Conclusion

Overall, our approach is highly successful; in the tournament, nearly 70% of the time, we outperformed all other players or all but one other player.

Perhaps the biggest hurdle to finding the optimal solution is processor time. A near-optimal solution could be found by performing complete search of all possible rotations and placements down to a fine granularity for the $n$th cookie, and for each of those placements, examining all possible placements for the $n+1$ cookie. However, for more than a very small number of cookies, this search is prohibitively expensive.

We address this issue by deploying several simpler strategies, each of which replicates a piece of this near-optimal strategy. Furthermore, we incorporate randomness to achieve a distribution of values without constraining ourselves to a large granularity or having to try every one of huge number of possibilities. Thus, each of our stategies provides an approximation of a near-optimal strategy, with varying degrees of success depending on the type of cookie being placed.

The observed success of our player derives from the fact that after we try several varied strategies, we return only the best of one. Thus, even though none of our strategies is good for all types of shapes, we consistently achieve high-performing results.