Hope is not a mathematical calculation, but it entails a risk

In Éric Rohmer's 1969 movie Ma Nuit Chez Maud- My Night At Maud's (which begins with a peek at the then-newly reformed Mass) Jean-Louis runs into his friend Vidal in local café. Vidal teaches philosophy at the university in Clermont, where Jean-Louise finds himself living. Surprised that they bumped into other, the two friends decide to sit, enjoy a drink, and talk. Jean-Louis asks his friend if he frequents the café. Vidal responds that he almost never goes there and, in turn, asks Jean-Louis the same question, to which he replies that he has never set foot in that café before. Vidal, commenting on their surprising encounter, remarks, "And yet our paths cross right here. How strange." Jean-Louis disagrees that their meeting is strange, noting that their "ordinary," that is, daily "paths never cross." "Therefore," he reasons out loud, "the point of intersection must be outside those ordinary paths."

After noting the unsurprising nature of their bumping into each other, Jean-Louis confesses that in his spare time he's "been dabbling in mathematics." He goes on to say that it would "be fun to calculate our chance of meeting in a two-month period." Vidal asks, "Can it be done?" Jean-Louis replies that it can certainly be done, pointing out that it is "a matter of data and how you handle it," assuming that the data is available. He goes on to say that in order to calculate this probability he would need information, such as where Vidal lives and works. He then asks Vidal if he is interested in mathematics. Vidal answers enthusiastically that he is and also notes that mathematics are increasingly important in contemporary philosophy. Vidal next mentions Pascal, not knowing that Jean-Louis has just purchased a copy of Pensées and is re-reading them in addition to studying mathematics, noting that Pascal's "arithmetical triangle is connected to his wager." He concludes that it is Pascal's mathematical precision that makes him "so amazingly modern," while also going to pains to note that "Mathematician and philosopher are one."

Pascal's triangle

Jean-Louis is intelligent enough to agree with both of Vidal's assertions (i.e., Pascal being so modern and the contemporary mathematician and philosopher being one). Unlike his friend, who is a self-professed Marxist, Jean-Louis, a committed Catholic, is unimpressed.: "Good old Pascal," Jean-Louis replies, which prompts Vidal, who seems a little impressed with his own insights, to ask, "Are you surprised?" This is when Jean-Louis confesses to his present re-reading of the Catholic philosopher and mathematician. Vidal is curious and asks, "And?" Jean-Louis pointedly says, "I'm very disappointed." Now Vidal is "really interested" and urges his friend to continue. Taking up Vidal's invitation, Jean-Louis begins, "Oh, I don't know" before he says, referring to Pascal,

I feel I know him almost by heart, yet he tells me nothing. It all seems so empty. I'm a Catholic, or at least try to be, but he doesn't fit in with my notion of Catholicism. It's precisely because I'm a Christian that his austerity offends me. If that's what Christianity is about, then I'm an atheist

He then asks Vidal if he is still a Marxist. "Absolutely," Vidal responds before continuing:

For a Communist Pascal's wager is very relevant today. Personally I very much doubt that history has any meaning. Yet I wager that it has, so I'm in a Pascalian situation. Hyopthesis A: Society and politics are meaningless. Hypothesis B: History has meaning. I'm not at all sure B is more likely to be true than A. More likely it is the reverse. Let's even suppose B has 10 percent chance of being true, and A has an 80 percent chance. Nevertheless, I have no choice but to opt for B because only the hypothesis that history has meaning allows me to go on living. Suppose I bet on A, and B was true, despite the lesser odds. I'd have thrown away my life. So I must choose B to justify my life and actions. There's an 80 percent chance I'm wrong, but that doesn't matter

To Vidal's impassioned discourse Jean-Louis wryly replies, "Mathematical hope: Potential gain divided by probability. With your Hypothesis B, though the probability is slight, the possible gain is infinite. In your case, a meaning to life. In Pascal's eternal salvation." Vidal says, "It was Gorky, Lenin, or maybe Mayakovsky who said about the Russian revolution that the situation forced on them to choose the one chance in a thousand. Because hope became infinitely greater if you took that chance than if you didn't take it."

Let us weigh up the gain and the loss involved
in calling heads that God exists. Let us asses the
two cases: if you win you win everything; don’t
hesitate then; wager that he does exist.

–Pascal