I dont see a point in storing cards in the database, it would just make things too complex. What I would do is just to create another Class in the java application named like CardDistribution, containing an array of 102 elements. Give each element an id of the card it holds.
When you want to save the game, serialize your CardDistribution object into JSON and persist it in a column in your Game table.
And when you read from the database just de-serialize your CardDistribution JSON into a java object and use it.