Can the test set of attributes be a subset of the training set's attributes? I'm currently writing an application for a trick-based card game, where agents are assigned points based on the accuracy of their predictions of how many hands they're going to win. The number of tricks predicted will display a level of confidence to the other agents as well as also potentially allowing the agent to choose the Trump suit.

I've compiled a set of attributes (such as cards in hand, score sum total in hand) that will be useful in the prediction, but it would be ideal if I could include previous predictions in the training set.

My question is can my test data [attributes] be a subset of the training data [attributes ∩ predictions] both of which are predicting the number of hands that the agent will win?
Well, if the test data would be the same from training data, your machine learning algorithm may overfit. Because you test your model with your training data it may perform very well, as it may see the pattern even in noise. And then it won't generalize on new data.

You should separate the test data (with which you see the accuracy) to the training data.