A legitimate dice suggestion:
The algorithm should be based on 63 rolls of the die, one roll for each pip. within those 63 rolls there should be one 2 and 12; two 3’s and 11’s; three 4’s and 10’s; four 5’s and 9’s; and five 6’s 7’s and 8’s.
This will make it so that every number is rolled within a 63 turn game. I just played a game(gameid-farm 9157) with 63 turns and 9 and 12 were never rolled. I have had similar outcomes with 4 and 10.
If a game goes more than 63 turns, then the algorithm can reset