The Question: How effective can a computer be at playing the card game Hearts against random players?

The Short Answer: Very effective.

In card play alone, this version of ROBS makes 27 regular evaluations or decisions about the cards in its hand. It makes an additional 4 evaluations if its trying to Shoot the Moon. The first 5 evaluations are rules. We can see how performance changes if we turn off all evaluations & turn them on one by one.  The link the each result is included here.

The orange line is a sample of Player 1's performance with random card play but skilled passing. It's interesting that thoughtful passing alone cuts the point total from 24.89% in our previous sample to  17.64%. The explanation for evaluation 6 & 7 being worse than playing randomly is that without any consideration but the rules, ROBS plays the highest possible card, worse than playing random. 

The graph follows an expected shape with diminishing returns from each new evaluation. There are two reasons for this. The first is that the most important basics of Hearts strategy were given first. Second, the later evaluations are more useful in competitive play. They are there for ROBS to avoid making exploitable plays from intelligent players. These types of strategies are useless against randomness or detrimental on occasion against random players.

Lastly, I tested setup 23 against the full 27 evaluations in 10,000 hands. 23 had the lowest overall score. The data output is not included but in 10,000 hands each the result was 24,544 points for all 27 against 24,671 for the first 23. In this situation they are clearly within each others ranges.