A 'Random Reward' is the benefit one can obtain from completing certain quests. Quests that can award random rewards are: Recurring Quests, Event Quests, Story Quests, and Side Quests. Quest rewards of goods, medals, coins, supplies and diamonds can be increased by having a Château Frontenac.
There are 9 different rewards. Diamonds appear only once per unique recurring quest. Among other rewards small & small have twice chance of showing (2/14), and goods have 5x chance (5/14) because there are 5 kinds of them. All other rewards have the same probability, which is 1/14.
↑The diamond reward is a one-time occurrence per unique recurring quest. A quest is unique from another quest when it has a different age or text. After receiving the diamond reward, the reward slot changes to medals.