collin/mahjong

e8590b15370e05e38015d39cf1b9fb3cfb0fd694 / README.md

1	# 台灣麻將 — four-player mahjong, on one touchscreen or over the wire
2
3	Sixteen-tile Taiwanese mahjong for four people sitting around a single laptop.
4	All four hands are on screen at once, each rotated to face its own edge and
5	each face down until its player taps it — the piece of card everybody used to
6	lay over their strip, done by the table itself. Every label is Chinese with
7	English underneath; the tiles themselves stay Chinese, because that is what the
8	tiles say.
9
10	開始 is the only button on the lobby (繼續對局 above it when there is a
11	save), and it says nothing else, because the table says the rest — three strips
12	offering 坐下 and a QR in the middle of the felt. It deals
13	you in at the bottom edge with the computer on the other three, on this device,
14	without a word said to any server. Everything people call a mode is that table
15	with different hands changing hands, one at a time, mid-game:
16
17	- somebody sits down at this screen and **taps a hand the computer has been
18	playing** — the tiles turn over and are theirs;
19	- somebody scans the tile lying in the middle of the felt — it says SCAN
20	and JOIN, and it gets knocked about by the discards like everything else
21	there — or a particular seat's own QR from its gear, and takes that hand onto
22	their phone;
23	- somebody opens the invite link from three cities away and takes one from
24	their own laptop, with the table turned so their seat is the near edge.
25
26	Each of those swaps one seat and redeals nothing, and each undoes: a hand goes
27	back to the computer with a tap, and one that loses its device gets given back
28	to the computer on its own so the table never stops. See
29	[one table](#one-table), [computer players](#computer-players) and
30	[playing online](#playing-online).
31
32	```
33	npm install
34	npm run dev # then open the browser full-screen (F11)
35	npm test # rules engine, the bots, and 200 randomly-played hands
36	```
37
38	## Screen layout
39
40	```
41	┌──── 對家 (rotated 180°) ────┐
42	上家 (rotated 90°) │ wall, and the discard pool │ 下家 (rotated −90°)
43	└──── 自家 (upright, near you) ┘
44	```
45
46	Seat 0 is the bottom edge, and play runs 0 → 1 (right) → 2 (top) → 3 (left),
47	which is the normal counter-clockwise 東南西北 order.
48
49	Each strip shows, from the player's edge inwards: nameplate (seat wind, 莊
50	marker, 聽 badge, chip count) → concealed hand → action buttons → melds and
51	flowers. Discards are not in the strips: they are thrown into the middle and
52	stay there for the hand, the way they would be on a table. (A phone has no
53	middle to throw into, so the compact layout keeps a discard row per seat — see
54	[on a phone](#on-a-phone).)
55
56	## Playing
57
58	- Your hand is face down at a shared screen, and a tap turns it over. It
59	covers itself again when the hand is dealt and when your turn ends — the two
60	moments the tiles stop being needed, and without them a hand turned over once
61	stays turned over all evening, which is the same as never having covered it.
62	蓋牌 beside 理牌 puts it back sooner. While it is covered the only button the
63	strip has is 看牌: every other one names a tile — 打出五萬, 吃 with these two
64	— and would say through the card what is under it. The 看牌 of whoever the
65	table is waiting on wears a gold ring, since whose go it is was never a
66	secret. Nothing is covered where the screen is playing one hand, which is a
67	screen that belongs to one player — three computers and you, or your own
68	tiles on your own device.
69	- The tile you just drew is held apart from the sorted hand with a gold ring
70	and a 摸 label, instead of being sorted invisibly into it. It merges into the
71	hand once you discard. 補花 replacements and kong replacements are marked the
72	same way.
73	- The wall is drawn in the centre as a square of four staggered sides, laid
74	out like a `#` the way it is built on a real table — every corner covered by
75	one wall carrying past the end of the next. All 144 tiles, at the size of the
76	tiles in your hand, because they are the same tiles. The gold stack is the
77	break point you draw from, and where that is depends on what the dealer threw:
78	stacks shrink to a single tile and then vanish as they are used, so the gap
79	opens wherever the dice opened the wall and grows from there. The 16-tile 底牌
80	tail at the other end is where kong and flower replacements come from, so the
81	square is eaten from both directions at once. See
82	[擲骰](#擲骰--where-the-wall-is-broken).
83	- Discard — drag a tile out of your row and it comes up out of your hand and
84	follows your finger anywhere on the table; let go and it goes in, from where
85	you let go and at the speed you let go at. Dragging along the row is still
86	arranging your hand — which of the two you meant is decided once, from whether
87	the movement is mostly along the row or out of it, and then it sticks. Let go
88	back over your own hand and the tile goes back. Tapping a tile twice, or the
89	打出 button, still works and lobs it in for you.
90	- The discard pool — every tile thrown lands in the middle and stays there
91	until the hand ends, with real weight: it skids, turns, knocks the tiles
92	already there out of its way, and comes to rest against them. Nothing is ever
93	stacked on anything — tiles are solved as rectangles, so two lying at an angle
94	lean on each other rather than overlapping. The tile still to be claimed is
95	the lit one.
96	- Over the wall or across the table — which of the two ways a tile goes in is
97	not a setting, it is whatever the wall allows. At the start of a hand the
98	square is a solid barrier and a discard has to be lobbed over it, so the
99	flick's speed decides how far across the pool it lands. As the wall is eaten
100	away, gaps open in front of one seat and then another, and from then on that
101	seat can slide a tile in instead — flat across the cloth at exactly the speed
102	it was flicked. Which it will be is a ray cast at the stacks actually standing
103	there, so a gap off to one side counts, and a stack worn down to a single tile
104	is low enough to go over. A seat whose wall is still up says 牆未開 on its
105	nameplate, so a lob is never a mystery.
106	- Throw it badly and it ends up in somebody's tiles — the middle stops
107	exactly where their hand starts, so a tile that comes off the pool arrives in
108	their lap, and one that falls short lands out by their seat. Either way their
109	row takes the knock and rocks back, and with 報牌 on they tell you about it —
110	喂，小心點 if you are lucky, 是在哈囉 or 你牌品很差欸 if you are not, and
111	never the same line twice running. How hard it got there only decides how
112	loudly. Never your own edge: you cannot be barged by your own discard.
113	- Arranging — drag any tile in your hand to reorder it; 理牌 sorts it back
114	into suit order. Hands are never auto-sorted after the deal, so an arrangement
115	you set up survives draws, claims and kongs.
116	- Rules — the `?` on your nameplate opens a bilingual rules panel anchored to
117	your own edge of the table and rotated to face you.
118	- Claiming — after a discard, every seat that can claim gets 胡 / 槓 / 碰 /
119	吃 / 過 buttons on their own strip, and they resolve by priority (胡 > 槓/碰 >
120	吃; ties go to the player nearest the discarder in turn order).
121	The table never blocks on a claim. The next player gets a 摸牌 button and
122	may draw whenever they like, which shuts the window on anyone who hasn't
123	called — exactly like shouting 碰 before the next player picks up. A claim
124	already declared still stands, so calling in time always wins the tile. If
125	everyone answers first, play advances on its own without the extra tap.
126	The seat that draws next gets no separate 過 button, because for them the two
127	are the same move: picking up is how you decline. Their button says 摸牌
128	either way; what they would be giving up by pressing it is the 碰 or the 吃
129	sitting next to it on the bar, so it does not have to be spelled out on the
130	tile as well. Wanting to decline but leave the window open for everyone else
131	is just waiting, which is what not pressing anything already does. (On a
132	phone the button still reads 過．摸牌 — a phone's bar is a row with room to
133	write on, and the hand it belongs to is not on the same screen as the table.)
134	- On your turn — 自摸, 暗槓 and 加槓 appear automatically when legal.
135	加槓 offers everyone else a 搶槓 chance.
136	- Where the buttons go — on the same row as your tiles, at the right-hand end
137	of it, where the tile you are about to throw already is. The bar is out of the
138	strip's flow, so a button arriving moves nothing: 打出 appearing when you
139	lift a tile used to shove the melds and flowers above it up the strip. Every
140	button on the bar is given one height for the same reason. A bar with more on
141	it than the room beside the hand stacks up the strip in tile-wide lines, most
142	urgent call at the bottom, rather than running off the end of it. And the room
143	for the first line is in the tile size itself: a strip is sized to hold sixteen
144	tiles, the slot it keeps for the tile it is about to draw, and one button —
145	which is why the tiles down the sides of a short window are the size they are.
146	- What the buttons say — the call is written down the tile the way the
147	character on a tile's face is, one on top of the next in the middle of the
148	face, with the English along the bottom edge. Two characters stacked are the
149	size a tile's own character is; two side by side had to be shrunk to fit
150	across it. A call too long for the height (電腦代打) takes a second column to
151	the left of the first, which is where the next column of vertical Chinese
152	goes. 打出 names no tile: the one it would throw is lifted out of the row
153	beside it wearing a gold ring, so saying 五萬 on the button as well only
154	crowds the face.
155	- Whose go it is — a screen with four people round it is the one place a
156	game can go quiet without anybody noticing: three of them are watching the
157	table and the fourth is looking at their phone. So the table says it loudly.
158	The strip of the seat being waited on lights from its inner edge, their name
159	goes gold at the far end of it, and seven seconds of gold drain along the
160	edge that faces the middle — from both ends towards the centre, because two
161	of the four strips are upside down from wherever you are sitting. **Nothing
162	happens when it reaches zero.** No tile is thrown for you and no seat is
163	skipped; the line the bar leaves behind breathes, and the table goes on
164	waiting. It is a nudge, not a rule. Said on a covered hand too — whose turn
165	it is was never one of the things the card is hiding — and only where the
166	screen is playing more than one hand, since a screen playing one has nobody
167	to tell. A phone at the table gets the same seven seconds
168	across its top, a gold rim edge to edge (red for a claim window), and one
169	short buzz as the game comes round to it.
170	- On the keys — ← and → walk the selection along your hand and space throws
171	the tile that is lifted. How long you hold space is how hard it goes: the
172	tile draws back out of the hand while the key is down and leaves when you let
173	go, so a tap slides it in and a long hold sends it across the square. Escape
174	puts it back. The wall still decides whether it can be slid or has to be
175	lobbed, exactly as with a finger.
176	- When a hand ends — a big arrow drops onto the winner's edge of the table.
177	It lives inside their strip, so it turns with the seat and lands on the right
178	person wherever they are sitting, and 一炮多響 lights up every seat that
179	called. A 流局 has no winner to point at, so it turns the hands over instead:
180	who was 聽牌 and the tiles they were waiting on, the same reveal as at a real
181	table.
182	- The gear — beside the `?` on every nameplate, and it opens that player's
183	own copy of the table's controls: undo, sound, full screen, 設定. Anchored in
184	their strip and turned to face their edge, like the rules panel, so what you
185	open reads the right way up to you and to nobody else. These used to be a bar
186	in the middle of the table, which is the one place that belongs to everybody
187	— the pile lands there and it is upside down to two of the four.
188	- Undo — 復原 in that panel takes back the last action, naming what it will
189	undo (`復原玩家 2 打五萬`). It is in all four panels rather than only the
190	seat that made the mistake, because whoever spots the mis-tap should be able
191	to reach it. Twenty actions deep, cleared when the next hand is dealt.
192	Snapshots live outside the saved state, so an undo does not survive a
193	refresh: what you can take back is what happened while everyone was still
194	watching it happen.
195	- Sound — on by default, muted from the 🔊 button behind any seat's gear, or
196	from settings. A dry clack as a tile goes down, and a distinct
197	two-note chime when a claim window opens, which is how a slow player notices
198	their 碰 is available before the next player draws it shut. Everything is
199	synthesised with a few oscillators (`src/game/sound.ts`) rather than sampled,
200	so there is nothing to load and the cue lands on the same frame as the tile.
201	Browsers refuse to start audio before the page has been clicked, so the first
202	sound anyone hears is the deal — triggered by the button that starts it.
203	- 報牌 (voice) — a second switch under sound calls the game out loud: 碰,
204	吃, 槓, 胡了, 自摸, and the name of every tile as it is discarded — 三條,
205	五萬, 東風. A flower says 補花 and then which one. A new call cuts off one
206	still being spoken; at table pace the newest is the only one that matters.
207	See [the voice pack](#the-voice-pack) for where the audio comes from.
208	- 方位音 (sound by seat) — a third switch, on by default. Every noise comes
209	out of the edge its seat is sitting at: 上家 to your left, 下家 to your right,
210	and 對家 across the table, where it is quieter and has the top taken off it —
211	a metre of air and three people's arms do not carry 12 kHz. So you can tell
212	whose 碰 that was without looking up, which is the whole point of hearing it.
213	Tiles out in the middle are placed properly rather than by edge: the physics
214	knows to the pixel where a tile landed, and that is where the knock comes
215	from. A device holding one hand turns the table so that hand is at the
216	bottom, and the sound turns with it. See [audio, by seat](#audio-by-seat).
217	- Settings — 設定 from the lobby, or from the game-over panel: player names,
218	底 / 台 / starting chips, the house-rule switches below, and sound. Kept in
219	`localStorage` separately from the save, so they carry over to the next game.
220	Stakes are locked once a game is under way — they'd otherwise rewrite chips
221	already won.
222
223	## One table
224
225	There were three buttons on this lobby — 單人對局, 四人同桌, 線上對戰 — and
226	they were never three games. Every party table played its unclaimed seats
227	hotseat-style at the screen already; every hotseat table would have taken a
228	phone if it had had a room to put it in; every online table filled its empty
229	chairs with the same computer players the solo game is made of. They differed
230	in who was holding which hand, and that is not something a lobby should have to
231	know before the tiles are dealt.
232
233	So there is one button, and the question it used to ask is answered
234	continuously instead. A hand is played by one of three things — **the computer,
235	somebody at this screen, or a device of its own** — and any of them becomes any
236	other while the hand is in progress, with nothing redealt and nobody consulted
237	but the person doing it.
238
239	\| \| played by \| becomes a person here \| becomes a phone \|
240	\|---\|---\|---\|---\|
241	\| 電腦 \| the bots in `autoplay.ts` \| tap the strip — 坐下 \| its QR, from its gear \|
242	\| 這裡 \| this screen, face down under a tap \| — \| its QR, from its gear \|
243	\| 手機 \| whoever scanned in \| they leave → the computer \| — \|
244
245	Opening a room is not the same as playing over one, and the difference is
246	what keeps a game against three computers off the wire. 開始 deals and then
247	joins a room in the background, so there is a code for the QR tile to carry
248	from the first tile — but all `publishTable` writes is a seat map. The game
249	itself is published the moment somebody actually walks into the room
250	(`publishGameIfOwed`, off `room.onJoin`) and not one move before it, so an
251	evening played alone costs one handshake and then silence. Nothing waits on any
252	of it: the deal happens first, on this device, and a page that never reaches a
253	server plays a full game.
254
255	The engine is the page's own either way. `NetTable` is a wrapper that goes on
256	around a live `Game`, not a second one, so a room arriving mid-hand changes
257	nothing on screen except that the QR tile appears.
258
259	The table's QR is a tile. It lies in the middle of the felt with SCAN above
260	the code and JOIN below it, white face, dark-green ink, in the two bands a suit
261	tile spends on its number and its suit — and it is a tile all the way down. It
262	is a body in the pool like any other (`TablePool.joinTile`): a discard thrown
263	at it knocks it aside and turns it, it can be picked up and put somewhere less
264	in the way or flicked off across the cloth, the same one light over the table
265	works out its sides from whatever angle it has ended up at, and it throws the
266	same shadow. Nothing about it is a dialog. Its face is painted rather than cut
267	out of the sprite sheet — `qrFace` in `ui/tileArt.ts`, handed to `drawTile` as
268	`image` — which is the only thing that makes it different from a 中. It is put
269	back in the middle when a hand is dealt, because by then the pile it was shoved
270	to the edge of has been swept away.
271
272	No room means no tile. A table that cannot reach a server is a table with one
273	fewer tile on it and nothing else different.
274
275	Each seat's QR is its own, and lives in that seat's gear beside the sound
276	and the undo, carrying `?room=…&seat=N`. Scanning it lands on that chair
277	without anybody having to say which one they are in: the hand leaves the shared
278	screen for good — face down there, not under a card that lifts — and the phone
279	gets it face up with the claim buttons and the throw. It wears the same white
280	tile face as the one on the felt, so a code to scan looks the same wherever it
281	turns up.
282
283	**A hand that loses its device is kept for fifteen seconds and then given to
284	the computer** (`EMPTY_SEAT_GRACE`). A phone locking itself looks exactly like
285	a phone leaving for good and only one of them means it, so the nameplate shows
286	⏳ and the table waits; when the wait is up the computer picks the tiles up and
287	play carries on. Nothing is lost either way — coming back takes the seat
288	straight off the computer again, and so does one tap on it at the table. The
289	same countdown covers the screen closing its lid: the room records which device
290	the table is being played at (`screen` in room state), and hands with neither a
291	device nor a table behind them go the same way.
292
293	The save follows the table. Whichever device is running the game writes
294	`localStorage` (`engine.persist = authority`; every mirror has it off, and no
295	business writing it), so 繼續對局 restores here and the room, if one is wanted
296	again, opens behind it exactly as it did the first time.
297
298	Covering is arithmetic, not a mode. A hand starts face down when this
299	device is playing more than one of them — which is the definition of a screen
300	several people are sitting round. One hand is one person, whether they are
301	playing three computers or holding their own tiles on their own phone, and
302	covering your own tiles from yourself is a tap in the way.
303
304	## Playing online
305
306	Every device that is not the table is on one room relay of our own:
307	`server/rooms.ts`,
308	a couple hundred lines of Node on `ws`. The relay knows nothing about mahjong:
309	rooms with codes, host election by join order, one bag of shared state only the
310	host may write, and events fanned out to everyone else. One client — the
311	host — runs the engine, publishes the whole `GameState` as room state after
312	every move, and plays intents the other devices send as events. The engine was
313	already a pure JSON state machine, so nothing in `src/game/` knows the network
314	exists — the same trick `autoplay.ts` plays, stretched over a wire. The client
315	end of the wire is `src/net/room.ts`; the rest of `src/net/` is the game
316	riding it.
317
318	- A device that holds one hand shows that hand. A phone shows just the
319	hand, face up, with the claim buttons — and the throw: flick a tile up off
320	the top of the phone and it sails in from your edge of the common screen, at
321	the speed and angle you let go of it (`NetThrow`, mapped into table
322	coordinates by `TablePool.throwFromNet`). Anything bigger shows the whole
323	table instead, turned so that seat is the bottom edge, with everyone else's
324	tiles face down. Same room, same seat map; the only thing deciding between
325	them is how much screen there is.
326	- A device that holds no hand yet gets the seat picker, and every seat is
327	offered — including the ones the computer is playing, which is the ordinary
328	way in, and the ones somebody already holds, which is how two people play one
329	hand off two devices. A seat's own QR names its chair and skips the picker.
330	- The device the table was opened on goes on showing the table: the felt,
331	the middle, the wall, the SCAN/JOIN tile lying among the discards, and every
332	hand no phone has taken, covered-with-a-tap like a hotseat game. With sound
333	on, the phone in each player's hand is what says their calls and the table
334	goes quiet for that seat — see [audio, by seat](#audio-by-seat).
335
336	Design notes, in the order they bit:
337
338	- Seats are claims on a shared map, `seats: {ids, name}[]` in room state,
339	arbitrated by the host. Your own hand's arrangement never goes over the wire
340	— the state carries a multiset and each device keeps its own order
341	(`src/net/handOrder.ts`), because a round-trip inside a drag gesture is lag
342	you can feel.
343	- The host can change. The relay re-elects — the earliest joiner still
344	connected — when the host leaves; every other client already mirrors the
345	full state, so the new host starts its engine from what it was just watching
346	and the game carries on.
347	- A hidden host must keep hosting. Browsers suspend requestAnimationFrame
348	and throttle timers in background tabs, so nothing in `src/net/` runs on a
349	loop: state writes flush on a microtask, everything inbound arrives over the
350	WebSocket (whose delivery is not throttled), and dead connections are the
351	server's ping loop's problem. A table screen somebody tabbed away from
352	keeps answering.
353	- Identity is a UUID in sessionStorage, chosen by the device and taken at
354	its word by the relay. The seat map is keyed on it, so a reload or a wifi
355	blip walks back into its own seat. No auth — this is a home server for one
356	table of friends.
357	- Fairness is social, not cryptographic. Room state carries the whole
358	game, wall and hands included — a friend with devtools open can cheat.
359	Moving the engine into the relay would fix that; the server is ours now, so
360	only the work stands in the way (TODO).
361
362	### Running it
363
364	```
365	npm run dev # vite, with the relay on /ws of the same origin
366	npm run build && npm run serve # production: dist/ + relay, one process
367	```
368
369	The relay always lives at `/ws` on the page's own origin. In development
370	`vite.config.ts` attaches it to vite's server, so `npm run dev` is the whole
371	stack; in production `server/index.ts` serves the built `dist/` and the relay
372	from one port (`PORT`, default 8080), listening on the LAN by default so
373	phones on the same wifi can scan straight in. Anything further away wants TLS
374	in front — a reverse proxy with a certificate — since phones only get camera
375	and fullscreen on https.
376
377	Rooms live in memory. A restart drops them; the next visitor on an old link
378	recreates the room empty, and a host mid-game republishes its state on the
379	next move. Joining a room writes `?room=` back into the address bar, so the
380	page URL — the host's included — is the invite link.
381
382	A QR pointing at `localhost` is a QR only the host's machine can scan, so the
383	server always gives the invite links a public face: `PUBLIC_URL` if set, else
384	it runs its own rsgrok tunnel (the house ngrok replacement) — spawned
385	the moment the server knows its port, the https URL read off the tunnel-up
386	line, no `:4040` inspection API (another agent may own that port). Every QR
387	and invite link wears that origin instead of the page's. If the tunnel dies,
388	or `rsgrok` is not on the PATH (`RSGROK_BIN` points elsewhere), links fall
389	back to the page's own address and the tunnel is retried on later joins.
390
391	The tunnel always asks for the same subdomain — `mahjong-table`, or whatever
392	`TUNNEL_NAME` says — so restarts land back on the URL people already have
393	instead of burning a fresh name each run. A name someone else already holds
394	kills that first attempt before it prints a URL; the retry then goes out
395	nameless and takes whatever it is given.
396
397	## On a phone
398
399	The table assumes four people sitting around a screen lying flat, and about
400	770px in both directions before the middle is worth looking at. A phone has
401	neither, so under `(max-height: 620px), (max-width: 820px)` it switches to the
402	compact layout: nothing is rotated, everything reads upright for the one person
403	holding it, the other three seats shrink to cards showing what is public about
404	them, and the depth that frees up goes to your hand, which is allowed to wrap.
405
406	There is no centre square there — the middle collapses to a one-line bar showing
407	what the wall square was telling you anyway — so there is nowhere to throw a tile
408	to. The compact layout therefore keeps a discard row per seat, and discarding
409	is tap-twice or 打出, exactly as it was. The pool and the throw are a full-size
410	feature.
411
412	The breakpoint is written down once, in `COMPACT_QUERY` in `src/ui/compact.ts`,
413	which sets a `compact` class on `<html>` for the CSS to key off.
414
415	## Computer players
416
417	Single player seats you at the bottom and gives seats 1-3 to the computer.
418	Their tiles go face down and their 聽 / 過水 badges come off, since both would
419	give the hand away; everything public — the pool, melds, flowers, chips — stays
420	exactly as it is, and everyone turns their hand over when the hand ends. They
421	throw their tiles in like anyone else, and under the same rule: a computer seat
422	whose wall is open slides them across, and one still walled in lobs them over.
423
424	The engine does not know the bots exist. `AutoPlay` (`src/game/autoplay.ts`)
425	watches the same state the screen does, and when the seat being waited on
426	belongs to the computer it calls the identical method the button would have
427	called — `discard`, `respond`, `declareConcealedKong`. So scoring, sound,
428	saving, 過水 and 包牌 all work without a special case, and a bot cannot make a
429	move a person could not. It never acts for you and never closes your claim
430	window: if the table is waiting on you, it waits.
431
432	How they play (`src/game/bot.ts`) is one idea applied everywhere. A hand is
433	judged at its resting size — the (5 − melds) × 3 + 1 tiles you hold between a
434	discard and your next draw — by its 向聽 first and by its 進張 count second.
435
436	- Discard — try every distinct tile, keep the one that leaves the best
437	resting hand. Ties go to whatever is hardest to build on: a lone honour with
438	most of its copies already gone, before a lone 五萬 that still has neighbours
439	to meet.
440	- 碰 / 吃 — only when the hand that comes out the other side is strictly
441	closer to home. Melding costs concealment and flexibility, so a claim that
442	merely holds the 向聽 steady is declined — which is why the bots pass on
443	pungs that would narrow a two-sided wait to a single tile.
444	- 槓 — judged more kindly: it pays 台 and fetches a replacement, so standing
445	still is good enough.
446	- 胡 — always taken.
447
448	What they watch you do (`src/game/danger.ts`) is the other half. Efficiency
449	alone throws whatever is fastest and pays for it; these bots read the table
450	first, off the face-up table only — discard rows, exposed melds, the 過水 locks
451	the nameplates already show. Two separate questions:
452
453	- How close does each seat look? Turns taken (a hand is usually settled
454	inside ten goes each, long before the wall looks finished, so counting the
455	wall is the wrong clock), melds exposed, and what they have been throwing
456	lately. Nobody discards 五條 out of a hand that still needs shaping — it comes
457	out once the shape is done, so late middle tiles are the tell. A 過水 lock is
458	a confession: to be locked out of a tile you had to have been able to win on
459	it.
460	- How likely is this tile the one they want? An honour can only be caught by
461	a pair or a triplet; a 五萬 sits in the middle of every run through it. A tile
462	they discarded themselves was not their tile when it went down — not proof
463	now, but the best evidence there is. A tile with no copies left unseen cannot
464	be a pair or triplet wait at all. Two melds in one suit means stay out of that
465	suit. And two dragon pungs down means the third dragon is not going anywhere
466	near the table, because 包牌 bills the feeder for the entire hand.
467
468	Whether any of that changes the discard depends on the bot's own hand. At 聽牌
469	it pushes — nothing short of 包牌 is worth breaking a ready hand for. Two or
470	three away with somebody live across the table and it will give up a whole 向聽
471	step to throw something safe, which is what folding is.
472
473	The estimate is checked against ground truth in the tests rather than assumed:
474	over the tiles bots actually considered, the ones the model rated below 0.2 deal
475	in 0% of the time and the ones above 0.8 deal in 10.5%, cleanly monotonic in
476	between. Switching the read on cuts deal-ins by about 13% over a few hundred
477	hands, takes hands from ~30 discards to ~38, and moves the draw rate from
478	almost nothing to about one hand in ten — which is what a table where people
479	stop feeding each other actually looks like.
480
481	What they know is still only what they can see. `unseenFor` counts the four
482	copies of each tile and subtracts the bot's own hand plus every discard and
483	exposed meld on the table. Neither module ever reads an opponent's concealed
484	tiles or looks at the wall.
485
486	There is no difficulty setting, and the reading stops at the discard: claims are
487	still judged purely on speed, and a bot will take a 碰 that walks it into
488	trouble.
489
490	向聽 lives in `src/game/shanten.ts`, apart from `hu.ts`, because the two want
491	different things: the win check has to be exact, and this one has to be fast —
492	it runs a few hundred times for every discard a bot considers. The tests hold
493	them against each other over random hands, since they work in completely
494	different ways and any disagreement is a bug in the fast one.
495
496	Undo behaves differently against the computer: rewinding into the middle of its
497	turn would only hand the move straight back to it, so one press goes back to
498	the last point you had a decision to make, computer replies and all.
499
500	## Saving
501
502	The game state is plain data, so a save is just its JSON in `localStorage`,
503	rewritten after every move. Close the lid, refresh, or run the battery flat and
504	nothing is lost — the lobby offers 繼續對局 Resume above 開始, showing the
505	round, hand number, chip counts and when it was saved. Which seats the computer
506	holds is part of the state, so a save comes back with the same hands in the
507	same places, and everybody who was on a phone scans back in exactly as they did
508	the first time — a room is opened around a resumed table the same way it is
509	opened around a fresh one, when somebody wants one. It is written by whichever
510	device is running the game (`engine.persist = authority`), so the mirrors on
511	everyone else's screens never fight it for the slot. A
512	save is validated before it is offered (four players, 144 tiles accounted for),
513	so a truncated or hand-edited one is ignored rather than loaded into a broken
514	table. `VERSION` in `save.ts` retires old saves if the state shape changes.
515
516	## Rules implemented
517
518	- 144 tiles (four of each suit/honour, eight flowers), 16-tile hands, dealer
519	draws the 17th.
520	- 補花 at the deal and on every drawn flower, replacements from the back of the
521	wall.
522	- 吃 only from 上家; 碰/槓/胡 from anyone. 明槓, 暗槓, 加槓, 搶槓, 槓上開花.
523	- 流局 when 16 tiles remain (`Rules.wallReserve`); the dealer keeps the deal on a
524	draw or on a dealer win (連莊), otherwise the deal passes and the round wind
525	advances every four passes. A full 四圈 game is 16 dealer passes.
526
527	### House rules (switches in `Rules`, all on the settings screen)
528
529	- 過水 `sacredDiscard` (on) — pass on a tile you could have won with and it
530	is dead to you until your own next draw; the seat shows a 過水 badge listing
531	what it is locked out of, so the missing 胡 button is never a mystery. A draw
532	from either end of the wall lifts it. `sacredClearedByClaim` (off) decides
533	whether taking a 吃 / 碰 / 槓 lifts it too — tables genuinely differ.
534	- 一炮多響 `multipleWinners` (off) — one discard pays out to every seat that
535	calls on it, each settled separately against the discarder. With it off the
536	tile goes to the caller nearest the discarder. Either way the table now waits
537	for other seats that can win before settling, so the nearest seat wins the
538	tile rather than the quickest hand — and the 摸牌 button still closes the
539	window on anyone dithering.
540	- 包牌 `liability` (on) — feeding the pung that completes a visible 大三元
541	or 大四喜 makes the feeder answer for the whole hand, in place of all three
542	payers. Only the seat that fed the last of those sets is on the hook, and
543	only if it came off a discard: a hand that assembled them itself, or closed
544	the set with a 暗槓, has nobody to blame.
545
546	### 台 scoring (`src/game/tai.ts`)
547
548	自摸 1 · 門清 1 · 門清自摸 +1 · 全求人 2 · 平胡 2 · 五門齊 2 · 正花 1 each ·
549	花槓 2 · 八仙過海 8 · 圈風 / 門風 1 each · 三元牌 1 each · 小三元 4 · 大三元 8 ·
550	小四喜 8 · 大四喜 16 · 碰碰胡 4 · 混一色 4 · 清一色 8 · 字一色 16 ·
551	三暗刻 2 / 四暗刻 5 / 五暗刻 8 · 獨聽 · 單釣 1 · 搶槓 1 · 槓上開花 1 ·
552	海底撈月 1 · 河底撈魚 1 · 天胡 16 · 地胡 16 · 人胡 8 · 莊家 1 (連N拉N → 2N+1)
553
554	Ambiguous hands are decomposed every legal way and scored at the best reading.
555
556	Payment (`Game.settle`): one unit is `底 + 台 × 台值`
557	(`DEFAULT_RULES` = 底 3, 台 1, 100 chips each).
558	放槍一家付 — the discarder alone pays one unit; on 自摸 all three pay one unit
559	each. 拉莊 is billed to the dealer alone when the dealer is a payer, and added
560	to the whole hand when the dealer wins.
561
562	House rules vary a lot; the tai table and payments are plain data/functions in
563	`tai.ts` and `types.ts` if yours differ.
564
565	## Audio, by seat
566
567	A sound at a mahjong table comes from somewhere. You know whose 碰 that was
568	because it came from your left, and you know a tile has been thrown hard at the
569	far corner without watching it go. Both of those are cheap to keep, and both
570	are gone the moment everything comes out of the middle of one screen.
571
572	Every cue is a seat's. `SoundCue` carries a `seat` alongside the kind and
573	the tile — the seat that threw, called, or won — and leaves it off the things
574	that belong to the table rather than to anybody: the deal, a 流局, an undo. The
575	engine says whose only because a sound has to come from somewhere; what that
576	means in the room is entirely the UI's business, as it always was.
577
578	A seat becomes a place. `App.tsx` turns a seat into a *position round this
579	screen* — 0 the near edge, 1 the right, 2 across, 3 the left — because that is
580	what the ear wants and the seat number is not: a device holding one hand turns
581	the table so that hand is at the bottom, and the sound has to turn with it.
582	`game/sound.ts` gives each position a bus of its own: a pan, a gain, and a
583	lowpass that opens all the way for the near edge and closes to 5 kHz for the
584	far one. Distance is two things at once — quieter, and with the top taken off
585	— because between you and 對家 there is a metre of air, a wall of tiles, and
586	three people's arms, none of which carry treble. Tiles out in the middle skip
587	the edges entirely and are placed continuously, panned by where on the felt
588	they actually landed; the physics knows that to the pixel. Buses are built once
589	per spot and quantised, so a pool full of skidding tiles reuses a handful
590	rather than building one per contact. Old Safari has no `StereoPannerNode`; it
591	plays where it always did.
592
593	**Where there is a table and phones round it, the words come out of the
594	player.** The split the sound should take is the one the room already has: the
595	table makes the noise, because the tiles are on the table, and the phone in
596	somebody's hand says their calls, because the calls are theirs. So the table's
597	screen drops the voice for a seat while keeping the clack, and the phone
598	holding that seat says 碰 and names its own discards and makes no table noise
599	at all.
600
601	Only a phone claims that job, and that is the whole of how the split knows
602	where it applies. A phone is small enough to be in a hand and a hand is in the
603	room; a friend playing from their own laptop three cities away is not, and
604	never takes the words away from anybody's table. It is a proxy rather than a
605	fact — software cannot know who is sitting where — but it is the one property
606	that actually correlates with it, and it fails in the harmless direction:
607	the worst a wrong guess costs is a call said twice in two rooms.
608
609	That only works if the phone really is going to say it, so it is asked rather
610	than assumed. `sound.voiceLive()` is the honest answer — sound on, 報牌 on, the
611	audio hardware awake, the pack decoded — and every device reports it to the
612	host whenever it changes (`EV_VOICE`). The host works out, seat by seat, which
613	hands have a device that will speak for them and publishes that as `voices` in
614	room state; a nameplate wearing 🔊 next to its 📱 is a seat the table has gone
615	quiet for on purpose. Mute the phone, put it to sleep, hand the seat back —
616	the flag drops and the table takes the calls back mid-hand. The device the
617	table is being played at never counts, even when it holds seats: it is the
618	table, and a table that fell silent on the grounds that it was about to speak
619	would say nothing at all.
620
621	A browser will not start audio before the page has been touched, and a phone
622	that arrived by QR may never touch anything that asks for it by name — so the
623	first touch anywhere unlocks it, which is also the moment it can start
624	claiming the job.
625
626	## The voice pack
627
628	A mahjong table only ever says about fifty things — 42 tile names and a handful
629	of calls — so the whole vocabulary is rendered ahead of time into
630	`public/voice/` (~330 kB of mp3) rather than left to whatever speech synthesis
631	the browser happens to have. On Linux that is usually espeak-ng, which is
632	intelligible but sounds like a modem; and on a machine with no Chinese voice at
633	all the feature would silently do nothing. Shipping the audio makes playback
634	instant, identical everywhere, and lets a call be cut off mid-word when the
635	next one lands, all through the same Web Audio graph as the chimes.
636
637	`scripts/voice.mjs` is the authoring step, not part of `npm run build`. It needs
638	[piper](https://github.com/OHF-Voice/piper1-gpl) and ffmpeg on PATH:
639
640	```
641	node scripts/voice.mjs # → public/voice/*.mp3 + manifest.json
642	PIPER_MODEL=/path/to/voice.onnx node scripts/voice.mjs # a different voice
643	```
644
645	The wording lives in that script, and some of it is deliberately not the bare
646	tile character: 東 alone is a direction where 東風 is the tile, and the dragons
647	are 紅中 / 發財 / 白板 the way they are actually called — which also gives the
648	phonemiser enough context to get the tone right, since 中 on its own is as
649	likely to come out zhòng.
650
651	The clips here were rendered with piper's `zh_CN-huayan-medium`. If you
652	redistribute this app, check that voice's model card in
653	[piper-voices](https://huggingface.co/rhasspy/piper-voices) for the terms
654	attached to it, the same way you would the tile art below — or re-render the
655	pack with a voice whose terms suit you, which is a single command.
656
657	## Tile art
658
659	`public/tiles/tiles.svg` is the postmodern tileset from
660	[gnome-mahjongg](https://gitlab.gnome.org/GNOME/gnome-mahjongg), extracted from
661	the installed binary's GResource — a 43×2 sprite sheet (second row is the
662	highlighted variant, used for a lifted tile). `public/tiles/back.png` is the
663	blank tile from its smooth theme, tinted jade, since a solitaire game has no
664	face-down art of its own.
665
666	How a tile is drawn on the canvas — the outline round it and the shadow under
667	it — lives in `src/ui/tileArt.ts`, and `npm run dev` serves `/tiles.html`, a
668	page of every face at every angle over the felt with a slider on each of those
669	numbers and the finished block ready to paste back. None of it can be judged
670	from the values: it is 246 white against a dark green at 35 pixels across, and
671	the only way to know is to look at it and move something. (`tiles.html` is not
672	one of the build's entry points, so it does not ship.)
673
674	The sheet is not a picture of a tile's face. It is a picture of a whole tile,
675	drawn in an oblique projection, with its own sides painted down the left and
676	along the bottom and its own light coming from the top right — a 16px bevel on a
677	128px cell. That is fine while every tile stands the same way up, and wrong the
678	moment they are scattered: rotating the sprite rotates a pre-rendered solid, so
679	a pool of discards ends up with a different sun on each tile.
680
681	So the art is cropped back to the flat face, and the solid is worked out
682	instead. A tile is a box lying on cloth: take the four corners of the rotated
683	rectangle, offset them by the projection (`depthAngle`, down and to the left,
684	the same direction the art used), and fill the two or three quads whose edges
685	the base falls away from — each shaded from the direction that edge faces *on
686	screen*. Turn the tile and the same physical side comes round to face a
687	different way and its shading changes with it, which is the whole point. No 3D
688	engine, no z-buffer: one projection vector and a dot product per edge.
689
690	Each cell of the sheet is cut out into its own canvas the first time it is
691	wanted. `drawImage` with a source rectangle is allowed to sample past that
692	rectangle when it resamples, and the row under every face is the highlighted
693	variant, whose border is bright blue — so a tile at any angle other than a right
694	one wore a blue fringe along one edge. Square on it never showed, which is why
695	it looked like a rotation bug rather than a spritesheet one.
696
697	A tile used to be drawn as two passes — a slab of ivory offset down the screen
698	with the face on top, so a sliver of the tile's own side showed along the bottom
699	edge. At the size a discard is actually drawn that never read as thickness; it
700	read as a second, paler shape stuck to the bottom of every tile. Shading it
701	better did not help, because the problem was that it was there. What gives a
702	tile its weight now is the shadow and the outline, both of which are true at
703	any size.
704
705	That art is GPL-2.0-or-later. Fine for playing at home; if you ever
706	distribute this app, either honour the GPL or swap the two files for art of your
707	own — `SPRITE_COL` in `tiles.ts` is the only mapping that would need updating.
708
709	Known gaps and house rules that aren't implemented yet are listed in
710	[TODO.md](TODO.md).
711
712	## Layout
713
714	```
715	public/tiles/ sprite sheet + tile back
716	src/game/tiles.ts tile codes, wall, shuffle, sprite mapping
717	src/game/hu.ts hand decomposition, 聽 detection, wait shapes
718	src/game/shanten.ts 向聽 / 進張 counting, for the computer players
719	src/game/bot.ts what a computer player discards and claims (pure)
720	src/game/danger.ts reading the table: who looks ready, which tiles are hot
721	src/game/autoplay.ts when it does it, and how long it appears to think
722	src/game/tai.ts 台 scoring
723	src/game/engine.ts state machine: deal, turns, claim resolution, settlement
724	src/game/ctl.ts TableCtl — the surface the UI drives, local or networked
725	src/game/wall.ts what is left of the square, and what still blocks a throw
726	src/net/room.ts the wire itself: join, reconnect, state, events
727	src/net/session.ts the room: host duties, seats, intents, migration
728	src/net/table.ts TableCtl over the wire: mirror + intents + hand overlay
729	src/net/protocol.ts what crosses the wire, in one place
730	src/net/handOrder.ts your own arrangement, kept on your own device
731	src/ui/Controller.tsx a hand held on a phone, plus the seat picker for any device
732	server/rooms.ts the relay: rooms, host election, state fan-out
733	server/index.ts production: dist/ and the relay from one port
734	src/table/physics.ts the discard pool: rectangles with weight, pure and testable
735	src/table/geometry.ts the table measured — colliders, launch points, throw gate
736	src/table/pool.ts game state ⇄ tiles in the middle, by diffing the discards
737	src/ui/tileArt.ts one tile drawn on canvas — sides, shadow, and the QR face
738	src/ui/ TileView, Hand (drag and throw), Seat, Center, Pool, Help
739	```
740
741	## The tiles in the middle
742
743	The pool is a small rigid-body solver (`src/table/physics.ts`) that knows nothing
744	about mahjong, the DOM, or the clock: fixed 1/120s steps, no randomness of its
745	own, and everything in table pixels. Given the same throws it produces the same
746	pile every time, which is what lets a refresh mid-hand come back to the pile you
747	had rather than a freshly scattered one — positions are derived from the hand
748	number and each tile's place in its thrower's discards, never saved.
749
750	The pile is handled directly. Press on a discard and it comes up out of the
751	pile, carried over the top of the others rather than ploughing through them;
752	let go slowly and it is set down there, flick and it goes off across the felt at
753	the speed it left your fingers — the same throw a tile gets out of a hand, made
754	from the middle of the table instead. Pressing on bare felt does nothing, and
755	the press passes through to whatever was really under it: the tiles are drawn on
756	a canvas with no elements to hit, so the hit test is against the physics and the
757	listener is a capturing one on the table itself.
758
759	A flick is the whole of a throw: the direction and the speed it leaves at are
760	the hand's, and nothing between the fingers and the felt changes either. The one
761	thing the table decides is height — with a standing wall in front of the
762	throw a flat tile would only skid into it, so it is lofted over instead, exactly
763	as far as it was thrown and simply in the air for the first part of the way. A
764	tile that carries past the square and out into the open stays there. (It used to
765	be re-aimed at the middle of the square when the flick's line missed it, which
766	put the tile on a line nobody had thrown and read, fairly, as a bounce off
767	nothing.)
768
769	What stops a tile is other tiles. There is no fence: the standing stacks of the
770	wall, the sets people have laid down and the sixteen each of them is holding are
771	all measured as colliders, so the pile is held in by the ring of tiles round it
772	exactly as it is on a real table, and spills through whatever gaps the wall has
773	been eaten into. The table's own edge is a backstop at the screen edge, there
774	only so a tile that got past all of that isn't lost.
775
776	A tile that only ever slid would look like a puck. What makes a pool of discards
777	look like one is that every tile in it has come to rest at some angle nobody
778	chose, and that is a thing to earn rather than to scatter in. A tile turns
779	because of where it was hit.
780
781	So a contact happens somewhere in particular. The separating axis test says which
782	way to push and by how much; `contactOf` says where, and the arm from there to
783	the tile's middle is what a turn is made of. A tile shouldered square in the back
784	is pushed along and does not turn at all. The same shove, moved along until it is
785	catching one end of the tile, turns it instead, and which way round follows from
786	which end. What touches is a footprint and not a point: a tile lying square to a
787	wall meets it along the whole of one side and is pushed through its own middle
788	however far along the wall it is, and the same tile at forty-five degrees meets
789	it on one corner and swings on round it. Everything a tile can hit is another
790	tile, so the standing stacks, the laid-down sets and the table's own straight
791	edge are all the same contact with the same friction across the face of it.
792
793	Two things keep that honest. The first is that a tile is not free to pivot. It is
794	lying flat on cloth, and the cloth under the whole of its face resists the turn
795	for as long as the contact lasts, so only a tenth of the moment a knock would
796	give a free rectangle actually reaches it (`FELT_HOLD`). Without that, a tile off
797	the corner of a stack comes away spinning like a top. The second is that the felt
798	is one patch of cloth doing one thing: what it spends stopping the slide it has
799	not got left for the turn, so the two share a single friction budget rather than
800	running as two brakes side by side. What that buys is the ending. A tile
801	flicked hard with a little turn on it used to stop turning early and skate on
802	looking dead, and one barely pushed with a lot of turn on it stopped dead and
803	went on spinning where it lay. They now run out together.
804
805	The turn a tile arrives with is the flick's own. `ui/flick.ts` reads a release
806	the same way wherever it was made, out of a hand or off the pile in the middle,
807	and the spin it reports is the angle the stroke swung through between its first
808	half and its second, over the time it took. That is a rate, in rad/s, which is
809	what a wrist actually does: a straight flick turns nothing however hard it is
810	thrown, and the same curve made twice as fast puts twice the turn on the tile.
811
812	It is drawn on a canvas that spans the whole table, not just the centre.
813	That is deliberate: `.slot` and `.seat` both clip their own contents, which is
814	why a tile can't be animated out of a strip as an element. On the canvas there is
815	nothing to clip it, so a tile lifted out of a hand crosses the table in one
816	piece.
817
818	The square is the whole wall: eighteen stacks of two a side, four sides, 144
819	tiles, the way it is built on a table. It used to be rebuilt to what was left
820	after a hand had been dealt — barely half of it — because eighteen full-size
821	stacks a side wants about 560px and no ordinary window has that between the top
822	and bottom strips. That bought a square at the price of it not being the wall:
823	a side ran out of stacks before it reached its corner, so the four of them never
824	met.
825
826	Nothing gives now, and in particular the tile does not. Every tile on the table
827	is one size — `--tile-w` in styles.css, in a hand, in the wall, and lying in the
828	middle — because they are the same tiles, and a tile that changed size between
829	the wall and your hand read as a different, smaller set sitting in the middle.
830	The square is built from that tile and is however big that comes to:
831	`wallSquare()` in `game/wall.ts` takes the tile and hands back the lengths, and
832	`WallRing` measures one rendered cell to find out what CSS made it. The wall
833	being bigger than the room between the strips is a fact about a 144-tile wall,
834	not a thing to solve by shrinking it.
835
836	The four walls are placed by CSS alone: each is pinned to its own edge of the
837	opening with `left`/`top`, runs its whole length from the corner it is built
838	from, and so carries one wall-depth past the far corner and over the end of the
839	next wall along. Every corner of the square is covered by exactly one wall and
840	no two overlap — that is the pinwheel. Nothing is rotated; a square wants no
841	rotation to describe it.
842
843	The overhang is exactly one wall-depth, which is what it takes to close a right
844	angle: two bands of thickness `t` meeting at an interior angle ψ overlap by
845	`t / tan(ψ/2)`, and at ninety degrees that is `t`. So the whole square measures a
846	wall's length plus one depth across, and leaves that length less one depth in
847	the middle — which is the opening, and which is what `.wall-ring` itself is.
848
849	The CSS only places what it is told: `.wall-side` is a row of stacks, laid across
850	on the two flat walls and down on the two upright ones, and `--wall-len` from
851	`WallRing` is the only length it is given. Every place in the wall is rendered
852	whether or not there is still a stack standing on it, because with the break
853	anywhere but a corner a wall is eaten from its middle — a row that closed the
854	gap up would drag the whole tail of the wall along the table behind it.
855
856	Where the four walls stand is found at the table itself rather than on a page
857	of sliders: take hold of a wall in a real game and push it. It goes where the
858	finger goes, and lets go saying where it landed — `[wall] top pushed to 0.5,-4.9
859	— top 0.5,-4.9 · right 0,0 · …` in the console, in tiles, which is the form
860	`WALL_PLACED` in `game/wall.ts` is written in, so what a push finds pastes
861	straight back in. Nothing about the hand moves: the wall is the same wall in the
862	same order and the next draw is still the next draw. There used to be a
863	`/wall.html` for this; the table is the honest place to do it, so that page is
864	gone.
865
866	## 擲骰 — where the wall is broken
867
868	The dealer throws three dice to open a hand, and the total does two jobs. It
869	counts round the seats — the dealer being one, and the count going the way the
870	turn goes — to pick whose wall is opened. Then the same number counts stacks in
871	from the right-hand end of that wall, and the break is behind them: the first
872	tile drawn is the next one along, and the drawing runs away to the left from
873	there, on round the square.
874
875	The square makes that cheap to say. Every wall is laid down from the corner its
876	own player's right hand falls on — that is what the pinwheel is — so the run of
877	72 places already starts at each seat's right, and the break is simply so many
878	places into the side the dice picked. `breakAt()` is those two lines.
879
880	Nothing about the tiles turns on it: the wall was shuffled before it was built,
881	so which stack is drawn first is decided either way. What it moves is where in
882	the middle of the table the gap opens and who has to reach furthest for the next
883	draw — which is the whole of what it does at a table too. The throw is made from
884	the same seeded rng that shuffled, so a seed replays a hand's gap as well as its
885	tiles.
886
887	Where the wall opened is thrown for once and then lived with, which is right at
888	a table and awkward to look at: half the question about the square is what it
889	looks like opened at each of the seventy-two places it can be opened at.
890	`game.reroll(1, 1, 1)` through `game.reroll(6, 6, 6)` from the console walks the
891	break all the way round, and `game.reroll()` throws afresh. It moves the gap and
892	nothing else: the tiles were shuffled before the wall was built, so nobody's
893	hand changes and the draw order is the draw order.
894	Nothing about the square is calculated twice. Its size lives entirely in CSS
895	(`--ws`, `--wd`), so `geometry.ts` measures it instead of restating that
896	arithmetic: `WallRing` already renders every stack as a real element tagged with
897	its index, and the colliders are those elements' bounding rects. That one
898	mapping is what makes the wall a physical object — the thing a thrown tile
899	bounces off, and the thing the throw gate casts its ray at.
900
901	### Seeing the colliders
902
903	Because every boundary is measured off the DOM rather than written down, the
904	only honest way to check a bounce is to draw the boxes in the coordinate space
905	the tiles are drawn in. Add `?colliders` to the address, or call `colliders()`
906	from the console while a hand is running:
907
908	\| drawn \| is \|
909	\| --- \| --- \|
910	\| solid rectangle at the screen edge \| the table itself. Nothing meets this in play — it is only there so a tile that got past everybody's tiles is still on the table afterwards \|
911	\| solid box on every tile \| a collider. Every tile on the table is one: the stacks still standing, the sets people have laid down, and the sixteen each of them is holding. Half stacks aren't drawn because they aren't colliders — a tile goes over them \|
912	\| dashed rectangle \| the wall square's opening — where a throw is aimed. It stops nothing, which is why the pile spills out of it \|
913	\| dotted rectangle, inset \| where the moving tile's own centre may be against the table's edge, which is its half width in from it \|
914	\| box hugging each pool tile \| the rotated rectangle it really collides with \|
915	\| dotted box round the moving tile \| the upright box the straight edges use instead. It comes apart from the rotated one as the tile turns \|
916
917	\| blue rays from a throw \| faint: the flick, as the tile was let go of. Bright: the line it was actually sent along, labelled `slide` or `lob`. These should lie on top of each other — the flick is the throw, and a tile leaving on a line nobody threw reads exactly like a bounce off something invisible \|
918	\| yellow cross \| where contact was actually made, fading over a second or so. One of these sitting in open felt with no box under it is a bounce off something that isn't a collider at all — a different bug from a box in the wrong place \|
919
920	Colliders mode is also a throwing sandbox: a flick throws for real but is not a
921	discard, so the tile stays in your hand, the turn never passes and the computer
922	players hold still. Throw the same tile at the same corner as many times as you
923	like. Sixty stay on the table before the oldest is swept off; `pool.clearLoose()`
924	sweeps them all. Tapping a tile to discard does nothing in this mode — throwing
925	is the thing being tested.
926
927	Add `pause=1` (`?colliders&pause=1`, or `pause()` from the console) to **stop
928	dead on contact**. The physics halts on the fixed step that resolved it and
929	drops the rest of the frame, so what's on screen is where the tile touched
930	rather than where it had got to by the end of the frame. Space carries on, →
931	takes one step, ↑ takes ten; the console says what it stopped on.
932
933	`colliders(false)` turns it off again. It repaints on toggle, so a settled table
934	doesn't have to be poked first. In a dev build `pool` is the live pool: the
935	overlay draws `pool.world.walls`, the physics' own copy rather than a fresh
936	measurement, so if what's drawn ever disagrees with the DOM it is the world that
937	went stale — which `pool.measuredAt` will show, since the stamp carries every
938	hand's shape.
939
940	## What is left of the wall
941
942	Four walls of eighteen full-size stacks want about 560px a side. No ordinary
943	window has that between the top and bottom strips, and the tile is not allowed
944	to shrink to make it fit — a tile in the wall is the same tile you play with, so
945	drawing it smaller was a visible lie.
946
947	What saves it is that nobody ever sees a whole wall: four hands come off the
948	front before the table is on screen, so barely half of it is left by then. So
949	only the stacks still standing are drawn, and they are laid out around a ring
950	cut to the middle rather than to eighteen — `ringLayout` in `game/wall.ts`
951	measures how many stacks a side can take (`WallRing` renders one hidden cell and
952	asks CSS how big it came out) and shares what is left over the four sides in
953	proportion. Every seat keeps a wall in front of it instead of the remainder
954	piling into one corner, and the order runs all the way round, so the break point
955	is still at the head of it and the 底牌 tail still at the end.
956
957	Shuffling the wall along as it is eaten costs nothing to look at, because every
958	stack shows the same green back — and it is what people do to a half-eaten wall
959	anyway.
960
961	`pool.ts` never listens for events. It diffs the discards against what it is
962	already drawing, keyed by `seat:index` — and those keys never shift, because
963	discards are only ever pushed and a claim only ever pops the one on top. So a
964	key that appeared is a tile to throw in and a key that went is a tile to take
965	off, which makes undo, 下一局, a claim and resuming a saved game all the same
966	code path. The engine has no idea any of it exists, and the save format did not
967	change.