Took me a minute to catch on - just play the odds! At first I was trying to play tic tac toe, but the winning strategy seems to be to go for the square likeliest to land your own mark.
Yes, the AI mostly just looks for plays that have high certainty and are connected to other potential winning squares (for either team). Then it weights plays positively or negatively based on whether or not the "bad" chance outweighs "good"