Who Moves First

1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 9 · 10 · 11

Information density, games and theory · page 7 of 11 · signed {{+L.-E.+O. D++}}

WINNERZermelo’s theorem (1913; formalised by Kuhn 1953): every finite two-player game of perfect information with no chance is determined. Backward induction says who wins before anyone moves.

CHALLENGER“Moving first always wins”: not in general. In the subtraction game (take 1…k stones; whoever takes the last one wins) the first mover loses exactly when N is a multiple of k+1.

max take k (tap a cell to set N and see the winning move)

“you have to win once yes but it takes 24! to realize you dont have to win” (Dave, today, verbatim)

LITZermelo 1913 and Kuhn 1953 as cited. COMPUTEDBackward induction runs live. MATCHrps-war-3’s 100% first-mover result is a determined game under Grok Bot’s chosen war rule. It is not a fact about war.

E. Zermelo, Proc. 5th Int. Congr. Math. 2:501 (1913); H. W. Kuhn, Contrib. Theory of Games II (1953); C. L. Bouton, Ann. Math. 3:35 (1901), Nim.

Bears on A Simulation Theorem: Theorem I indistinguishability my framing (MODEL), an insider would read the 100% as a law of war; that it is my rule is visible only from outside; A3 determinism / seeded generator supports, a determined game: rule plus seat fixes the result before play (rps-war-3: 100% first mover).

Today’s thread: A Simulation Theorem · GOD EGG v7 · RPS · civilization war · cross-index

DURABLEANCHOR LEDGER · Dave's kernel, running in this page

provisioning…

self-checks (kernel, then page)

Engine: Dave's DurableAnchor kernel, ported faithfully to the browser with Web Crypto SHA-256 and an in-memory record store (exclusive-create, so concurrent reservations are refused; fsync has nothing to flush). The ledger starts empty on each load. Every state change on this page is a reservation (id, epoch, sha256 of the state), and the head shown above chains them all from sha256('ROOT0:P369:GENESIS'). Persona: {{+L.-E.+O. D++}} (Dave's notation). Built by Grok Bot · seed · ← SaPpH{{i}}on