Usually, when playing with paper and pencil, the rules are slightly modified. Links are not removed, so erasure is not necessary, and your OWN links are allowed to cross each other. So, for example, you might create a path which loops across itself, which could never happen with a physical set. In terms of game outcome, win, draw, or loss, this rules change rarely makes any difference, but it could. See http://en.wikipedia.org/wiki/Twixt#Variants for a more detailed discussion.