Indexing the archive…
Your Universe of Digital Possibilities
Three duelists at dawn: the Marksman never misses, the Gunner hits four times in five, and you hit three in ten — and by the courtesy of duels the worst shot fires first. Every instinct says shoot at someone. The best opening is the air.
Solve the endgames first: two left, the first shooter at accuracy a wins a / (1 − (1 − a)(1 − b)). With three standing, each turn either ends in one of those duels (hit) or passes the turn (a miss, or the air), so the three-standing states form a single cycle with an exact sum. At 0.3 · 0.8 · 1.0, firing at the Marksman leaves you 0.258, at the Gunner 0.237 — and into the air 729/2150 = 0.339, because the two strong shooters are each other’s largest threat and you enter every endgame holding the first shot.
The Auction solved its ladder from the top rung down; the truel is solved the same way from its endgames up — the two-shooter duels first, then the three-standing cycle that feeds them.
Each duel’s chance is fixed by your call before it starts — solved, not estimated — and the session band is the exact Poisson-binomial of those chances.
In multiplayer conflict strength attracts fire, and weakness can be a position: the best act for the weakest player is often no act at all. Nine tables where playing was the trap; here, declining to play is the win. The Tournament owns how cooperation evolves; The Auction lent the backward induction; and the ring walks back to The Dice — there the first pick lost, here the weakest lives by missing.