This is Pascal's Wager. It isn't proof for the existence of God, but it can help in the search for God in the absence of any proof. As originally proposed by Pascal, the Wager assumes that logical reasoning by itself cannot decide for or against the existence of God; there seem to be good reasons on both sides. Now since reason cannot decide for sure, and since the question is of such importance that we must decide somehow, then we must "wager" if we cannot prove. And so we are asked: Where are you going to place your bet? If you place it with God, you lose nothing, even if it turns out that God does not exist. But if you place it against God, and you are wrong and God does exist, you lose everything: God, eternity, heaven, infinite gain. "Let us assess the two cases: if you win, you win everything, if you lose, you lose nothing."The vertical lines represent correct beliefs, the diagonals represent incorrect beliefs. Let us compare the diagonals. Suppose God does not exist and I believe in him. In that case, what awaits me after death is not eternal life but, most likely, eternal nonexistence. But now take the other diagonal: God, my Creator and the source of all good, does exist; but I do not believe in him. He offers me his love and his life, and I reject it. There are answers to my greatest questions, there is fulfillment of my deepest desires; but I decide to spurn it all. In that case, I lose (or at least seriously risk losing) everything.
The Wager can seem offensively venal and purely selfish. But it can be reformulated to appeal to a higher moral motive: If there is a God of infinite goodness, and he justly deserves my allegiance and faith, I risk doing the greatest injustice by not acknowledging him.