Leftmost Node
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Leftmost Nodes are the nodes searched first from the root inside a depth-first search approach like Alpha-Beta or Principal Variation Search. If those nodes have an even ply distance from the root, that is the same Side to move, their alpha-beta Window is the same as the root window, {rootAlpha, rootBeta}. An odd ply distance implies a window of {-rootBeta, -rootAlpha} inside a Negamax framework.
Since the root window is typically wide open (except MTD(f)), either {-oo, +oo} or an aspiration window around the score from the previous iteration inside an iterative deepening framework, leftmost nodes have the same wide open window and will likely increase their initial alpha to establish a principal variation, to return an exact score. The left most Leaf Node with its static heuristic value, established by the evaluation is the leaf with the greatest probability to influence the value of the root. In Principal Variation Search, leftmost nodes are PV-Nodes.
