The opponent’s Queen, for example, should always be attacked when gaining a bonus roll as the math is always in favor of the attacker. For example, if rolling a double Bishop allows you to attack the opponent’s Queen, you will have a ~42.13% chance of rolling a Bishop to capture the Queen. If you fail, the opponent will have a ~42.13% chance to roll a Queen and capture your Bishop.
When the opponent has an overall advantage in a specific game, look for opportunities to place the opponent in Check. Although the opponent has a ~92.52% chance from being diced out, it’s an opportunity for a lucky win.