The illegal/invalid line (6.A.5, 6.D.8). The document separates an order that is impossible in this position from one this position allows that merely did not come off. The first is ignored and its unit is holding like any other; the second means the unit tried to leave and cannot be propped up where it stands. An army sent across water with a fleet on the route and no convoy ordered is the second; the identical order with nobody in the sea at all is the first. Guessing at this once cost four passing cases to buy one. Reading the document cost nothing -- it says so outright, in the note under 6.D.8 and again under 6.D.32. A support that only looked like a hold (6.A.5). "Supports A Yorkshire" and "Supports A Yorkshire - Yorkshire" are the same shape once parsed, and the case turns on the difference: the first holds a unit down, the second supports a move nobody can legally make. The extractor was throwing that away; it now keeps it, and the fixture is regenerated. The head of a cycle (6.F.22). Kruijswijk's resolver guesses that an order fails, sees what follows, then guesses the other way. Only the outermost order in a cycle may do that, because its answer is the one everything else was computed against. This engine let any order that reached the dependency list first declare the cycle its own -- and an inner one takes both guesses with its callers' provisional answers held fixed, gets the same result twice for that reason, and writes it down as settled. The cycle then becomes invisible: the backup rule never runs and Szykman's rule never fires, and the position resolves to whichever of its two consistent readings the search happened to walk into first. It had been doing this on every paradox and getting away with it, because on a first-order paradox both readings agree. Also carried across from the reference algorithm: an order that resolved itself while a nested call was away must not have the guess written over it. Three remain. 6.F.28 and 6.F.29 are sixth-order paradoxes -- the same twenty-six orders with one support between them, and the point of the pair is that the answer swings on it, where this resolver gives both the same answer. 6.G.19 the document itself gives three answers to, calls a little bit pedantic, and advises adjudicators not to offer at all.
340 lines
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Markdown
340 lines
18 KiB
Markdown
# Great Powers
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A browser rebuild of the classic seven-power negotiation game: one human
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against six computer powers, in one sitting.
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Not the name you expect, and [NOTICE.md](NOTICE.md) will make the argument at
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length once there is more to notice. The short version is the one the
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starship game already made on this site: the rules are free to rebuild, the
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trademark and the published artwork are not. "Great Powers" is what those
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seven were called at the time.
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## What this is, and what it is not
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**One human, six computer powers, one sitting.** The original is seven people
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over weeks. A hub with no traffic cannot deliver that, and nobody is going to
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wait months for six strangers — so the other six are played by the machine
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and a game is finished in an evening.
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**It still has to be a negotiation game.** A version where you simply write
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orders is a good movement puzzle and not this game. So:
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- **Both sides open.** Bots approach you with proposals; you approach them.
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Neither waits for the other.
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- **On real terms.** Offers are concrete and about this turn or the next few
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— support this move, keep out of that province, no attack until 1903 — and
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are accepted or refused on their merits, not by a die roll.
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- **Betrayal is a move, not a bug.** A bot can agree to support you and then
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not do it, and so can you. Bots remember who kept their word, tell each
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other, and price you accordingly. That is the game.
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The press is **structured rather than free text**: typed offers, deterministic
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reasoning, and no model anywhere in it. That makes betrayal auditable — you
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can read exactly why a power turned on you — and testable, which free text
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would not be.
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## The look and the sound
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**The map is the standard board's geometry, under the same licence as this
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project.** The outlines come from the diplomacy engine at
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<https://github.com/diplomacy/diplomacy>, which is AGPL-3.0, extracted by
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`tools/map.py` into `src/game/board.json`. Every colour and every mark drawn
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on it is ours; see [NOTICE.md](NOTICE.md).
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Three earlier attempts drew it from scratch and all three were worse.
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Dividing the plane by nearest province gives a tidy board that looks nothing
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like Europe. Drawing the adjacency graph gives something unimpeachable about
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the rules and not a map at all -- circles joined by lines. Fifty-six polygons
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placed by eye gives fifty-six islands. Drawing Europe accurately is real work,
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somebody did it properly, and they published it under a licence that invites
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exactly this.
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**Clicking still answers with the rules, not the picture.** A shape cannot say
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that a fleet on Spain's north coast may not enter the Gulf of Lyon while one
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on the south coast may, because both coasts are the same shape. So selecting a
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province lights up exactly where its unit may legally go, taken from the
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adjacency graph.
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**It gets the whole screen.** The other three games live in a four-by-three
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cabinet because the machines they are rebuilding did. This one is not
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rebuilding a machine, and seventy-five provinces plus somebody trying to talk
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you out of Galicia do not fit in a letterbox. The map takes the viewport.
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**The music is not cartoony, and that is the point.** It is 1914: serious,
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and intense. The joke of this game is that something charming to look at is
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the cruellest thing on the site, and the score is what says so.
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**And the turn should be heard.** Orders resolve in silence in every online
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version of this game, which is a waste of the one moment anybody cares
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about. Armies grinding into each other, guns at sea, a convoy escorting
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something across, a unit being built, a unit falling back -- each of those is
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a different noise, generated by the synth like everything else on this site.
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**The endings get their own.** This game does not end in a win or a loss, it
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ends in one of four things, and they do not sound alike:
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- **the solo** -- eighteen centres, and the only unambiguous victory there is;
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- **elimination** -- your last centre gone, which can happen in 1903 and
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leaves you watching;
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- **the draw** -- nobody reaches eighteen and the survivors agree to stop.
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This is what actually happens most of the time, and it is neither a win nor
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a loss, so it cannot borrow either of their tunes;
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- **somebody else's solo** -- you are still on the board and it is over
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anyway, which is the bleakest of the four and should sound like it.
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## The board
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Seventy-five provinces, two adjacency graphs — an army walks the land, a
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fleet follows the water — and three provinces with two coasts that do not
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connect, where a fleet has to say which one it is on.
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The topology is a fact about a published game and free to use. The artwork is
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not, and there is none here: the map this game draws is generated from the
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data, the way the cave game's dodecahedron is.
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`npm test` checks the board against itself. The one that earns its keep is
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symmetry: an adjacency list this size is typed by hand once and wrong in
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three places unless something looks. It found the Skagerrak wired to the
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Baltic on the first run — which would have quietly opened a back door into
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the Baltic and made Denmark worthless.
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## The published test cases
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`tools/datc.py` turns the Diplomacy Adjudicator Test Cases into
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`src/game/datc.json` -- the orders and their annotated outcomes, not the
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document's prose, which is Lucas Kruijswijk's writing. Every one of the 176
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published cases is parsed and run.
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| Section | | Passing |
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| --- | --- | --- |
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| 6.A - 6.G | movement | 136 / 139 |
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| 6.H | retreating | 18 / 18 |
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| 6.I | building | 7 / 7 |
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| 6.J | civil disorder | 13 / 13 |
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They are the reason this adjudicator is worth trusting: they found that
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orders were never validated, that the paradox rule did not terminate, that
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civil disorder was measuring the wrong distance, and that five of my own
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hand-written cases rested on a support Paris cannot give.
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Three cases are excluded rather than failed. 6.A.6, 6.B.10 and 6.B.11 state
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their setup in prose -- "Germany has a fleet in London" -- and the fixture is
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built from order lines, so it cannot carry a unit nobody ordered.
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Three are known deviations, written down so they are not rediscovered as
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surprises:
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| Case | What it is |
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| --- | --- |
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| 6.F.28, 6.F.29 | Sixth order paradoxes: the same twenty-six orders with one extra support between them, which the document uses to show that the answer swings on it. The resolver gets five of the six sub-paradoxes right in both and the sixth wrong, and gives the same answer to both positions when the point is that they differ. These are positions nobody assembles by accident. |
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| 6.G.19 | Whether an unnecessary fleet in a convoy chain signals intent. The document gives three different answers by edition, calls the question "a little bit pedantic", and advises that web adjudicators should not offer the order at all -- which is the line this one takes. |
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### What the failing cases were worth
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They found three real faults, which is the whole argument for running
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somebody else's tests rather than only your own.
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**The illegal/invalid line (6.A.5, 6.D.8).** The document separates an order
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that is impossible *in this position* from one this position allows that
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merely did not come off. The first is ignored and the unit is holding like
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any other; the second means the unit tried to leave and cannot be propped up
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where it stands. An army sent across water with a fleet on the route and no
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convoy ordered is the second (6.D.8); the identical order with nobody in the
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sea at all is the first (6.D.32). Guessing at this once cost four passing
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cases to buy one. Reading it properly cost nothing.
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**A support that only looked like a hold (6.A.5).** "Supports A Yorkshire"
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and "Supports A Yorkshire - Yorkshire" are the same shape once parsed, and
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the case turns on the difference: the first holds a unit down, the second
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supports a move nobody can legally make. The extractor now keeps the
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distinction; it was losing it.
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**The head of a cycle (6.F.22).** Kruijswijk's resolver guesses that an order
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fails, sees what follows, and guesses the other way. Only the *outermost*
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order in a cycle may do that, because its answer is the one everything else
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was computed against. This engine let any order that reached the dependency
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list first declare the cycle its own -- and an inner one takes both guesses
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with its callers' provisional answers held fixed, gets the same result twice
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for that reason, and records it as settled. The cycle then becomes
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invisible: the backup rule never runs, and the position resolves to
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whichever of its two consistent readings the search walked into first. It
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had been doing that on every paradox and getting away with it, because on a
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first-order paradox both readings agree.
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Sections H, I and J -- retreating and the winter -- have engine code but no
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harness yet; their cases are shaped differently and need one.
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## The bots
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`src/game/evaluate.ts` prices a position and `src/game/bot.ts` plays it.
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Everything a power does comes out of two numbers, and they are deliberately
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few: when a power turns on you, you are entitled to know what it thought it
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was getting and be furious about the price rather than confused by it.
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`chooseOrders` returns its reasoning as a list of sentences for exactly that.
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Centres are the only thing that counts. Units are how you get them and are
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worth nothing in themselves -- a power with eight units and four centres is
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losing, and will have four units by the winter.
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Two things the tests had to teach it. It garrisons a threatened centre it is
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already standing on, because scoring only *moves* had it defending Berlin by
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marching the Munich garrison there -- abandoning one centre to save another
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of identical value. And it never shoves at its own countryman, which has no
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strength at all and is two units wasting a turn on each other.
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The price of breaking a promise is **how far this power trusts the partner**,
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not how far the partner trusts it. Pricing it the other way round gives a
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power that has been lied to four times a high cost of retaliating, because it
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has been scrupulous itself and is still well thought of, which is exactly
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backwards. An ally who has already betrayed you is worth nothing to protect.
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Bots open negotiations rather than only answering them. `propose()` works
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from the plan the power has already made: it decides what it wants to do this
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turn, notices where that will not work alone, and goes looking for somebody
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who could make it work. Help taking something defended, first; then a quiet
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border over ground neither of them owns; then peace outright, when a
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neighbour is over your centres and your ambitions are elsewhere. Three
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approaches a turn at most, because six powers all talking at once is a
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mailstorm rather than a negotiation.
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Each overture carries what the power actually says, so it can be put in front
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of a human as a message rather than as a form.
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**A power will offer a quiet border to somebody it is attacking somewhere
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else**, and that is deliberate. Germany marching on French Belgium while
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suggesting both sides leave Burgundy alone is not a lie and not incoherent: a
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promise about Burgundy is a promise about Burgundy, and it will be kept to
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the letter by somebody who is robbing you at the same moment. A bot that
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refused to make that offer would be playing a politer game than this one. It
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will not, however, ask the power it is attacking to *help*, or offer it peace
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while the orders say otherwise.
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## Giving orders
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Clicks on the board, because that is where the question is. Select a unit,
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pick a verb, and the provinces the next click will accept light up -- so
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nobody writes a move the rules were never going to allow, and nobody has to
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learn a notation to find that out.
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Everything offered comes from the rules rather than from the map, which is
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the same split the map itself is built on. A fleet on the north coast of
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Spain is drawn identically to one on the south coast and can go to entirely
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different places; no shape can express that, and the highlight has to.
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Orders are drawn where they are given: an arrow to where a unit is going, a
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dashed line to what a support is holding up, a ring round a unit that is
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staying. The list beside the board says the same thing in the rules' own
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words, because an arrow cannot tell you that the support you meant for Vienna
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is being given to Budapest. Anything the rules will not take is struck
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through in the list as it is written, rather than after the turn.
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## The turn
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`src/game/game.ts` is the loop, and it has no interface attached on purpose:
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a whole game can be played out in a test from the opening to whatever end it
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finds. That is the only way to answer the question that actually matters
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about the bots -- not whether each order looks sensible, but whether seven
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powers left alone reach a conclusion.
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Spring orders, retreats, autumn orders, retreats, then the winter, which is
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the only phase that changes who owns anything.
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Before the orders, everybody talks. Computer powers approach each other,
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answer on the merits, and what they agree binds that turn and is judged at
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the end of it. Approaches to the human are handed back rather than answered
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for them.
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**The game is called at the end of 1912.** Diplomacy has no clock of its own:
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it ends on eighteen centres, or when the players agree to stop -- and
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agreeing to stop is a conversation seven computer powers are never going to
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have. Left alone they reach a standoff and hold it, which is what a table of
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equally cautious players does and is why real games are called.
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So: eighteen centres wins outright, and if nobody has them by the end of 1912
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the survivors draw. Twelve years is a long evening and a real tournament
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length, and **the draw is a proper ending here rather than a failure to
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finish** -- it is the commonest way this game actually ends.
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Worth saying plainly: seven bots left alone draw. They take centres off each
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other now, which they could not do at all before, but none of them breaks
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away to a solo. Beating six of them is the game.
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## The other two phases
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A beaten unit that finds somewhere to stand is a nuisance for years; one that
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does not is gone. And the winter is where a good spring turns into a bigger
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army, or does not. Both are decisions, and both were being taken *for* the
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player while the rest of this was built, which quietly removed half the
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consequence of the turn they had just played.
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They are offered as places rather than as a notation, for the same reason the
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orders are: the rules already know what is allowed, so the interface only
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ever offers what is. A beaten unit lists the provinces it may fall back to and
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nothing else; the winter lists the home centres that are yours and empty, with
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a fleet offered only where a fleet could sit.
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The game steps past anything with no decision in it. A retreat phase where
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none of your units was thrown out, or a winter where your centres and units
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are level, is not a choice -- it is a screen asking you to press Done.
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## Writing a support
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Support is the order the whole game turns on, and it was the order this
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interface was worst at taking.
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The rule is that the supporting unit must be able to reach the province the
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supported unit is *going to* -- not the province it is standing in. The board
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was offering the wrong set: only units standing next door. So Vienna could
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not support Venice into Tyrolia, which is a perfectly ordinary order --
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Vienna and Tyrolia touch, Vienna and Venice do not -- and there was no way
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to say it. It also offered support to hold for units too far away to prop
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up, wrote the order anyway, and let the adjudicator quietly turn it into a
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hold after the turn was submitted.
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That question now lives in `src/game/targets.ts` with the rest of the rules,
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where it is eight tests rather than a closure in a component.
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The second half was that a stray click threw away a half-written order. You
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picked Support, picked the unit to help, missed the destination by a
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province, and the whole thing silently became a fresh move somewhere else.
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A two-part order now stands its ground and says no; clicking the unit giving
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the order takes you back to the start of it. And the unit you picked to
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support is marked on the board in a different colour from the unit giving
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the order, because otherwise the second half is written blind.
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## Ordering a convoy
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The rules have had convoys all along -- fifty of the DATC cases are about
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them, including the paradoxes -- but for a while you could not order one.
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The board offered an army the provinces it could walk to, and a crossing is
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by definition not one of those, so the army's half of a convoy could not be
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written. The fleet's half could, which made it worse: the verb was there and
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did nothing anybody could use.
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An army on a coast is now also offered the coasts a chain of crewed seas can
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reach, drawn in blue and with long dashes so a crossing does not look like a
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march. A sea counts if there is a fleet standing in it, whoever owns it. A
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fleet that has not been ordered to convoy still counts: it is a thing that
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could be arranged, which is what the negotiation is for, and the adjudicator
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will bounce the crossing if it was not.
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That is deliberately not the question the rules ask when they *judge* a
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convoy, which is whether water could ever get there. That one says yes to
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most of Europe. Offering thirty provinces because a chain of fleets is
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conceivable would be worse than offering none.
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Clicking a blue coast writes the move `viaConvoy`, which is not a formality:
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the rules allow a unit to be convoyed to a province it could have walked to,
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and the two orders resolve differently.
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The two halves are written separately, as they always have been, and the
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order list says so while only one of them exists -- `A Yorkshire → Norway`
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sits there in red until `F North Sea convoys Yorkshire → Norway` joins it,
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and then both go black. Nothing was added to make that happen. The validator
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already knew.
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## Still to build
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- bots strong enough to solo against each other, not only to draw
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- the music, the battle sound, the four endings
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