Audamir

Colony: what holds for the layout and for play

None of the eight layouts of Colony favours the player who starts; they differ in the opening, draws and length. What holds for the jump and the copy, the endgame and simple rules against the AI.

Game: Colony

Colony has no chance in it, so what the setup does can be measured: the map, the start position and the empty cells give eight layouts. All the numbers come from games of AI opponents; people were not measured.[1]

Layouts

The map of the layouts of Colony: the four start positions and what the measurement says of eachThe four start positions of Colony: a map of 58 or 61 cells and a start with three or one piece each. 58 cells, three pieces each: first flip on move 3.7, first player wins 48%, draws 4.4%, length of a game 115 moves. 58 cells, one piece each: first flip on move 13.9, first player wins 48%, draws 3.9%, length of a game 114 moves. 61 cells, three pieces each: first flip on move 3.7, first player wins 49%, draws 0.0%, length of a game 131 moves. 61 cells, one piece each: first flip on move 13.8, first player wins 47%, draws 0.0%, length of a game 132 moves. The dark cells on the 58-cell map are blocked.58 cells, three pieces eachfirst flip on move3.7first player wins48%draws4.4%length of a game115 moves61 cells, three pieces eachfirst flip on move3.7first player wins49%draws0.0%length of a game131 moves58 cells, one piece eachfirst flip on move13.9first player wins48%draws3.9%length of a game114 moves61 cells, one piece eachfirst flip on move13.8first player wins47%draws0.0%length of a game132 movesred player (you)blue player (opponent)blocked cellNormal AI against Normal AI, 800 games per layout (empty cells off and on together), game 0.126.2
The map of the layouts of Colony: the four start positions and what the measurement says of each

Normal AI against Normal AI, 800 games per row (empty cells off and on together):

Map and startFirst flip on moveFirst player winsDrawsMoves
58 cells, three pieces each3.748%4.4%115
58 cells, one piece each13.948%3.9%114
61 cells, three pieces each3.749%0.0%131
61 cells, one piece each13.847%0.0%132
  • Neither the first move nor the side of the board decides in any layout: the player who starts wins 50.0% against the Weak AI, 48.0% against the Normal AI and 51.6% against the Strong AI (±1.7 points for the Weak and Normal AI, ±6.1 for the Strong AI).[2] The choice “who starts” is a matter of feel.
  • With one piece each nothing is flipped for the first thirteen moves and there is hardly any jumping; after that it plays as with three pieces.
  • The 61-cell map has no draws (an odd number of cells, the board is full at the end) and its games are longer: 15 to 20% pass 150 moves.
  • The empty-cell rule ends 2 to 4% of the games of the Normal AI and changes the result in about one game in a hundred.

Copy and jump

A copy and a jump in a real game of ColonyFour views of the whole board of 58 cells from one game of the Normal AI against the Normal AI. At the top a copy on move 48: before the move the blue player has 8 pieces and red 21, copies one piece to a neighbouring cell, flips 3 red pieces and after the move it is 12 to 18. At the bottom a jump on move 38: blue has 7 pieces and red 18 before the move, a piece jumps two cells, an empty cell is left where it stood, it flips 3 red pieces and after the move it is 10 to 15.Copy (move 48): the piece stays, a new one appearsbefore the moveblue 8, red 21after the moveblue 12, red 18Jump (move 38): the piece moves, its cell becomes emptybefore the moveblue 7, red 18after the moveblue 10, red 15piece that movestarget of a copytarget of a jumpcell it leftflipped piecesNormal AI against Normal AI, the 58-cell layout with three pieces, game 0.126.2
A copy and a jump in a real game of Colony
  • The board fills only with copies: a game has exactly 52, 56, 55 or 59 copies, depending on the layout, and ends with a copy into the last empty cell. Everything else is jumps.
  • By a search to depth 5 a copy is better more often in the opening (42% of positions against 34%), a jump in the middle of the game (41 to 46% against 21 to 29%). When the search sees the end of the game in the endgame, the result is better after a jump in 60% of the positions and after a copy in 18%.[3]

Endgame

  • The player who leads 40 moves before the end wins 51% of the games of the Normal AI, 12 moves before the end 69%, one move before the end 87%.
  • The player who plays the last piece was behind before it in 86% of the games of the Normal AI and won only 27%; against the Strong AI 93% and 14%. Why was not investigated.

Against the AI

The rules are played by a script as a stand-in for a person; a real person would hold them with mistakes.

RuleWeak AINormal AIStrong AI
the highest number of the hint54.5%0.0%0.0%
always copy45.8%0.5%0.0%
look at what the opponent takes back97.8%1.8%0.0%
  • A principle that was not measured: counting before the move what the opponent takes back beats the Weak AI; against the Normal AI one must also see one's own next move.[4]

Notes

  1. See (forthcoming article no. 64). ↩︎
  2. Measurement colony.js --layouts and a script that keeps every move, 400 games per row (Strong AI 32), eight layouts, game 0.126.2. ↩︎
  3. See (forthcoming article no. 65). ↩︎
  4. 200 games against the Weak and the Normal AI, 40 against the Strong AI; game 0.126.2. ↩︎