# No-Connecting-4

Imagine a game of connect 4 where Player1 wins by Player2 connecting 4, and Player2 wins by forcing the board into a filled board without any 4-in-a-rows. A tie happens if Player1 connects 4.

Now Let's assume neither of them want to tie.

My question is, with perfect play by both players, will the game result in a win for Player1, Player2, or will it be a draw?

The board size is 7 columns, 6 rows!

• Like the physical game, each piece in a column starts from the bottom? – JonTheMon Nov 8 '14 at 18:10
• @JonTheMon As to be expected, yes. – warspyking Nov 8 '14 at 18:17
• No answers yet... I'm actually surprised. – warspyking Nov 9 '14 at 0:59
• Player2 can guarantee a tie. I conjecture that Player1 can also guarantee a tie, but I can't seem to prove it. – 6005 Nov 9 '14 at 13:49
• @Goos I can't wait to see an answer :D – warspyking Nov 9 '14 at 19:27

As mentioned in the comments, Player2 can guarantee a tie. An easy strategy for this is to just always move on top of Player1's last move. Due to the number of rows being even, this is always possible. Therefore only Player1 pieces can end up in the bottom row, and he'll end up with a 4 in a row before Player2 does.

Therefore Player1 cannot win. The best player1 can do is force a tie, which if possible means with perfect play player2 cannot win either.

Since the normal play of connect 4 is solved in favor of Player1, this means Player1 can always get 4 in a row no matter what Player2 plays.

Therefore, with perfect play the result of the game is a draw.

• I can't award the bounty yet, but good job! – warspyking Nov 15 '14 at 19:13

Player1 wins = normal Player2 win/player1 lose

Player2 wins = normal tie

tie = normal Player1 win/player2 lose

for this, Player2 has larger chance to get tie and win (as only he wins, player1 win will count 1), but if Player1 use strategy to force player2 win, then Player 1 wins

Player1 as slightly larger chance, since he lose, he will win, he win, it counted as tie, the only thing he need to do is not to get tie.

since they perfect play connect four, mostly they get is tie, so that Player2 will win.