Beginners will often overlook a simple threat to connect four discs; it is therefore important to always check all vertical, horizontal and diagonal lines before making a move.
In more advanced play, one aims at forcing a win by making two threats simultaneously; conversely, one should prevent the opponent from doing so. For instance, in the figure on the right, it is green's turn. Yellow will win on their next turn irrespective of green's move because of the threat of extending the diagonal of three consecutive yellow discs to four by dropping a disc either on the third or on the last column, only one of which can be blocked by green.
As a general rule of thumb, discs played in the center columns are more valuable than border column discs, because they participate in more potential fourdisc lines (and accordingly limit the opponent's opportunities).
Among good players, the short term goal is to connect three discs, thereby preventing the opponent from playing in a certain column. Towards the end, the game then often turns into a complex counting match: both players try to win by forcing the other to play a certain column.
In these situations, it is useful to realize that, if it's your move, then after filling an even number of places, it's still your move. Every column has an even number of places.
Beyond this, it turns out that the strategies for the first and second player differ markedly. Every three aligned discs of one color create a hole, a place which when filled with the right color would yield fourinarow. A hole is called even or odd depending on whether it occurs in an even or oddnumbered row (with the bottom row being numbered 1). In order for white (the first player) to win, white needs more odd holes than black; the even holes don't matter. In order for black (the second player) to win, black needs at least two more odd holes than his opponent, or the same number of odd holes and at least one even hole. (These rules are somewhat simplified: it gets more complicated if several holes occur in the same column; most of the time, holes occurring above other holes are useless.)
 Wikipedia
