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rabbott
Posts: 1649
Posted 18:12 Oct 27, 2016 |

This diagram (from Snipd) shows a minimax (sub)tree from a starting point (the top row) in which there are three open positions. It is X's turn to move.  

The second row shows the three possible moves by X. That leaves two open positions for O.

The third row shows those moves.

The bottom row shows the final move by X into the only open position left.

 

 

 

The red numbers show the value for each board configuration: 0 means tie game; 1 means X wins.

The blue arrows pointing upward show the values for the higher level games. X chooses the move with the higher value; O chooses the move with the smaller value.

Although not shown on the diagram, X would choose as the first move the right-most move, which would produce a value of 1 and a win. So the value of the top-most position is 1.

Last edited by rabbott at 18:14 Oct 27, 2016.