Introduced by Moshe Rosenfeld, on October 2nd 2009, as a medium importance open problem from graph theory, the Gold Grabbing Game is defined as follows: Fix a tree T and for every vertex V that belong to V(t) a non-negative integer g(v) which we think of as the amount of gold at v. On each turn, a player chooses a leaf vertex v of the tree, takes the gold at this vertex, and then deletes v. The game ends when the tree is empty, and the winner is the player who has accumulated the most gold. Problem is to find an optimal strategy for the players. In this paper we suggest how to create a randomly built Binary Search Tree (BST) and show a Maximum-BST and Delete-BST algorithms. Furthermore, we show a winning strategy for Player 1 (Jane) in a gold grabbing game if the game is played on binary search tree T. The future work consider a question: Is there a winning strategy for Jane if the game is played on another class of graphs,instead of a binary search tree?