The position is

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 0, 0, 0, 0
2, 0, 2, 1, 0, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
         Red can win in , 4, moves by putting its piece(1) in column, 5

                              leading to position

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 0, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
   The reasonable moves for Black are to move in columns, 1, 2, 3, 4, 5, 6, 7

               if Black moves in column, 1, then the position is

0, 0, 0, 0, 0, 0, 0
2, 0, 0, 0, 0, 0, 0
1, 0, 1, 0, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
                 from which Red can win in, 2,  moves. Indeed

                        --------------------------------

                                The position is

0, 0, 0, 0, 0, 0, 0
2, 0, 0, 0, 0, 0, 0
1, 0, 1, 0, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
         Red can win in , 2, moves by putting its piece(1) in column, 4

                              leading to position

0, 0, 0, 0, 0, 0, 0
2, 0, 0, 0, 0, 0, 0
1, 0, 1, 1, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
                  This is a double-or-nothing in columns, 3, 7

               --------------------------------------------------

               if Black moves in column, 2, then the position is

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 0, 0, 0, 0
2, 2, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
                 from which Red can win in, 2,  moves. Indeed

                        --------------------------------

                                The position is

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 0, 0, 0, 0
2, 2, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
         Red can win in , 2, moves by putting its piece(1) in column, 4

                              leading to position

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 1, 0, 0, 0
2, 2, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
                    This is a multiple-or-nothing in columns

                                    2, 3, 7

               --------------------------------------------------

               if Black moves in column, 3, then the position is

0, 0, 0, 0, 0, 0, 0
0, 0, 2, 0, 0, 0, 0
1, 0, 1, 0, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
                 from which Red can win in, 3,  moves. Indeed

                        --------------------------------

                                The position is

0, 0, 0, 0, 0, 0, 0
0, 0, 2, 0, 0, 0, 0
1, 0, 1, 0, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
          Red can win in , 3, moves by putting its piece(1) in columns

                                      4, 7

                      We will only prove it for column, 7

         Red can win in , 3, moves by putting its piece(1) in column, 7

                              leading to position

0, 0, 0, 0, 0, 0, 0
0, 0, 2, 0, 0, 0, 0
1, 0, 1, 0, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 1
            The reasonable moves for Black are to move in column, 4

               if Black moves in column, 4, then the position is

0, 0, 0, 0, 0, 0, 0
0, 0, 2, 0, 0, 0, 0
1, 0, 1, 2, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 1
                 from which Red can win in, 2,  moves. Indeed

                        --------------------------------

                                The position is

0, 0, 0, 0, 0, 0, 0
0, 0, 2, 0, 0, 0, 0
1, 0, 1, 2, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 1
         Red can win in , 2, moves by putting its piece(1) in column, 2

                              leading to position

0, 0, 0, 0, 0, 0, 0
0, 0, 2, 0, 0, 0, 0
1, 0, 1, 2, 0, 0, 0
2, 1, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 1
                  This is a double-or-nothing in columns, 2, 4

               --------------------------------------------------

               --------------------------------------------------

               if Black moves in column, 4, then the position is

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 2, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
                 from which Red can win in, 2,  moves. Indeed

                        --------------------------------

                                The position is

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 2, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
         Red can win in , 2, moves by putting its piece(1) in column, 2

                              leading to position

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 2, 0, 0, 0
2, 1, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
                  This is a double-or-nothing in columns, 2, 4

               --------------------------------------------------

               if Black moves in column, 5, then the position is

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 0, 2, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
                 from which Red can win in, 2,  moves. Indeed

                        --------------------------------

                                The position is

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 0, 2, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
         Red can win in , 2, moves by putting its piece(1) in column, 4

                              leading to position

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 1, 2, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
                  This is a double-or-nothing in columns, 3, 7

               --------------------------------------------------

               if Black moves in column, 6, then the position is

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 0, 0, 2, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
                 from which Red can win in, 2,  moves. Indeed

                        --------------------------------

                                The position is

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 0, 0, 2, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
         Red can win in , 2, moves by putting its piece(1) in column, 4

                              leading to position

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 1, 0, 2, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 0
                  This is a double-or-nothing in columns, 3, 7

               --------------------------------------------------

               if Black moves in column, 7, then the position is

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 0, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 2
                 from which Red can win in, 3,  moves. Indeed

                        --------------------------------

                                The position is

0, 0, 0, 0, 0, 0, 0
0, 0, 0, 0, 0, 0, 0
1, 0, 1, 0, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 2
          Red can win in , 3, moves by putting its piece(1) in columns

                                      3, 4

                      We will only prove it for column, 3

         Red can win in , 3, moves by putting its piece(1) in column, 3

                              leading to position

0, 0, 0, 0, 0, 0, 0
0, 0, 1, 0, 0, 0, 0
1, 0, 1, 0, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 2
            The reasonable moves for Black are to move in column, 4

               if Black moves in column, 4, then the position is

0, 0, 0, 0, 0, 0, 0
0, 0, 1, 0, 0, 0, 0
1, 0, 1, 2, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 2
                 from which Red can win in, 2,  moves. Indeed

                        --------------------------------

                                The position is

0, 0, 0, 0, 0, 0, 0
0, 0, 1, 0, 0, 0, 0
1, 0, 1, 2, 0, 0, 0
2, 0, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 2
         Red can win in , 2, moves by putting its piece(1) in column, 2

                              leading to position

0, 0, 0, 0, 0, 0, 0
0, 0, 1, 0, 0, 0, 0
1, 0, 1, 2, 0, 0, 0
2, 1, 2, 1, 1, 2, 0
1, 1, 2, 2, 2, 1, 0
2, 1, 2, 2, 1, 1, 2
                  This is a double-or-nothing in columns, 2, 4

               --------------------------------------------------

               --------------------------------------------------