Published on Feb 11, 2016

### Abstract

The objective: I am using the game Connect-Four to study artificial intelligence. I wanted to determine the effects of ply depth (the number of plies, which are turns by a single player, that the program looks ahead) and the effects of getting the first move on both the chance of winning and the time taken.

### Methods/Materials

To do this, I wrote some computer programs in C to simulate games between computer-controlled players.

### Results

I found that increasing the ply depth increases the chance of winning, as does getting the first move.

I found that the effect of a single ply depth increase was greater than the effect of getting the first move.

I found that when two identical players faced off, there would be more draws if both had even ply depths. I also found that increasing the ply depth by 1 make the program take about 7 times as long per move.

### Conclusions/Discussion

My results agree with my hypothesis, though I did not expect the result with more draws at even ply depths. Each extra ply taking 7 times as long fits with the prediction based on branching width.

This Mathematical project is to create an artificial-intelligence program to play Connect-Four and use it to test the effects of going first and looking further ahead in possible moves on the chance of winning and on the time taken.