|Hexagon of Worms|
The first few times I played this game I tried to judge which would be the best symbol to use for the next clearing operation. As you go along the number of symbols increases. The game starts with three, and I got to the point where there were eight. Eventually, I think because I was tired, and because with the large number of symbols, progress was very slow, I gave up on trying to pick the best symbol and just started playing them in rotation. What was surprising is that this technique seemed to work as well as making a choice.
I went back and played the game a few more times using this rotation scheme. Sometimes it failed after only a few levels, but once it got as far as I had ever gotten using my original technique.
I am sure there is a mathematical explanation for this, but I am satisfied with my empirical results.
Update February 2017 replaced missing image.