In this paper, we introduce and study a new scoring game on graphs called smash and grab. In this game, two players, called Left and Right, take turns removing a vertex of the graph as well as all of its neighbours that become isolated by this removal. For each player and each of their turns, they score the number of vertices that were removed on their turn. The game ends when there are no more vertices remaining, and the player with the highest final score wins. We denote by Ls(G) the difference between Left and Right's final scores in G when Left starts and both players play optimally (they both aim to maximise their scores). We mainly study this parameter for different graph classes. We notably prove that Ls(F)≥0 for any forest F (i.e., the first player cannot lose). We then use this result to compute the exact value of Ls(G) for particular forests such as unions of paths and subdivided stars. The result in paths then solves the case of a unique cycle. Finally, we prove that, for a generalisation of the game, computing the score is PSPACE-complete.

We characterize pairs of complementary nonhomogeneous Beatty sequences $(A_n)_{n>0}$ and $(B_n)_{n>0}$, with the restriction $A_1=1$ and $B_1\geq 3$, for which there exists an invariant take-away game having $\{(A_n,B_n),(B_n,A_n)\mid n> 0\}\cup\{(0,0)\}$ as a set of $P$-positions. Using the notion of a Sturmian word arising in combinatorics on words, this characterization can be translated into a decision procedure relying only on a few algebraic tests about algebraicity or rational independence. This work partially answers to a question of Larsson, Hegarty, and Fraenkel, raised in [Theoret. Comput. Sci., 412 (2011), pp. 729--735].

MCTS (Monte Carlo Tree Search) is a well-known and efficient process to cover and evaluate a large range of states for combinatorial problems. We choose to study MCTS for the Computer Go problem, which is one of the most challenging problem in the field in Artificial Intelligence. For this game, a single combinatorial approach does not always lead to a reliable evaluation of the game states. In order to enhance MCTS ability to tackle such problems, one can benefit from game specific knowledge in order to increase the accuracy of the game state evaluation. Such a knowledge is not easy to acquire. It is the result of a constructivist learning mechanism based on the experience of the player. That is why we explore the idea to endow the MCTS with a process inspired by constructivist learning, to self-acquire knowledge from playing experience. In this paper, we propose a complementary process for MCTS called BHRF (Background History Reply Forest), which allows to memorize efficient patterns in order to promote their use through the MCTS process. Our experimental results lead to promising results and underline how self-acquired data can be useful for MCTS based algorithms.