ProLibertateGames/docs/RULES-tayu.md

Ta Yü — implemented rules

This is the ruleset the engine enforces. Anything marked toggle is exposed in the game setup screen.

Ta Yü is a connection game by Niek (Nicolas) Neuwahl, published by Kosmos in 1999 and nominated for the Spiel des Jahres that year; Goliath reissued it in 2009. It has been out of print for years, which is why it is rebuilt here.

Players lay 1×3 river tiles outwards from the centre of a large board. Each tile carries three river mouths, and a mouth may never be walled off against the blank flank of another tile — that constraint is what makes every placement depend on everything already down. One side runs water to the north and south edges, the other to the east and west. Scoring multiplies your two opposite edges together, so a river that reaches only one of them is worth nothing at all.

The rulebook could not be obtained, so parts of this are reconstructed. Which parts, and how much to trust each, is set out under Provenance. Read that before treating a number here as gospel.

Table

• Players — toggle. Two or four.
  • Two. Seat 0 takes north–south, seat 1 east–west.
  • Four. Two partnerships: seats 0 and 2 play north–south, seats 1 and 3 east–west, so partners are never seated next to each other.
• Opponent — toggle. Gentle or full strength. See the computer opponent.
• Tiles — toggle. Two, three or four copies of every tile — 56, 84 or 112. Three is the reissued game and four is the 1999 original. The publisher itself cut it from four to three to shorten the game, which is the same reasoning behind offering two.

The three-player "flood" variant is not implemented — see Known gaps.

Board

An 18 × 18 grid of cells. Rows count from the north edge, columns from the west.

Each edge has 18 possible exits, one per edge cell, where a river can run off the board. Three exits on each edge are marked and count double.

Tiles

Each tile is 1 × 3 and carries exactly three river mouths on its perimeter, all joined to one another across the face of the tile — so water entering any mouth can leave by either of the other two.

A 1×3 tile has eight places a mouth can sit. Taking the tile lying east–west with its cells numbered 0, 1, 2 from the west:

Slot	Where
N0 N1 N2	north flank, above each cell
S0 S1 S2	south flank, below each cell
W	the west end
E	the east end

Choosing 3 of those 8 gives 56 arrangements, and a tile can be turned end for end, which pairs them off: N0↔S2, N1↔S1, N2↔S0, W↔E. No arrangement is its own mirror under that turn, so the 56 collapse to exactly 28 distinct tiles.

84 = 3 × 28. The reissued set is three copies of every tile that can exist, and the 1999 original's 112 is four copies. Both counts landing on a whole multiple of 28 is the main reason to trust this reconstruction of the geometry.

Of the 28, 12 have their three mouths on three different flanks of the rectangle, which matches the reissued tiles being marked with a concentric ring on the centre stud — so those tiles are drawn with a ring here too.

The engine generates the set rather than listing it, so the tiles and the count cannot drift apart.

Turn

1. Draw one tile from the bag, face up. There are no hands and no hidden tiles: everyone sees what you drew, and the only concealed information in the whole game is the order of the bag.
2. Place it, in any of its four orientations.
3. If the drawn tile has no legal placement anywhere it is set aside and the turn passes. It does not come back.

Because a tile is only ever drawn for a seat that can play it, the player on the clock always has at least one legal placement.

The opening tile

The first tile must cover at least one of the four centre cells — (8,8), (8,9), (9,8), (9,9). Every one of the 28 tiles can legally open, so the first turn can never jam.

Every tile after the first

A placement is legal when all of the following hold.

• The three cells are empty and in a straight line on the board.
• Every one of the tile's three mouths is accounted for. Take each mouth and look at what lies across it:
  • an empty cell — fine, the river runs on into open ground;
  • off the board — fine, and that is a scoring exit;
  • a tile with a mouth facing back — fine, the two join up;
  • a tile with a blank flank there — illegal. A river may never dead-end against the side of another tile.
• The tile's own blank edges must not wall anything off either. A blank part of the new tile landing against an existing tile's mouth is illegal for the same reason read from the other direction.
• The tile must join the network. At least one of its mouths must meet a mouth of a tile already down.

The engine enforces the two blanking rules as a single comparison: where a new tile abuts an existing one, both sides must agree — mouth to mouth, or blank to blank.

One consequence worth knowing, because it is what keeps the engine simple: since every tile joins the network by a mouth, and all three mouths of a tile are connected across its face, everything on the board is always one single river system running back to the opening tile. Nothing ever has to trace connectivity, and a mouth at the board's edge is a scoring exit by construction. TayuRulesTest and the offline verification harness both check this holds over whole games.

End of the game

The game ends when the bag is empty, or when nothing left in it can be placed anywhere. In practice a full 84-tile bag ends with a handful set aside — the board jams before the bag runs dry.

Scoring

Count each side's exits on each of its two edges. An ordinary exit counts 1; one of the three marked exits on that edge counts 2. Then, for each side:

score = (exits on one edge) × (exits on the opposite edge)

North–south multiplies its north count by its south; east–west multiplies east by west. A side that reaches only one of its two edges scores nothing — that is the whole tension of the game, and it happens in real play, not just in theory.

Higher score wins. Equal scores are a draw.

Where the marked exits sit

Positions 3, 8 and 13 along each edge, counted clockwise from that edge's first cell, giving the board four-fold rotational symmetry so no side is better served than another. This is a choice, not a reproduction — see below.

Playing it on a phone

18 × 18 cells works out under 20dp a cell on a phone, which is too fine to tap accurately, so laying a tile is two steps rather than one:

• Tap the board to line a placement up. Cells that the drawn tile could cover are dotted, and the placement appears as an amber ghost.
• Tap the same cell again, or press Turn the tile, to cycle through the other legal ways the tile could cover that cell. This is also how the tile gets turned — it has four orientations but only some of them fit, and a rotate control that landed on illegal positions would be worse than useless.
• Lay the tile commits it.

A tap on a cell the tile cannot cover is ignored rather than treated as a deselection, so a fingertip landing one cell wide does not throw away a placement that took several taps to line up.

Rivers are drawn as channels running from each mouth into a pool at the middle of the tile. Exits show as a dot outside the board in the colour of the side that edge belongs to, and the four edges are tinted the same way, so it is possible to see at a glance which rivers are working for whom.

The computer opponent

It rates every legal placement on the board that placement would produce, weighing what its own axis would score, what the opponent's would score, and which way the still-open river mouths are pointing.

That last term is what makes it play sensibly at all. Both scores sit at zero for most of a game — a product needs both edges — so an opponent that looked only at the score would have nothing to choose between its first fifty placements.

Two settings, because only two could be shown to differ:

Setting	What it does	Measured
Gentle	Rates a placement only on what it scores at that moment, which is usually nothing, so it lays a plausible but aimless river	Beats random placement about 3 games in 4; loses to full strength about 4 in 5
Full strength	Adds blocking, and notices which way the open mouths point	Won 20 of 20 against random placement, from either axis

TayuAiTest holds both to those figures, and also checks that random against random comes out even — if it did not, the board or the scoring would favour an axis and every other result would be meaningless.

A third setting that blocked harder was written and dropped: it played full strength dead even over 30 games, so shipping it as a step up would have been a claim that could not be backed.

Provenance

Everything here is reconstructed from secondary sources. The rulebook itself could not be reached: outbound web requests are blocked by the build environment's network policy, so only search-result summaries were available, and BoardGameGeek's rules files were out of reach entirely.

Attested by sources: designer and year; 84 tiles in the reissue and 112 in the original; 1×3 tiles with three connections each; the board's round indentations, and the opening tile going in one of the four centre ones; the mouth-accounting placement rule and the ban on a river ending against a blank; north–south against east–west; the multiplicative scoring; marked exits counting double, three to a side; the game ending when nothing can be placed; the existence of a three-player flood variant.

Reconstructed here, and the parts to check against a real copy:

• The board is 18 × 18. One source describes the physical board as having 18 × 18 indentations; several others say 19 × 19. 18 × 18 is used because it is the reading under which "the four centre indentations" is true — a 19 × 19 grid has a single centre cell, not four. BOARD_SIZE in TayuModel.kt is the only thing that has to change if a rulebook settles it the other way.
• The 28-tile set and its geometry. Derived, not read off a component list. It is trusted because 84 and 112 are both exact multiples of 28, and because 12 of the 28 touch three flanks, matching the ringed tiles in the reissue.
• All three mouths on a tile interconnect. Consistent with every description found, but never stated outright.
• The marked exits at 3, 8 and 13. Their real positions are unknown. Three mirror-symmetric marks are impossible on an even-length edge, so the real board cannot be reflectively symmetric within a side either; a rotationally symmetric layout was picked as the fairest guess. Cosmetic to the rules, and structural only to the final score.
• An unplaceable drawn tile is set aside and the turn passes. The other reading is that the game simply ends there.

This is the same posture as the Sequence board layout: where the real thing could not be verified, ship an honest substitute and say so, rather than a guess dressed up as authentic.

Known gaps

• The three-player flood variant is not implemented. Sources agree it exists and that the third player tries to stop the other two reaching the edges, but nothing found says how the flood scores, and inventing a scoring rule would be shipping a different game. Two- and four-player tables cover the family case; this can be added if the rulebook turns up.
• No draw-a-replacement rule. A tile that cannot be placed is gone for good rather than swapped, which is the simpler of the two readings.
• A full 84-tile game is long — 84 placements, and every one of them is a real decision. The two- and three-copy settings exist for that reason.
• The AI does not look ahead. It rates the board one placement deep. It plays a strong positional game because the heuristic is aimed at the right thing, not because it is searching.