Interestingly, after they learn how to play against starting in the center, starting in the corner gives a great winning chances for a game or two because they will then try blocking in the corner as learned previously. So, probability of my win starts at about about 5/6 initially (1/2 * 1/3 they make the correct first two moves), though it fairly quickly drops to 2/3 where it remains longer.
Probability they are putting o randomly in one of remaining corners is just 1/3. If they don't fail this test, then I am putting another x in the same line so their first o now blocks my line. Starting in the center: in the first few games (more with younger daughter), win chances are pretty good - half of the time they put their first o on the edge instead of the corner. (well, it was about 1/2 as they sometimes didn't see upcoming 3 in a line) Then, chance of their draw was about 2/3 theoretically - chance they put o somewhere on the side, forcing me to block and then we rapidly fill the whole board by eliminating the obvious 3 in a line options. Starting in the corner: everyone put o in the center. From experience of playing against kids that don't have the game solved (daughters, ages 5 and 7 at the time of play), starting in the corner gave about 1/3 chance to win and starting in the center gave about 5/6 for first few games and then 2/3.
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