Don't question how it works, it just does™. Now, if the ai moves its ▲, you move your ▲, and if the ai moves its ◆, you move your ◆. There's a marked path you're always moving in that direction. The picture shows the strat when the ai plays top-left the strat for bottom-right is essentially a mirror (play top-left yourself and move anticlockwise) Not much to say here, except that picking the correct marble to walk with is important. Variant B (bottom-left/bottom-middle outer) Don't undo for this in full game runs it is too unlikely for that to happen. There's also an IL meme hiding in here: if the ai plays top-left inner, you can just move ◆ up for an instant win. I know it looks like you're just gonna get blocked at bottom-middle-inner, but the ai normally considers the more indirect threat on left-inner more important. Note that we just need to set up at most one mill, since the game should end before the opponent reaches the flying phase. The blue arrows show your mill setup in the movement phase. In each variant, your last placement is marked with a ◆ in the corresponding image. Otherwise you can follow the branches as marked. Some spaces are unmarked undo if the ai plays there. We can distinguish four distinct variants: Now there's 10 different moves for the ai and all of them can occur. These considerations can save a bit of undos if you have sufficiently decent spatial awareness, although they are not that important in the greater scheme of things. You may need to undo a few moves, but you're pretty likely to not need too many.ĭo note that the order the ai plays in doesn't matter too much, and there are obviously rotations and reflections possible additionally, there is another game-theoretic symmetry by interchanging the inner and outer rings. On turn 6, replace the marble that just got milled. This strat works decently well against any difficulty, although Normal ai is probably the fastest. I doubt this particular strat is optimal for the IL though, since you do give an early mill to the opponent. Obviously, the latter one is faster, and this strat is designed to reliably get a win with at least four opponent pieces remaining. In Nine Men's Morris, one can win by either milling the opponent down to two men, or by blocking the opponent so they have no moves. I believe this case is a draw as well.Update : Added some faster variants and removed the old variant C () Anything else isn't moving towards a victory. If player 1 moves c3-b3 to threaten a win, player 2 moves a1-b1 to block, and the players would then reverse those moves causing a stalemate. I can't see any way player 1 can force a win here. Player 1 would then move a2-b1, player 2 would move c2-b3, and the game would be a stalemate.Ĭase 3 (1. b1-a2 is the best move as it threatens a player 1 win, but player 2 just responds with b3-c2. Unlike in Three Man's Morris, here Player 1 must move to a2 to prevent a loss (player 2 threatens b3-a2). Player 1 can then force either of the following boards:Ĭase 2 (1. Given that, player 2 should respond by playing in a corner (say A3). If player 2 instead plays C1 on turn 3, player 1 can move b2-a2 to win. This generates the following board, where player 1 can move a1-c1 to win: 1 2 3 I'm going to gloss over a lot of the piece orientations during setup in general, the optimal piece orientation is implied by the subsequent moves a player wants to threaten.Īs player 1, you want to start in the middle with your piece orthogonal (B2+).Ĭase 1: If player 2 responds in the middle of a side (say B3), player 1 can force a win by playing 2. Those solutions give a good starting point for this game. There are two possible victories, depending upon the second player's moves, the first being: 1. The Libro de los Juegos lists the following solutions ( translation from here): ![]() The classic Three Men's Morris was solved in the 1200's as a first player victory. I'm assuming that this game has something akin to Chess's draw due to Threefold Repition if not, the optimal result of the game is that you play forever, in which case the only winning move is not to play. Unlike Three Men's Morris, the extra movement options under the rules you cite mean the game is likely a draw under optimal play. The game you are describing is more similar to Three Men's Morris than to Tic Tac Toe.
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