halacha - Games (on Shabas) that involve writing: whose writing?

I don't have good sources handy, but apparently some forbid the Shabas playing of games in which one usually writes, even if playing without writing: Scrabble, in which one writes scores, is sometimes given as an example.

Does this depend on what that person usually does, or on what people usually do?

For example, Uno is a game that (at least in some versions) is played in rounds: the scores are subtotaled and written after each round. I know a family that would not have played it on Shabas because of the restriction on playing games that use writing. To allow themselves to play it on Shabas, they developed an alternate scoring system: instead of writing scores, they kept scores by placing bookmarks in books. (If a player's score was 127, he placed his bookmark between pages 126 and 127, facing page 127.) They used this method during the week also, so that the game became, for them, one in which writing was not utilized, and they could play it on Shabas. Is this valid?

Of course, I'm not asking for an halachic ruling here: everyone should consult his own rabbi. I'm asking, rather, for arguments and sources pro and con.