Skip to main content
complete revision
Source Link
Kristal Cantwell
  • 6.5k
  • 1
  • 25
  • 45

In misere tic tac toe on a 3x3 board with each player being x the secondfirst player will win. If thethe first player doesn'twill play the center square(2,2) then WLOG the second player will play (1,1) player canor (4-i2,4-j3) then if the second player has played (1,..1) the first will play (2,3). And if the second player has played (2,3) the first will play (1,1). Now there are four squares in response to anywhich the second player can move without losing: (1,2),(1,3),(3,2) and (i3,j1) of. If the firstsecond player and plays (1,2) the first player will be forced toplays (3,1) and on the next move the second player must form a line of three and the first player wins. If the firstsecond player plays to(3,1) the center square thenfirst player plays (1,2) and on the next move secondthe second player can play to the center of onemust form a line of three and the rows or columnsfirst player wins. Then there will be four squares left that theIf the second player plays (1,3) the first player canplays (3,2) and on the next move to without forming the second player must form a line with two x'sof three and losingthe first player wins. But whatever this move is it leave exactly one square left forIf the second player to move toplays (3,2) the first player plays (1,2) and after that move is made every remainingon the next move by the firstthe second player will result inmust form a line with two spots filled with x's thatof three and the secondfirst player can fill in and win wins. So But this exhausts all cases so the secondfirst player willmust win in this game.

In misere tic tac toe on a 3x3 board with each player being x the second player will win. If the first player doesn't play the center square then the second player can (4-i,4-j,...) in response to any move (i,j) of the first player and the first player will be forced to form a line first. If the first player plays to the center square then the second player can play to the center of one of the rows or columns. Then there will be four squares left that the first player can move to without forming a line with two x's and losing. But whatever this move is it leave exactly one square left for the second player to move to and after that move is made every remaining move by the first player will result in a line with two spots filled with x's that the second player can fill in and win. So the second player will win.

In misere tic tac toe on a 3x3 board with each player being x the first player will win. the first player will play (2,2) then WLOG the second player will play (1,1) or (2,3) then if the second player has played (1,1) the first will play (2,3). And if the second player has played (2,3) the first will play (1,1). Now there are four squares in which the second player can move without losing: (1,2),(1,3),(3,2) and (3,1). If the second player plays (1,2) the first player plays (3,1) and on the next move the second player must form a line of three and the first player wins. If the second player plays (3,1) the first player plays (1,2) and on the next move the second player must form a line of three and the first player wins. If the second player plays (1,3) the first player plays (3,2) and on the next move the second player must form a line of three and the first player wins. If the second player plays (3,2) the first player plays (1,2) and on the next move the second player must form a line of three and the first player wins. But this exhausts all cases so the first player must win in this game.

Source Link
Kristal Cantwell
  • 6.5k
  • 1
  • 25
  • 45

In misere tic tac toe on a 3x3 board with each player being x the second player will win. If the first player doesn't play the center square then the second player can (4-i,4-j,...) in response to any move (i,j) of the first player and the first player will be forced to form a line first. If the first player plays to the center square then the second player can play to the center of one of the rows or columns. Then there will be four squares left that the first player can move to without forming a line with two x's and losing. But whatever this move is it leave exactly one square left for the second player to move to and after that move is made every remaining move by the first player will result in a line with two spots filled with x's that the second player can fill in and win. So the second player will win.