Toppling Dominoes knock them over, one side at a time
Blue (Left) topples a blue domino, Red (Right) a red one, and either player may topple a green one. The domino falls east or west and takes every domino on that side with it. Whoever cannot move loses. Every row has an exact value (numbers, ↑, ⧾ tinies, nimbers, hot games), shown on the right. With hints on, the arrows above your dominoes are marked ✓ when the topple keeps the win and ✗ when it throws it away.
value of the row
Toppling Conjectures, rechecked
How the values are computed
A topple removes a prefix or a suffix of the row, so every position that can arise is a substring and a row of n dominoes has at most n(n+1)/2 followers. Each substring is valued once from its options and reduced to canonical form (dominated options deleted, reversible ones bypassed), so equal games get the same id. Outcomes are checked against a plain win/lose search that never looks at values.
Checked against the literature
The repository recomputes A. Fink, R. J. Nowakowski, A. N. Siegel and D. Wolfe, Toppling Conjectures, Games of No Chance 4, MSRI Publications 63 (2015) 65–76: the values in its figures, the f(G) = 1:G construction, the uniqueness of numbers, the tinies, the m forms of *m, the lemmas on infinitesimals, and Conjectures 22, 33–35 and 37–39, on every row up to a fixed length. Conjecture 39 fails in exactly the cases where b = c, because {a | b ‖ b | d} is then just the number b.