Fencer: Because it's less confusing. With the table as it is, and the dice under the table, I can't see the dice and the names above the table. If my score was always displayed on the right (or always on the left), I can easier see what my score is (because it's always on the same side).

Let me ask you this, what's the advantage of half of your games having your score on the right, and half of the games having your score on the left?