Section 8.3, listSprouts, Chomp and Grundy's game offer distinct proposed self-play challenges

Sprouts. Players join spots by noncrossing curves, add a spot on each new curve, and keep every spot’s degree at most three. The normal-play outcome conjecture for the standard $n$-spot opening remains open despite substantial progress with exact solvers (Čížek et al., 2026). Learning to exploit the evolving region structure, and to choose winning moves in intermediate positions, would be a stronger test than predicting opening outcomes from $n$ alone.

Chomp. A move removes a chosen square and all squares above and to its right; taking the distinguished corner loses. Strategy stealing establishes a first-player win on every nontrivial rectangle, but does not supply the winning moves (Berlekamp et al., 2001–2004). Larger boards and their irregular intermediate positions offer a challenge beyond solved special families; the analysis of Chomp continues to pose open problems (Nowakowski, 2025). The benchmark should test move selection and generalisation across shapes, not just the known opening winner.

Grundy’s game. A move splits one heap into two nonempty unequal heaps. Whether its nim-value sequence is eventually periodic remains an open problem (Nowakowski, 2025). This offers a test of whether self-play discovers useful structure in component values and how they combine. Testing unseen heap sizes and sums of heaps can distinguish such progress from memorising a finite table.