Each reward shown has equal odds of being doubled. The odds are based on the number of items shown:

For 10 items - Each item has the following chance of doubling: 30.0000%
For 9 items -  Each item has the following chance of doubling: 33.3333%
For 8 items -  Each item has the following chance of doubling: 37.5000%
For 7 items -  Each item has the following chance of doubling: 42.8571%
For 6 items -  Each item has the following chance of doubling: 50.0000%
For 5 items -  Each item has the following chance of doubling: 60.0000%
For 4 items -  Each item has the following chance of doubling: 75.0000%