Indexing the archive…
Your Universe of Digital Possibilities
Call any three coin flips; Vega calls hers after hearing yours. A fair coin then flips on a running tape until one call appears. Every possible call has a beater, and her answering rule is three symbols long. The fair coin was never the game — the order of speaking was.
XY reads as a binary number: its bit k is 1 when the last k symbols of X equal the first k of Y. Four such overlaps give the exact odds that B appears before A in a fair-coin stream — HHH loses to THH 7 : 1 — and the same self-overlap AA sets the mean wait (HHT 8 flips, HTH 10). Against b₁b₂b₃ the beater is b̄₂b₁b₂.
The same circle as The Dice, drawn in time instead of space: THH beats HHT, HHT beats HTT, HTT beats TTH, TTH beats THH — and every other call is beaten by one of those four. Whoever speaks first has chosen a node on a ring with no top.
The exact central interval for K, the count of wins in n independent plays at win probability p — computed from the rules alone, before a single play. A record inside it is the rules working; a record outside it happens one time in twenty, and the band says so in advance. When the chance of each play is fixed before it is played but differs from play to play, the same band comes from the Poisson-binomial sum.
A fair coin cannot be beaten, but a call can: runs that overlap themselves (HHH, HTH) wait longer and lose to the answer built from their own beginning. The audit here is the absorption solve; the elegance is Conway’s four overlaps; they agree to the last digit. The Dice is the same non-transitive circle in space; The Walk owns the coin’s random walk; and The Host is the edition’s other lesson about who moves first.