jwiedlin wrote:I believe the discrepancy for dice "1" rolls lies in the behavior of risk attacks.
A roll of a "1" on an individual die by an attacker will more likely result in the loss of an attacking troop. This reduces the chance of a future attack. A stack of 4 attackers versus a stack of 20 defenders has the possibility of rolling "6" 30 times, but can only roll "1" a maximum of 4 times.
No. While your first sentence is correct -- rolling a 1 does make you less likely to attack next than rolling a 6 -- the distribution is theoretically independent of what has previously happened. If I roll ten winning battles in a row, I'm just as likely to roll a 1 in the next roll as a 6. The problem is indeed that the dice were drawn from a non-uniform distribution.