Choose a card game, using as a source one of the Internet Web sites like the ones listed on our home page. Investigate a particular game situation and estimate the probabilities of various outcomes. Note that the best strategy should produce highest winnings in a large number of games.
For instance, compute the frequency of straight flushes in a randomly chosen poker hand of 5 and 7 cards.
This project can be taken many steps further, up to implementing a program in the R language which will play poker according to optimal rules. However, as anything that is done right, such a project would require a lot of time. Therefore, I only mention is as "the ultimate goal". Keeping the "big picture" in mind is important in each problem, as without it you will right programs that are too narrow in their scope and to difficult to modify for the "big program".