Statement

Giorgio and William enjoy playing together the Magnamagna game, a typical Italian two-player game inspired by the well-known practice. After collecting bribes from contestants, they first arrange them into a long line of N items of nominal value V_i for i=0… N-1 (from left to right). Then, they play in turns each time choosing between two possibilities: (1) take the leftmost item and gain its value (`L'), (2) take the rightmost item and gain its value (`R'). In any case, taking items from the interior of the line is never allowed. Thanks to months of exhaustive research, Giorgio claims to have finally found the optimal strategy for this game, allowing him to collect the most possible money on every play. He thus decided to let William play first so as to compensate the strategic gap. Giorgio's strategy is indeed very simple: each time he chooses the move with the highest smartness...