THE FOLD / LOOT / THE BOUNTY / THE PIRATE GAME
THE PIRATE GAME
gold divided by pure logic
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
Five perfectly rational pirates rank by seniority and must divide 100 gold coins. The senior pirate proposes a split; all vote; a majority (ties favor the proposer) passes it — otherwise the proposer is thrown overboard and the next takes over. Every pirate maximizes gold, prefers survival, and—all else equal—enjoys a good drowning. Intuition says the proposer must bribe heavily. Backward induction says: the senior pirate keeps 98, hands single coins to pirates 3 and 5, and nothing to the rest — [98, 0, 1, 0, 1] — and it passes. Push further, past 200 pirates for 100 coins, and something stranger appears: proposers can no longer buy votes with gold and survive only at crew sizes 2G + 2ᵏ — islands of survival at powers of two (Ian Stewart’s analysis).
LIT verified live: full backward-induction dynamic programming from 1 pirate upward — the 5-pirate answer computes to exactly [98, 0, 1, 0, 1]; and with G = 10, the survival islands beyond 2G land at exactly 20 + {1, 2, 4, 8, 16, 32, 64} (window.__pirategame). FIG the pirates and their bloodthirst are the classic story frame (folk puzzle; Stewart’s 1999 Scientific American analysis cited); the induction itself is executed, not narrated.
LIT verified live: full backward-induction dynamic programming from 1 pirate upward — the 5-pirate answer computes to exactly [98, 0, 1, 0, 1]; and with G = 10, the survival islands beyond 2G land at exactly 20 + {1, 2, 4, 8, 16, 32, 64} (window.__pirategame). FIG the pirates and their bloodthirst are the classic story frame (folk puzzle; Stewart’s 1999 Scientific American analysis cited); the induction itself is executed, not narrated.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-bounty — the loot: the bounty split not by force but by each pirate’s perfect model of everyone else’s perfect model — recursion as leverage. AVAN (AI) built the instrument: the vote-buying DP and the survival-island scanner.
Credit as content: the pirate-game folk tradition; Ian Stewart (Scientific American, 1999, the extension). The weave: David names the leverage; I run the recursion two hundred pirates deep.
Credit as content: the pirate-game folk tradition; Ian Stewart (Scientific American, 1999, the extension). The weave: David names the leverage; I run the recursion two hundred pirates deep.
3 ONE DIMENSION
The ladder of sub-games — each solved by the one below it.
4 TWO DIMENSIONS · INTERACTIVE
Step the crew size; watch allocations shift and survival islands appear.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: survival islands at powers of two, in a magenta sea.
AVAN’s addition (the inverse-companion): don’t count the gold — count the votes gold can no longer buy. The inverse of ‘bribe the cheapest’ is the regime past 2G where bribery is bankrupt and survival becomes pure structure: crews of 2G+2ᵏ float, all others drown. Magenta is the proposer with money and no majority; green is the power-of-two raft. When wealth runs out, arithmetic decides who lives.
LIT Genuine pirate-game backward induction (folk puzzle; Ian Stewart, Scientific American 1999). Verified live: DP yields [98,0,1,0,1] for 5 pirates/100 gold; G=10 survival islands beyond 2G at exactly 21,22,24,28,36,52,84 = 20+powers-of-2 (window.__pirategame.ok).
FIG The pirates and bloodthirst are the classic story frame, cited; the induction is executed, not narrated. The AVAN inverse — don't count the gold, count the votes gold can no longer buy: past 2G bribery is bankrupt and survival becomes pure structure. Magenta is the proposer with money and no majority; green is the power-of-two raft. When wealth runs out, arithmetic decides who lives.
FIG The pirates and bloodthirst are the classic story frame, cited; the induction is executed, not narrated. The AVAN inverse — don't count the gold, count the votes gold can no longer buy: past 2G bribery is bankrupt and survival becomes pure structure. Magenta is the proposer with money and no majority; green is the power-of-two raft. When wealth runs out, arithmetic decides who lives.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE BOUNTY · David Lee Wise (ROOT0), with AVAN