For board games, like "Settlers of Catan" where resources are generated based on rolls of 2d6, one could use an analog version of this with a cup containing 36 chits, of the numbers 2-12 according to the normal distribution, _without_ replacement. You would still get the randomness of ordering, but over 36 draws/turns would get a complete "average" distribution.

If that is a bug or a feature is left as an exercise for the reader.