveResult
46-41Win
46-37Win
46-32Win
46-28Win
46-23Win
46-19Win
46-14Win
46-10Loss
46-5Win
47-41Draw
48-42Draw
49-43Draw or win
50-44Draw
47-42Draw
48-43Draw
49-44Win
50-45Win

Some dependency probes were unavailable or exceeded the memory budget. Unknown alternatives were not treated as draws; categories without an example may be incomplete.

The Black-starting-rank category additionally inspected 0 candidate boards, working outward from White's starting rank, with a limit of 20000. It shows the closest proven winner found; unavailable results remain unresolved.

Example reader: 3198 block reads; 0 invalid or unreadable dependency files/blocks excluded.