GUESSING ABOUT GUESSING
In joint work with Ron Graham and Sam Spiro we study a simple card guessing game where the optimal strategy is elusive. There are 'obvious' greedy strategies (guess the card which is most likely to show up next) which, while not bad, are certainly not optimal. We have upper and lower bounds, and depending on the hype level you can tolerate, they are either 'pretty far apart' OR 'quite close'. These same experiments occur in taste testing and the evaluation of clinical trials. Evaluating the results of actual trials (does the guessing subject have talent or are they guessing at chance level) raises the problem that we don't really know what the guessing subject is doing (they probably don't know either). This can be overcome with a technique called 'skill scoring'. This can also be applied to asses the effectiveness of experts (eg weather forecasters of wall street pundits). Finally some nice combinatorial identities appear.