Find a great strategy to a pentomino type game

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I have a game.



Given an $8times 8$ square and a set, which contains the pentominoes and four $1times 1$ squares. Players alternately pick one item from the set. Then players (starting with the player who had chosen the first item) take turns in placing pentominoes on the board so that they do not overlap with existing tiles and no tile is used more than once. The objective is to be the last player to place a tile on the board.



So I need a great strategy. I am sure there doesn’t exist a winning strategy (and if so, then it is complicated), so I only need a strategy which helps to win. enter image description here




game-theory combinatorial-game-theory polyomino




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  • 3




    What's the origin of this problem? What have you tried so far? (There most certainly does exist a winning strategy, since the game is finite and always has a winner). Also, your description of the problem suggests that the pentominos could be flipped (since $12times5+4=64$), but your image is of the 18 'one-sided' pentominoes; which is it?
    – Steven Stadnicki
    Jul 31 at 15:47










  • You are able to rotate and mirror each pentomino
    – Leo Gardner
    Jul 31 at 20:27










  • Please help to find as good strategy as possible
    – Leo Gardner
    Jul 31 at 20:28














up vote
2
down vote

favorite












I have a game.



Given an $8times 8$ square and a set, which contains the pentominoes and four $1times 1$ squares. Players alternately pick one item from the set. Then players (starting with the player who had chosen the first item) take turns in placing pentominoes on the board so that they do not overlap with existing tiles and no tile is used more than once. The objective is to be the last player to place a tile on the board.



So I need a great strategy. I am sure there doesn’t exist a winning strategy (and if so, then it is complicated), so I only need a strategy which helps to win. enter image description here




game-theory combinatorial-game-theory polyomino




share|cite|improve this question

















  • 3




    What's the origin of this problem? What have you tried so far? (There most certainly does exist a winning strategy, since the game is finite and always has a winner). Also, your description of the problem suggests that the pentominos could be flipped (since $12times5+4=64$), but your image is of the 18 'one-sided' pentominoes; which is it?
    – Steven Stadnicki
    Jul 31 at 15:47










  • You are able to rotate and mirror each pentomino
    – Leo Gardner
    Jul 31 at 20:27










  • Please help to find as good strategy as possible
    – Leo Gardner
    Jul 31 at 20:28












up vote
2
down vote

favorite









up vote
2
down vote

favorite











I have a game.



Given an $8times 8$ square and a set, which contains the pentominoes and four $1times 1$ squares. Players alternately pick one item from the set. Then players (starting with the player who had chosen the first item) take turns in placing pentominoes on the board so that they do not overlap with existing tiles and no tile is used more than once. The objective is to be the last player to place a tile on the board.



So I need a great strategy. I am sure there doesn’t exist a winning strategy (and if so, then it is complicated), so I only need a strategy which helps to win. enter image description here




game-theory combinatorial-game-theory polyomino




share|cite|improve this question













I have a game.



Given an $8times 8$ square and a set, which contains the pentominoes and four $1times 1$ squares. Players alternately pick one item from the set. Then players (starting with the player who had chosen the first item) take turns in placing pentominoes on the board so that they do not overlap with existing tiles and no tile is used more than once. The objective is to be the last player to place a tile on the board.



So I need a great strategy. I am sure there doesn’t exist a winning strategy (and if so, then it is complicated), so I only need a strategy which helps to win. enter image description here





game-theory combinatorial-game-theory polyomino





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 5 at 2:47









Herman Tulleken

782416




782416









asked Jul 31 at 15:39









Leo Gardner

35911




35911







  • 3




    What's the origin of this problem? What have you tried so far? (There most certainly does exist a winning strategy, since the game is finite and always has a winner). Also, your description of the problem suggests that the pentominos could be flipped (since $12times5+4=64$), but your image is of the 18 'one-sided' pentominoes; which is it?
    – Steven Stadnicki
    Jul 31 at 15:47










  • You are able to rotate and mirror each pentomino
    – Leo Gardner
    Jul 31 at 20:27










  • Please help to find as good strategy as possible
    – Leo Gardner
    Jul 31 at 20:28












  • 3




    What's the origin of this problem? What have you tried so far? (There most certainly does exist a winning strategy, since the game is finite and always has a winner). Also, your description of the problem suggests that the pentominos could be flipped (since $12times5+4=64$), but your image is of the 18 'one-sided' pentominoes; which is it?
    – Steven Stadnicki
    Jul 31 at 15:47










  • You are able to rotate and mirror each pentomino
    – Leo Gardner
    Jul 31 at 20:27










  • Please help to find as good strategy as possible
    – Leo Gardner
    Jul 31 at 20:28







3




3




What's the origin of this problem? What have you tried so far? (There most certainly does exist a winning strategy, since the game is finite and always has a winner). Also, your description of the problem suggests that the pentominos could be flipped (since $12times5+4=64$), but your image is of the 18 'one-sided' pentominoes; which is it?
– Steven Stadnicki
Jul 31 at 15:47




What's the origin of this problem? What have you tried so far? (There most certainly does exist a winning strategy, since the game is finite and always has a winner). Also, your description of the problem suggests that the pentominos could be flipped (since $12times5+4=64$), but your image is of the 18 'one-sided' pentominoes; which is it?
– Steven Stadnicki
Jul 31 at 15:47












You are able to rotate and mirror each pentomino
– Leo Gardner
Jul 31 at 20:27




You are able to rotate and mirror each pentomino
– Leo Gardner
Jul 31 at 20:27












Please help to find as good strategy as possible
– Leo Gardner
Jul 31 at 20:28




Please help to find as good strategy as possible
– Leo Gardner
Jul 31 at 20:28










1 Answer
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This game is described in Golombs' Polyominoes (p. 8-9). He writes:




It is difficult to advise what strategy should be followed, but
there are two valuable strategic principles:



  1. Try to move in such a way that there will be room for
    an even number of pieces. (This applies only when there
    are two players.)

  2. If a player cannot analyze the situation, he should do
    something to complicate the placement so that the next
    player will have even more difficulty analyzing it than
    he did.



Since this reference is quite old, you may be able to dig up some further work on this topic.



Here is a proof that the first player can always win: Pentominoes: A First Player Win. They describe various ways in which the search algorithm can be sped up; doing the opposite then can be a good way to implement number (2) above. They also give two winning moves.






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    1 Answer
    1






    active

    oldest

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    oldest

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    active

    oldest

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    up vote
    0
    down vote













    This game is described in Golombs' Polyominoes (p. 8-9). He writes:




    It is difficult to advise what strategy should be followed, but
    there are two valuable strategic principles:



    1. Try to move in such a way that there will be room for
      an even number of pieces. (This applies only when there
      are two players.)

    2. If a player cannot analyze the situation, he should do
      something to complicate the placement so that the next
      player will have even more difficulty analyzing it than
      he did.



    Since this reference is quite old, you may be able to dig up some further work on this topic.



    Here is a proof that the first player can always win: Pentominoes: A First Player Win. They describe various ways in which the search algorithm can be sped up; doing the opposite then can be a good way to implement number (2) above. They also give two winning moves.






    share|cite|improve this answer

























      up vote
      0
      down vote













      This game is described in Golombs' Polyominoes (p. 8-9). He writes:




      It is difficult to advise what strategy should be followed, but
      there are two valuable strategic principles:



      1. Try to move in such a way that there will be room for
        an even number of pieces. (This applies only when there
        are two players.)

      2. If a player cannot analyze the situation, he should do
        something to complicate the placement so that the next
        player will have even more difficulty analyzing it than
        he did.



      Since this reference is quite old, you may be able to dig up some further work on this topic.



      Here is a proof that the first player can always win: Pentominoes: A First Player Win. They describe various ways in which the search algorithm can be sped up; doing the opposite then can be a good way to implement number (2) above. They also give two winning moves.






      share|cite|improve this answer























        up vote
        0
        down vote










        up vote
        0
        down vote









        This game is described in Golombs' Polyominoes (p. 8-9). He writes:




        It is difficult to advise what strategy should be followed, but
        there are two valuable strategic principles:



        1. Try to move in such a way that there will be room for
          an even number of pieces. (This applies only when there
          are two players.)

        2. If a player cannot analyze the situation, he should do
          something to complicate the placement so that the next
          player will have even more difficulty analyzing it than
          he did.



        Since this reference is quite old, you may be able to dig up some further work on this topic.



        Here is a proof that the first player can always win: Pentominoes: A First Player Win. They describe various ways in which the search algorithm can be sped up; doing the opposite then can be a good way to implement number (2) above. They also give two winning moves.






        share|cite|improve this answer













        This game is described in Golombs' Polyominoes (p. 8-9). He writes:




        It is difficult to advise what strategy should be followed, but
        there are two valuable strategic principles:



        1. Try to move in such a way that there will be room for
          an even number of pieces. (This applies only when there
          are two players.)

        2. If a player cannot analyze the situation, he should do
          something to complicate the placement so that the next
          player will have even more difficulty analyzing it than
          he did.



        Since this reference is quite old, you may be able to dig up some further work on this topic.



        Here is a proof that the first player can always win: Pentominoes: A First Player Win. They describe various ways in which the search algorithm can be sped up; doing the opposite then can be a good way to implement number (2) above. They also give two winning moves.







        share|cite|improve this answer













        share|cite|improve this answer



        share|cite|improve this answer











        answered Aug 5 at 2:33









        Herman Tulleken

        782416




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