All Columns Pattern Set 3.a.3 in Connect 4
Connect 4 in 3 Moves
Deduction Path: All Columns and Disc Omission on Re1ppp.
Number of Patterns: 2
Pattern List: re1ppp, re1re0pp
Deduced From: re1ppp
Winning Move: re0 of re1re0pp
After playing this winning move the pattern set specified under deduced from pattern sets hereunder is created by following (in reverse direction) the deduction path above.
Deduced From Pattern Sets:
Pset 2.a.1 (re1ppp, Deduction Path: All Columns and Opponent Disc Omission on Depth of Re0ppp)
Deduction Source for Pattern Sets:
Condition List:
- Re1re0ppOnTopOfOneColumn: There exists exactly one column with exactly one empty position that corresponds with the re0 position of re1re0pp pattern(s). All re's of all re1re0pp patterns involved are specific columns that don't need a re1ppp pattern because if the player plays the winning move, re0, all involved re1re0pp patterns are transformed into re1ppp patterns.
- AllOtherOpenColRe1ppp: In an all columns pattern set for winning in M moves every other open column, besides specific columns with other specific conditions, has a re1ppp pattern. In other words all other columns are closed or have a re1ppp. As such an opponents move on any other open column creates a re0ppp enabling the player to win.
- AfterMoveNoFasterWinForOpponent: After the players winning move, as specified by the winning move property above, no pattern set (pset) of the opponent may exist on the board that implies a faster win for the opponent. If the player can choose more than one column to win, it is sufficient no faster opponent win exists after the players move on one of those winning columns. For example for psets 3.x.y (connects 4 in 3 moves) no psets 1.v.w (connects 4 in 1 move) of the opponent may exist after the specified players move.
Connect 4 Board Example List:
PSPSSSPPPPSPPSSPPPSSPPSSSPPSSSSPSSPEPSSPEPE
PSPSSPPPPSPPPSEPPPSSPESSSPSPESSPSPPEPSSESSE
PSPSSSPPPPSPPSSPPPSSPPSSSPSSPSSPSSPEPSSEPPE
PSPSSSPPPPSPPSSSPPSSPPSSSPPSSSSEPSSEPPEEPPE |