Yes, it could be interesting to examine the RNG for the poker sites. There would be enough material to cover 15 pages and you could take it to whatever complexity you like.
However, I would believe this to be too big a task for a 16 year old. The data collection would be hard. Whatever computations on the data, I would guess she does not have the knowledge to interpret the results. The "die hard" test suite I know of to test for randomness is quite complex and it takes a professor to conclude anthing based on the results :-)