Blaise Pascal was a brilliant French mathematician, physicist, inventor, and philosopher. He was also a strong Christian with an interest in apologetics. He died young at age 39. When he died, he had been writing notes for an eventual book on apologetics which he unfortunately did not live to complete. After his death, his notes were compiled and published as “Pensees”. He is best known in apologetics for his “Wager.”

Pascal laid the foundation for modern probability theory and applied elements of game theory to demonstrate that belief in the Christian God is rational. Decision theory is about how to make good decisions in circumstances of risk or uncertainty. Pascal’s wager is a practical argument for belief in God. In his Pensées, Pascal argued that people can choose to believe in God or can choose to not believe in God, and that God either exists or he does not. It is a forced wager; everyone is forced to bet by virtue of the fact they exist.

If a person believes in the Christian God and this God actually exists, they gain infinite happiness; if a person does not believe in the Christian God and God exists, they experience infinite loss. On the other hand, if a person believes in the Christian God and God does not exist, then they receive some finite disadvantages from a life of Christian morality; and if a person does not believe in this God and God does not exist, then they receive some finite pleasure from a life lived unhindered by Christian morality. As Pascal states, “Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.”

Pascal’s Wager can be summarized thus:

• If God exists and you bet on him, you have infinite gain.
• If God exists and you bet against him, you have infinite loss.
• If God does not exist and you bet on him, you have finite loss.
• If God does not exist and you do not bet on him, you have finite gain.
• It is a forced wager; everyone plays.

Michael Rota (PhD, Philosophy) crafted a powerful demonstration with Pascal’s Wager, using the standard Bayesian formula. He focused on just one aspect of the physical fine-tuning argument———namely that the effective cosmological constant must fall within an extremely narrow life-permitting range. The cosmological constant expresses the energy density of space, or vacuum energy that arises in quantum mechanics. It controls the expansion of the Universe. The Cosmological Constant, or the space energy density is fine-tuned to one part in 10¹²⁰, recognized by Christian and non-Christian scientists and philosophers. Any larger by one part in 10¹²⁰ and the Universe would have collapsed back in on itself, prohibiting life. Any smaller by one part in 10¹²⁰ and the stars could not have formed, again prohibiting life.

Rota’s result using a Bayesian formula shows that one would have think the existence of God is unlikely at 10³² odds . . . a very, very, very poor wager indeed. Only a fool would take those odds. Rota explains this in his book Taking Pascal’s Wager: Faith, Evidence and the Abundant Life. While superfically elementary at first glance, Pascal’s Wager is in fact more complex than it appears. Rota does a good job of fleshing out its nuances.

To see the logic here, Rota provides the following scenario:

Imagine again that a trusted third party flips a coin but doesn’t say whether it lands heads or tails. This time a wealthy person credibly makes you this offer: if you choose to play and it’s heads, then she’ll give you one million dollars, while she’ll give you twenty-five dollars if it’s tails and you’ve chosen to play. If you choose to pass and it’s heads, no money will be exchanged, but if you choose to pass and it’s tails, she’ll give you one hundred dollars.

If Christianity is true, so much is gained, while if naturalism is true, not much is lost.