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In this paper we present a new theoretical model to find out an optimalweight associated with a soccer player under the presence of a stochastic goaldynamics by using Feynman path integral method, where the action of a player ison $\sqrt{8/3}$-Liouville Quantum Gravity surface. Before determine the optimalweight we first establish an Infinitary logic which can deal with infinitevariables on the strategy space then, a quantum formula of this logic has beendeveloped and finally, based on this we are able show the existence of aLefschetz-Hopf fixed point of this game. As in a competitive tournament, allpossible standard strategies to score goals are known to the opposition team, aplayer's action is stochastic in nature and they would have some comparativeadvantage to score goals. Furthermore, conditions like uncertainties due torain, dribbling and passing skill of a player, whether the match is a day matchor a day-night match, advantages of having home crowd and asymmetricinformation of action profiles have been considered on the way to determine theoptimal weight.

Scoring a Goal optimally in a Soccer game under Liouville-like quantum gravity action