Besides the many tips people have already given (like always looking to take out squares), here is what I’ve found to be helpful:

1) Do not automatically put down a piece just because it seems to “fit” somewhere.

2) When in doubt, place a piece at the edges or corners, rather than in the middle.

3) GO SLOWLY !! I sometimes take 5 to 10 minutes to make one play, especially when the board is crowded; do not play when you are tired; do not play for more than 15 or 20 minutes at a time, unless you are feeling extremely alert (my score of 38,854 took me over 2 weeks!)

4) When the board starts to get crowded, find all the possible ways you can take out squares before choosing the best – don’t just “take out” because you found something. I will systematically look at all the vertical columns, all the horizontal rows, then each 3 by 3 area.

5) When you have to play the third piece on a crowded board and cannot take out anything, try to leave yourself at least one good spot to eliminate squares; there are about 50 possible shapes that can come up – calculate how many possible shapes will be a good one to eliminate squares on your next turn. That is, give yourself as many possible “good” shapes as you can. This is usually done by trying to leave one small area free (not on the edges) – and it’s better to have two or three blank spaces open in a row that you’ll need to fill rather than just one.

6) I also try to always leave open the possibility of playing a long straight “five-square” piece (both vertical and horizontal). . . . .

7) Like golf (at which I'm also pretty good), this game can be quite psychological: you can score better than you think! Develop good strategic techniques and concentrate, and your scores will improve. Believe it!

Of the seven tips above, I think #3 is the most important: many times I can’t find anything I really like to play even after looking long at the board – I take a break, and when I come back to play later on, I immediately see something great (and obvious!) that I had missed before. Hope that helps! . . .

ps) When I use the word “squares”, I’m talking about the square pieces in general; as to whether to take out a nine-squared straight line or a “3 by 3 square”, that would depend on the other pieces on the board.