It is played exactly the same as the Nine Men version but with Twelve pieces and a board with diagonals on it. With all of the aspects of Nine Men’s Morris but even more to think about (as you have more pieces and diagonals to consider) it can be a quite challenging game. This is a game that is much more complex and I’me much happier I went to the effort to make a board for it. Three in a row, just like Tic Tac Toe! Twelve Men’s Morris: So is it worth spending an hour branding a game board for it? Probably not, just variate your games of Tic Tac Toe every once in a while. Quite possibly the shortest game I have ever played taking literally about a minute to play (like Tic Tac Toe) and coming to an immediate win, lose or draw! However even the version I created, which lacked the diagonals of Tic Tac Toe could still just as easily by played on paper because there is no movement phase like in Nine and Twelve Men’s Morris. Now there are different versions of Three Men’s Morris but one of them is exactly the same as Tic Tac Toe, So I made the one that wasn’t (for obvious reasons). So when you have a piece of wood, the tools and the know-how, just make one! Three Men’s Morris: However, I'm seeing so few draws I wonder whether there's a bug in my simulation code.Aside from that, versions are expensive and difficult to come by. Intuitively this makes sense because a draw requires all 9 squares to be filled in, which means the odds of an illegal move by that point are at their highest. In my simulations, I see a majority of invalid games (as one would expect), and some games where 'x' or 'o' wins, but I almost never see drawn games. So the 'x' player might try to play an 'o' (resulting in an invalid game), or might try to play an 'x' in a square that already contains an 'x', etc. To elaborate, on each turn, each player is playing randomly without even knowing what the legal moves are. Given a randomly-played game between two players who don't even know the rules, how would I calculate the odds of the four possible outcomes: x wins, o wins, draw, invalid game I have a toy problem I've been playing with simulating for fun and learning, and I'd like to have a deeper understanding of the math involved.
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