Perhaps we've been looking at the wrong part of the dice system. The dice are random and we probably can't reduce streakiness by reworking the random numbers while still maintaining that randomness, but we should also consider the dice compare method. The dice compare method, where the attacker's and defender's highest dice are compared, then the second highest dice are compared, was lifted from the RISK board game. In the board game, the settings are manual for initial troops, so typically each player places a few large groups of armies on one continent to obtain that continent's bonus by the second or third round. I've played the board game for decades and in the RISK Tournament of Champions for 18 years and never has dice streakiness been a complaint. The reason is that attackers typically use large armies to conquer and rarely attack with only a few armies. The only time they do is during an elimination when the attacker is running low on armies and must get the defender's cards to run the board. With large armies, many dice are rolled and losing streaks are almost always counterbalanced by winning streaks. This dice compare method was chosen for the board game because it requires only 5 dice no matter how many attacking and defending armies there are. However, this may not be as appropriate for the Conquer Club environment in which the automatic setting for initial troops is typically used. Plus, there's no reason to limit the compare method to only 5 dice since the server could easily handle a large number of dice for each attack.
This suggests some alternatives, one of which is to use the Axis and Allies game's method where one die is rolled for each attacking army piece and one for each defending piece. This would require more dice rolls during each attack and thus more random numbers, thus reducing the effects of streaks. There are other ways to increase the number of dice rolled for each attack, so let's hear your thoughts.