Victor allis connect four dissertation

The asymptotic complexity is defined by the most efficient (in terms of whatever computational resource one is considering) algorithm for solving the game; the most common complexity measure ( computation time ) is always lower-bounded by the logarithm of the asymptotic state-space complexity, since a solution algorithm must work for every possible state of the game. It will be upper-bounded by the complexities of each individual algorithm for the family of games. Similar remarks apply to the second-most commonly used complexity measure, the amount of space or computer memory used by the computation. It is not obvious that there is any lower bound on the space complexity for a typical game, because the algorithm need not store game states; however many games of interest are known to be PSPACE-hard , and it follows that their space complexity will be lower-bounded by the logarithm of the asymptotic state-space complexity as well (technically the bound is only a polynomial in this quantity; but it is usually known to be linear).

Always look out for force wins or force losses . Look out for your opponent trying to make a three-in-a-row diagonal directly linked to a three-in-a-row horizontal, which is a winning combination. This is an excellent strategy as it forces you to block one winning space, only to lose on the next turn. Think well ahead on each of your turns and see how you can reverse the position.

Forced moves can often give you a winning position . Building 3-in-a-row vertically will seldom not be seen by your opponent. They will have no option but to block it, or else they will lose. This means that they will effectively lose a chance to build a winning position by blocking you. But you will have 3 of your pieces all stacked together, which can be readily built next to, and you will now have many ways to branch out. You opponent will face a difficult job blocking off all your paths as a result, and this puts you in a good position for a win.

Try to kill off columns when you are behind . Often when you start second you will feel like you are always defending. To make things easier, try getting a 3-in-a-row combination in either the 6th or 2nd columns. You will reduce he options and may disrupt your opponent's strategy. If they try to stop you from blocking column, they will waste moves and give you to go on the offensive.

When your get a chance count the spots left on the board . Towards the end of the game, hen you get a chance, count the spots to see who is going to go where when you have to place disks in dead columns. Counting the spots will help you see if you are going to block your chances or will give your opponent an easy win. If you count remaining spots, and see that you are going to win, play defensive and work on using the dead columns to get a chance to win.