I don’t know if there are any economic theorems about how markets incorporate information from their participants, but if we assume that they incorporate all of the information then it must be that the market participants had seen every number equally often except for seeing one extra three. So you should update as though you had seen an extra three, to get odds of 1:1:5:1:1:5. Then it would be worth placing a bet on six and against each other number.
I don’t know if there are any economic theorems about how markets incorporate information from their participants, but if we assume that they incorporate all of the information then it must be that the market participants had seen every number equally often except for seeing one extra three. So you should update as though you had seen an extra three, to get odds of 1:1:5:1:1:5. Then it would be worth placing a bet on six and against each other number.