There are a great many logical fallacies in how the Wager is applied. Often the Wager is suggested as some sort of proof or last-ditch argument for God. But since it was embedded in the Pensées, which was Pascal's life project to defend Christian thought, it seems unlikely he intended for the Wager to stand alone. Whether anyone would be convinced by such an argument seems not to be the main thrust of Pascal's formulation of the Wager.
The very introductory statement to his argument shows that Pascal concedes that God cannot be proven in the Aquinian sense:
If there is a God, He is infinitely incomprehensible, since, having neither parts nor limits, He has no affinity to us. We are then incapable of knowing either what He is or if He is. This being so, who will dare to undertake the decision of the question? Not we, who have no affinity to Him.
Who then will blame Christians for not being able to give a reason for their belief, since they profess a religion for which they cannot give a reason? They declare, in expounding it to the world, that it is a foolishness, stultitiam; and then you complain that they do not prove it! If they proved it, they would not keep their word; it is in lacking proofs, that they are not lacking in sense.
It makes more sense to view Pascal's Wager as a precursor to Alvin Plantinga's Warranted Christian Belief. In contradiction to Cartesian skepticism, we are free (even compelled) to act on believes that we cannot prove from first principles. Any reasonable reading of Pensées would conclude that Pascal is not trying to take the risk out of choosing the Christian faith. Rather, he was defending the faith from the charge that it is irrational.
The Wager takes on added weight when you consider that Pascal himself made a bet and took up an ascetic lifestyle near the end of his life. It was this time that the Wager was formulated and it was not published in his lifetime. It's difficult to ignore the possibility that Pascal took the Wager quite seriously. He summarized the argument by making this precise point:
The end of this discourse.—Now, what harm will befall you in taking this side? You will be faithful, honest, humble, grateful, generous, a sincere friend, truthful. Certainly you will not have those poisonous pleasures, glory and luxury; but will you not have others? I will tell you that you will thereby gain in this life, and that, at each step you take on this road, you will see so great certainty of gain, so much nothingness in what you risk, that you will at last recognise that you have wagered for something certain and infinite, for which you have given nothing.
"Ah! This discourse transports me, charms me," etc.
If this discourse pleases you and seems impressive, know that it is made by a man who has knelt, both before and after it, in prayer to that Being, infinite and without parts, before whom he lays all he has, for you also to lay before Him all you have for your own good and for His glory, that so strength may be given to lowliness.—Pensée 233
And I suppose that is the primary fallacy of Pascal's Wager: it can mean little to nothing to people who have not thrown themselves into the pattern of thought that Pascal himself followed. It is unpersuasive since it builds on uncommonly held premises.
On a personal note, I find the Wager touching, even though or perhaps because, it is flawed. I love T. S. Eliot description of Pascal: "a man of the world among ascetics, and an ascetic among men of the world." A normal Christian considering the sacrifice he made would be content to contemplate the words of Jesus in Mark 8:34-38 (ESV):
And calling the crowd to him with his disciples, he said to them, “If anyone would come after me, let him deny himself and take up his cross and follow me. For whoever would save his life will lose it, but whoever loses his life for my sake and the gospel's will save it. For what does it profit a man to gain the whole world and forfeit his soul? For what can a man give in return for his soul? For whoever is ashamed of me and of my words in this adulterous and sinful generation, of him will the Son of Man also be ashamed when he comes in the glory of his Father with the holy angels.”
But not Blaise Pascal, mathematician. Instead, he converted Jesus' idea into an example of the relatively new field of probability. And while the problem was setup in a way that it is easily rejected as an apologetic of Christianity, it is still valid and useful as a mathematical puzzle.