Key Takeaways

Note: this report shows the results of games played with the following modification: all random rolls (attacks from wolves and attacks from sheep) always resolve favourable to the player (except for Red sheep attacks, which always succeed regardless of target). The AI players are unaware of these “beneficial” rolls, so they make decisions as if they were playing the true game. All other game rules are kept: players can lose if the Shepherd reaches an unlocked gate, a cultist reaches the center of the board, or at least one of the remaining gates can’t be locked due to sheep deaths (sacrifices or Red killing fellow sheep).

This modification allows us to analyse the effect of the random outcomes of the combats and the difficulty of the game attending only to the initial random setup (board configuration, effect selection and ordering, and gate ordering) and random servant spawning.

Takeaway 1

Fewer sheep make the game harder and more sensitive to setup randomness. The win rates observed when all rolls are favourable to the player show that the game is more difficult with fewer sheep. In particular, the game is very hard for 3-sheep games, and relatively hard for 4-sheep games. There is also a higher variability of victories on 3 and 4-sheep games with respect to the setup, showing a high sensitivity to the setup in terms of game difficulty. 5 and 6-sheep games are easier to play, achieving high win rates overall and with a smaller sensitivity to the setup. This data reinfocers what was discovered previously: the randomness of the game and the initial setup leads to very different results.

Takeaway 2

3-sheep games are harder due to early cultist pressure and fewer power-ups. The data suggests different possible reasons for 3-sheep games to be harder than the rest. One of them is the round by which the second gate is closed. Closing the second gate of the game by round 3 seems to be a divisive factor for winning or losing the game: the data shows that when the second gate is closed later than this, the chances of winning the game drop.

Additionally, in 3-sheep games (which have the lowest winning rate of all sheep counts), sheep use significantly less the action Power-up, doing more attacks instead. This suggests that in these games, sheep are forced to do more attacks on enemy units to avoid losing the game, without being able to spare an action to power-up instead.

Finally, there is a high amount of games lost (by cultists) as early as in round 3, for any sheep count. This suggests that the pressure from cultists is very high since the very beginning of every game. The fact that all sheep attacks are successful in this game mode is an even stronger evidence that this is a strong factor for the high game difficulty.

Takeaway 3

Pink and Yellow sheep are strongest, while Black is weaker in 3-sheep games. The Pink (first) and the Yellow (second) sheep are the strongest among the herd, corresponding to higher winning rates for all sheep counts. The other sheep seem to be of equal strength, although 3-sheep games show that the Black sheep is significantly weaker than the others for this sheep count.

Takeaway 4

The board configuration affects game difficulty most in setup. The order in which gates are listed is not a strong factor for the difficulty of the game. Contrarily, it is the distribution of the tiles on the board what has a stronger impact on game difficulty.

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Game Overview


Tangled Yarns is a cooperative game played over 12 rounds. The game is played over a hexagonal board, where each hex has one border preventing figure movement and is one of 6 types: either a colour (red, black, blue, green, yellow), or desert. The Shepherd moves around the outside of the board on a 12-space track, triggering special rules for the round and spawning Cultists (which move towards the center of the board each round) or Wolves (which chase and attack the players; they cannot move into the center hex, and meeting in the same hex creates a ‘wolf pack’ such that those wolves move and attack together from that point on).

The players control one or more sheep characters with different abilities (including modifiers to health, attack, movement speed or defense, as well as action modifiers such as being allowed to jump over walls). The players must work together to defeat the Cultists before they reach the center, defend from the Wolves killing sheep, and close Gates before the Shepherd reaches them, all of which are loss conditions for the players. Gates require sheep to occupy hexes on the board of unique colour combinations and use a ‘Lock’ action in the same round; this closes the Gate, and also turns the used hexes to the Desert type such that they cannot be used again. Sheep can also collect bonuses (and start the game by choosing a free one in ‘easy mode’), each matching a different terrain type (to power-up their movement, attacks, defense, jumps or rotation of tiles). Attempting to collect bonuses on a Desert hex awards the sheep with a random bonus.

The players win by closing all the gates and surviving until the Shepherd completes travel across its track.

Actions

Players can always Move on their turn: the sheep can move up to its movement speed (or more by using bonuses); they cannot cross hex borders unless they have a jump ability; they can also not move through hexes with wolves. Then, they can choose between several main actions:

  • Attack: If they occupy a hex with one or more enemies (Cultists or Wolves), they can decide to attack one or more of them. Friendly sheep on the same hex can aid in a cooperative attack, adding their attack to the total attack value. The defense of opponents are is reduced by 1 for each ally taking part in the attack (other than the initiator of the attack). The result of the attack is random, biased by the sheep attack power and the enemies defense. Bonuses can be used to enhance attacks.
  • Lock: If the sheep occupy board hexes of the right types to lock a gate, they can use this action to do so (a requirement for winning the game).
  • Power-Up: The sheep receives a bonus based on the hex type they currently occupy (or random if on Desert). All bonuses can be shared freely between sheep.
  • Sacrifice: The sheep takes 1 point of damage, but pauses the Shepherd advance and its active effect for the round. If the sheep was completely healthy, it is now corrupted and respawned in the center of the board. Corrupted sheep have different abilities based on specific character traits. If the sheep was already corrupted, it is removed from the game instead. If not enough sheep remain in the game to close remaining gates (or at least 1 until the end), the players lose.

The same damage rules are applied when the sheep get attacked by the Wolves; only 1 sheep receives 1 damage in a successful wolf attack, regardless of how many figures are in the same hex.

Finally, sheep can end their turn by rotating the tile they occupy (or adjacent tiles with bonuses or abilities), unless occupied by a cultist, to modify path configurations that figures can take on the board. Rotations are restricted to 60 degrees if the sheep is corrupted.

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Game parameters

The following game parameters can easily be adjusted to change game functionality:

  • NTilesRatius: The radius of the board (default 3)
  • nEffects: The number of special round effects (default 4)
  • lastTurn: How many rounds there are in the game, or the length of the Shepherd’s track (default 12)
  • nGates: How many gates there are to close (default 6)

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AI Players

The players used to generate the data are all based on a tree-search algorithm (Monte Carlo Tree Search). At each decision point in the game, this algorithm creates a tree of statistics describing possible outcomes of various actions tried, up to a certain depth into the game (often the end for short games). It then picks the action most likely to lead to good outcomes.

Data

The following data is externally imported and can be adjusted for different game configurations. Not specified below is the possibility to run games with specific sheep characters.

Shepherd Effects

  • CLAW (Wolves have a movement of up to 3 hexes)
  • FANG (Wolves have an attack of 4)
  • DISEASE (No character traits can be used)
  • KINDNESS (Cultists have a defense of 3)
  • BITE (Wolves can reattack if they lose first attack)
  • QUIET (The land cannot be altered in any way this turn)
  • SHIFTING (All lines in the inner ring open to the center)
  • LIGHTNESS (Cultists further from center move one hex towards the center)
  • GIFT (Wolves can jump walls)
  • RAGE (Wolves have a defense of 2)
  • SPIRIT (Defeated cultists respawn at a random corner hex)
  • BEGUILING (Sheep attack is reduced by 1)

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Bonuses

  • Red: Increase attack by 1
  • Black: Rotate 1 extra tile
  • Green: Add 1 extra jump
  • Blue: Increase defense by 1
  • Yellow: Add 1 extra move

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Tokens

Sheep
  • Pink:
    • Attack: 2 (corrupted 0)
    • Defense: 1 (corrupted 1)
    • Move: 4 (corrupted 4)
    • Cannot rotate tiles
  • Red:
    • Attack: 3 (corrupted 4; must stop and attack any creature, including sheep, it shares a hex with)
    • Defense: 2 (corrupted 1)
    • Move: 2 (corrupted 2)
  • Yellow:
    • Attack: 2 (corrupted 2)
    • Defense: 1 (corrupted 1)
    • Move: 2 (corrupted 2)
    • Can Lock adjacent hex (line of sight required if corrupted)
  • Black:
    • Attack: 2 (corrupted 2)
    • Defense: 1 (corrupted 1)
    • Move: 2 (corrupted 2)
    • Can choose bonus received from Power-Up action. If corrupted, the bonus received is randomly changed.
  • Blue:
    • Attack: 2 (corrupted 2)
    • Defense: 1 (corrupted 1)
    • Move: 2 (corrupted 2)
    • Can rotate adjacent hex (line of sight required if corrupted)
  • Green:
    • Attack: 2 (corrupted 2)
    • Defense: 1 (corrupted 1)
    • Move: 2 (corrupted 2)
    • Can jump over walls if not corrupted
Servants
  • Cultist:
    • Attack: 0
    • Defense: 2
    • Move: 1
  • Wolf:
    • Attack: 3
    • Defense: 1
    • Move: 2

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Servant Cards

The following is the definition for the servant cards, with adjustable parameters. ‘Sheep’ refers to the number of sheep in the game required for that card to be a possible choice.

Idx,Sheep,Cultists,Wolves
1,3,2,0
1,4,2,0
1,5,2,0
1,6,3,0
2,3,1,2
2,4,1,1
2,5,1,2
2,6,1,2
3,3,1,1
3,4,1,0
3,5,1,1
3,6,1,1
4,3,1,0
4,4,0,0
4,5,1,1
4,6,1,0
5,3,0,1
5,4,1,1
5,5,0,0
5,6,0,1
6,3,1,0
6,4,0,1
6,5,0,1
6,6,1,0
7,3,0,1
7,4,0,1
7,5,1,0
7,6,0,1
8,3,1,1
8,4,1,0
8,5,1,1
8,6,1,1
9,3,1,1
9,4,1,1
9,5,1,1
9,6,1,1
10,3,0,1
10,4,0,1
10,5,0,1
10,6,0,1
11,3,0,3
11,4,0,3
11,5,0,3
11,6,0,4

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Gate Cards

The following is the definition for the gate cards, with adjustable parameters. ‘Sheep’ refers to the number of sheep in the game required for that card to be a possible choice.

Gate,Sheep
"YELLOW,RED","3,4"
"BLACK,GREEN",3
"BLUE,RED",3
"BLUE,BLACK,GREEN",3
"BLUE,RED,YELLOW",3
"BLACK,YELLOW,GREEN","3,4"
"BLACK,RED,BLUE",4
"BLACK,YELLOW,GREEN,BLUE","4,6"
"BLUE,YELLOW,GREEN,RED",4
"BLUE,RED,BLACK,GREEN","4,5"
"RED,GREEN,YELLOW",5
"BLACK,BLUE,GREEN,RED,YELLOW","5x3,6"
"YELLOW,BLUE,BLACK",5
"GREEN,BLACK,BLUE,YELLOW,BLUE,RED",6
"BLACK,GREEN,YELLOW,RED",6
"BLACK,BLUE,YELLOW,GREEN,YELLOW,RED",6
"RED,BLACK,BLUE,RED,GREEN",6

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Setup Boards

3 Sheep boards

1744635929175

1744639792095

1744648355719

1744650164569

1744654872283

1744656320853

1744658207893

1744662628767

1744663901475

1744665676416

4 Sheep boards

1744514700429

1744530703175

1744538615116

1744554404808

1744567478573

1744575892781

1744583543652

1744590976877

1744606079099

1744627153130

5 Sheep boards

1744710440204

1744757485182

1744773814906

1744784093485

1744791302806