The significance of faith proven by decision theory – Pascal's wager game is correct and refutes atheism completely

Pascal's wager game showed that the atheistic view is always inferior compared to the theistic. The reason is that an infinitely high reward for the theist is always opposed to a finite payoff for the atheist, given that the existence of God cannot be excluded. However, an atheist can also obtain the infinite reward just by choosing strategy "believe", i.e. by pretending faith, but without really believing. As God may be demanding and grants the reward only those in firm faith, the inspection of faith by God is needed, which is included in the present analysis, i.e. God tests the faith. In addition, the infinitely high reward is removed from the payoffs, i.e. the believer goes out empty, and is even charged cost of faith. It shows that believing in God and worshipping is still the best option regardless, even if we believe that praying is in vain and has absolutely no value. The analysis also shows that the faith should even be so strong that we give our entire life to God and retain nothing for us since this is not only the safe rescue, but the rationally optimal choice of the extent of worship, and thus the unique salvation. Finally, all common criticisms to the wager game have been reinvestigated in detail; logic and mathematical analysis showed that they fail against the consideration of eternal punishment