Figuring the Odds in God’s Casino—Pascal Revisited

Figuring the Odds in God’s Casino—Pascal Revisited

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“If you’re living like there’s no God,” a popular bumper sticker warns, “you’d better be right.”  A fringe of flames at the sticker’s base provides a clue to the hellish price of error.

Whether consciously or not, this modern folk wisdom sums up “Pascal’s Wager,” the living legacy of Blaise Pascal, a brilliant 17th century mathematician, scientist and theologian.

As the bumper sticker suggests, the rise of a dynamic secular society has created a new sense of urgency about securing the foundations of theology.  If Intelligent Design represents a skirmish into ‘enemy’ territory, the revival of Pascalian reasoning may be regarded as the theism’s last ditch, or better still, an impregnable fortress to which believers may retreat from the assaults of scientific materialism.

“Pascal,” says Christian philosopher Peter Kreeft, “is three centuries ahead of his time.  He addresses his apologetic to modern pagans, sophisticated skeptics, comfortable members of the new secular intelligentsia …  He belongs to us …Pascal is our prophet [1].” 

But what exactly does this 17th century ‘prophet’ have to say on the modern podium?  To find out, we take a fresh look at the man, his wager, and its implications.  And we arrive at a startling conclusion: in a contemporary context, Pascalian reasoning leads us not to specified faith but toward ethical agnosticism.

Blaise Pascal was born to privilege and tragedy.  His father, Etienne, earned a good living as a lawyer, and the family appears to have been close.  Yet, as so often happened in the days before modern medicine, unbearable loss struck when Blaise was just three.  His mother, Antoinette, died of a mysterious illness.  Blaise himself suffered from frequent bouts of debilitation.  Still, Etienne took to being a single parent with grace, and within a few years went so far as to give up his commissions to devote himself to the education of his son.

Pascal, without doubt, was among the brightest math students ever to be home-schooled. At the age of 12, his sister claimed, young Blaise independently discovered a Euclidean Theorem (the sum of the angles of any triangle in Euclidean space is always 180 degrees).  As a young man, he designed a working mechanical calculator, and would perhaps be considered the father of the computer if progress had not more or less stalled until the creation in 1946 of ENIAC.  But it was in probability theory that really Pascal shone.  And it was the application of probability to theology that led to what we call “Pascal’s Wager.”

The wager appears as part of the apologist’s Pensees.  These fragmentary “thoughts,” penned in Pascal’s dying days, express his conviction that faith lies beyond the reach of empiricism or indeed of reason [2]. 

“If there is a God, He is infinitely incomprehensible since, having neither parts nor limits, He has no rapport with us.  We are therefore capable of knowing neither what He is nor if He is (Pensees, 233) [3].”

Pascal reasoned that the only move left to man is to calculate the odds. This he was admirably suited to do.  In modern language, here is the result:

 * If I wager for God and I’m right … infinite gain (unending joy in heaven); * If I wager for God, and I’m wrong … minor loss (earthly sacrifice).  * If I wager against God and I’m right … minor gain (a licentious life); * If I wager against God, and I’m wrong … infinite loss (unending torture in hell)

The logic of Pascal’s Wager is at once easy to grasp and hard to shake.  In addition to its simplicity and apparent soundness, it appeals to feelings that many of us harbor: a fearful conscience and a sanctimonious desire to see others punished.  These find continual expression in both religious and secular culture.  Mozart’s Don Giovanni is a classic example of a perfidious life followed by eternal punishment.  Dickens’ cautionary Scrooge tale also depends on Pascalian logic.  And that’s just the theme our evangelizing bumper sticker picks up on today.

I’ve paraphrased Pascal here, but in case anyone finds the gambling metaphor offensive, let’s examine his own words once more:

“… if there were three lives to be won … you would be imprudent, when you are forced to gamble, not to risk your life to win three lives in a wager …  where there is an equal chance of loss and of gain.  But there is an eternity of life and of happiness [to be won] [4]!”

Underlying that logic, however, is a specific and contestable assumption: to believe in God, Pascal implies, is all that’s needed to qualify for “infinite gain”.  Pascal has already told us that if God exists, he is incomprehensible and uncommunicative.  It is therefore impossible in principle to know by what means or indeed whether we can “win” an eternity of life and happiness.”

This calls to mind St. Paul’s insistence that, “being justified by faith, we have peace with God through our Lord Jesus Christ (KJV, Rom. 5:1).”  And of course, that’s just what Pascal believed as well.  But those of us who live in the world’s most religiously diverse country are obliged to ask: what is faith?

I must agree from the outset that faith is primarily considered to be, as the Oxford Concise Dictionary of World Religions puts it, an “acceptance of religious claims.”  Yet faith is considered to be distinct from theology, and it certainly has a secular meaning as well.  When a husband says to his wife about to go to bat in the bottom of the ninth in a softball game, “Honey, I have faith in you,” he is not expressing his religious conviction that she is the Goddess of Swat.  Undoubtedly, though, the same word is being deployed.  What underlies the two uses?

At its most basic, I believe, faith is simply an unshakeable belief that something good will come of it all.  Note that this is both more and less than a belief in God.  I might believe in a malevolent god and so lack faith, or I might believe that destiny is with me, and so have faith.  Note, too, that this is distinct from optimism, which holds that everything will turn out for the best.  In faith, there is plenty of scope for tragedy.

And while optimism may rest on statistics, a strategic plan, or a hunch, to put religious content into faith requires a theological leap.  How do we know what lies behind the belief that “something good will come of it”?

Paul, of course, believed he had a direct revelation on the road to Tarsus.  Pascal himself experienced what he took to be a mystical revelation on the night of November 23, 1654.  Even then, his adherence to Jansenist Christianity in particular came about because a pair of brothers in the sect healed his father after an accident.  One may wonder what would have happened if a couple of wandering Buddhists had stopped to lend Pére Pascal a hand.

In any event, the premise that “belief in God” presents a 50-50 chance of resulting in infinite reward is clearly contradicted by many theologies.  Of the world’s 30,000 or so religions and religious sects, a great many specify an exclusive creed and set of rites a believer must adhere to in order to qualify for infinite reward.  Christianity is no exception.

How does a Christian achieve salvation, and so claim the infinite reward?  The Fundamental Evangelistic Association is quite explicit on this point: if you don’t adhere precisely to their doctrine, you are damned.  Here, in part, is what that doctrine says:

 “We believe that man is justified on the single ground of faith in the shed blood and bodily resurrection of our Lord and Saviour Jesus Christ.    The adding of works, baptism, sacraments, or any other condition placed upon man in order to obtain God’s gift of salvation by faith alone in the finished work of Christ results in “another gospel” that is under God’s curse [5].”

 This contrasts sharply with the Catholic position:

 Catholics receive Christ’s saving and sanctifying grace, and Christ Himself, into their souls when they are baptized. Yet they also know that Christ has established certain conditions for entry into eternal happiness in Heaven–for example, receiving His true Flesh and Blood (John 6:54) and keeping the commandments (Matt. 19:17).  If a Christian refuses or neglects to obey Our Lord’s commands in a grave matter (that is, if he commits a mortal sin), Our Lord will not remain dwelling in his soul; and if a Christian dies in that state, having driven his Lord from his soul by serious sin, he will not be saved [6].

This muddies the salvational waters considerably.  But there’s at least one more position to consider.  Some Christians believe in predestination, the doctrine that God has already decided who will be saved and who is damned.  And, remarkably, that’s more or less the position that Pascal himself adhered to.

So, within Christianity alone, a believer is required to make choices that will lengthen his odds considerably.  We’re no longer flipping a coin, but rolling the dice.

But what of other religions?  In what sense does Islam have less of a claim to Truth than Christianity?  As Diderot, an early critic of Pascal, remarked, “An Imam could reason just as well this way [7].”  And how is the disbelief of Jews in Jesus as the Messiah to be discounted?  Some faiths, such as Hinduism, proclaim many channels to truth, but even the Hindus specify certain procedures for an improved station in a future life.

Pascal’s metaphysics deter us from using any empirical or rational method to choose among theologies.  Not only does God surpass our ability to know him, but as Pascal eloquently put it, “The heart has its reasons, which reason does not know.”

Still, in a decision as consequential as this, can we rely on the intuition of the heart?  If so, it’s passing strange that the hearts of people born in Shi’ite Muslim communities nearly always guide them to be Shi’ite Muslims, while the hearts of people born in Amish communities nearly always tell them to be Amish. The heart, it seems, follows the herd instinct.

And so we come back to this essential point: The great fallacy in Pascal’s reasoning is to equate belief in God’s existence with infinite reward [8].  In fact, to invest one’s faith in any particular theology is apparently to accept odds of at least many thousands to one, and possibly much longer than that.

Of course, some may argue that an infinite reward divided by any finite number of chances is still infinitely attractive.  But real world experience teaches us otherwise.  Any statistician will tell you that it is unwise to bet a substantial amount on a state lottery.  With odds typically at 80 million to 1 against, it doesn’t matter how big the reward; it’s still a poor choice for anything but a casual flutter.

We really don’t know the odds of salvation — by some theologies they could be similarly poor.  “Many are called,” says the Gospel of Matthew, “but few are chosen [9].”

Even if the odds depended on generally picking the right great religion (say, five to one?), before accepting such a bet we must consider two questions: What do we stand to lose?  And what can we do to shorten the odds?

First, let’s examine the claim that there is little or no risk involved in giving up one’s earthly life.  Pascal’s argument makes sense only if we agree that there is little sacrifice involved in committing to belief in God.  Yet Pascal himself adopted a quite ascetic theology: “All that God does not permit is forbidden (Pensees, 668) [10].”

If one gives up all earthly pleasures and pursuits to bet on the existence of God and is wrong, then the only frame of reference is earthly life itself.  In that event, the loss is total, which is to say, practically infinite.

Pascal himself made a sad demonstration of this point.  Here, from the Catholic Encyclopedia, is an account of his life following his mystical conversion:

“After this he practiced the most severe asceticism, renounced learning, and … gave himself more and more to God.  He multiplied his mortifications, wore a cincture of nails which he drove into his flesh at the slightest thought of vanity, and to be more like Jesus crucified, he left his own house and went to die in that of his brother-in-law…  He died at the age of thirty-nine, after having received in an ecstasy of joy the Holy Viaticum, for which he had several times asked, crying out as he half rose from his couch: ‘May God never abandon me [11]!'”

 There are numerous examples of people who mutilate themselves in pursuit of religion, and even more of people who abandon rational belief and behavior. But rarely has the world lost so fine a mind as Pascal’s to religious passion and premature death.

Still, if reasonably assured of an infinite reward, anyone would be justified in bearing considerable sacrifice. So the question becomes, what, if anything, can we do to shorten the odds?

Let’s assume that God, if He exists, is benevolent and just.  To assume otherwise is to throw in our hand.  An evil or arbitrary God may certainly exist, but if so we have no idea how to play the game, and so we would assuredly be better off to focus on enjoying the life we have.

Assuming that God is benevolent and just, however, implies that we know what benevolence and justice are.  And indeed we do.  For human nature, with its endowment of rationality and compassion, gives us the understanding, motivation and tools we need to grasp these concepts and put them into practice.  With that in mind, isn’t it safe to assume that God will deal fairly with us even if we haven’t discovered and embraced the one true faith from among all the pretenders?  Indeed, provided that we lead our lives in an ethical manner, we should find extra merit with God.  Surely, leading an ethical life for its own sake [12] deserves greater merit than simply choosing a theology at random or in response to threats and  promised rewards (a selfish and irresponsible move if ever there was one).

The balance tips even farther in favor of ethical agnosticism when you consider that various theologies require obedience to contradictory moral standards.

For example, some Christians read into Scripture an overarching commandment to love their neighbors, even if they happen to be homosexuals.

Others read Scripture differently.  “God hates fags,” proclaims Rev. Fred Phelps, and for him, that’s reason enough to hate them too.

Which theology should a Christian choose?  If the answer is anything but the one most closely aligned with the ethics derived from reason and compassion, then we must conclude that either God is unjust or that we are morally as well as rationally blind to God.  Either way, the game is up.  Given the odds against picking a winner among thousands of arbitrary theologies, some of which allow for only a few winners among the believers, decision theory, which Blaise Pascal created, counsels against staking our earthly lives on such a long shot.

Fortunately, Pascal was wrong in at least one other claim.  He insisted that we must choose, that we cannot remain suspended between belief and atheism.  That may well be true of a specified faith.  Try as I might, I cannot make myself believe that Neptune rules the seas nor Zeus the thunderclouds.  But, once again, this is not the kind of deity Pascal proposes in the context of the Wager.

It seems plain that if God is utterly unknowable, then we are free to be agnostic about him, just as we may be about the existence of life elsewhere in the universe.  And that being so, we are free to make the most rational wager available.  Here, then, is Pascal’s Wager reformulated for our times:

If I stake my faith on a specific theology…


* I may be misled into repugnant behavior, and * my earthly sacrifice may be extreme, and * my chances of infinite gain will be very small


If I stake my faith on ethical agnosticism…


* I risk little or nothing, for I cannot influence an arbitrary God, and * I gain freedom from the burdens of doctrinal belief, and * I maximize my chances of reaping an infinite reward, if such there be.

 Like so many modern things, this formulation lacks the simple eloquence of the past.  It lacks the mathematical rigor of the original as well.  And yet, I venture to say, this new version of the Wager is far more sound.

I must acknowledge, however, that it depends on the obscurity of God.  This is something Pascal waffled on.  He was, above all else, a determined Christian apologist, who elsewhere resorted to biblical prophecies and other dubious claims in aid of his cause.  And yet, to parry the arguments of skeptics, he frequently insisted that God lies beyond all human apprehension.

“…He has hidden Himself from their knowledge, and … this is even the name he has given to Himself in the Scriptures, deus absconditus [13].”

 In this, I believe, Pascal was indeed three centuries ahead of his time.  Our broadening horizons of knowledge about human nature and human culture show more plainly than ever that God, if he exists, remains inscrutable.

Systematic knowledge was in its infancy when Pascal wrote.  A great scientist, he nevertheless stumbled badly when applying science to his apologetics: “Why cannot a virgin bear a child?  Does a hen not lay eggs without a cock [14]?”  Umm, not one that ever hatched [15].

Science today reveals a vast universe whose only plausible hints of the divine are life itself and the conditions that allow for it.  Even these, however, may be explained by an entirely naturalistic account.

Under the circumstances, Pascal’s Wager indeed takes on fresh importance.  But only, I suggest, when revised in the light of our new and sobering knowledge.  The choice of ethical agnosticism does not, admittedly, satisfy a craving for religious passion or zeal.  But it has this virtue: in the most fundamental sense, it is an act of faith.  Such a wager amounts to a stubborn belief that, whether rewarded or not, if a life is well led some good will come of it.


[1] Peter Kreeft, Christianity for Modern Pagans: Pascal’s Pensees Edited, Outlined and Explained (San Francisco: Ignatius Press, 1993), 13, 189.  Quoted in Rick Wade, “Blaise Pascal: An Apologist for our Times,”

[2] Alban Krailsheimer, Pascal.  (New York: Hill and Wang, 1980)

[3] Jean Mesnard, Pascal.  Trans., Claude and Marcia Abraham.  (University, Alabama: Alabama University Press, 1969), 47-48.

[4] Mesnard, 49-50.

[5] Fundamental Evangelistic Association, “Doctrinal Statement.”

[6] The Augustine Club, “Why Do Catholics Try to Earn Their Own Salvation?”

[7] Quoted in Ian Hacking, “Logic of Pascal’s Wager,” in Gambling on God, ed.  By Jeff Jordan.  (Lanham, Maryland: Rowman and Littlefield, 1994), 24.

[8] Not the only fallacy, however. Philosophers have identified many others, including the question of whether belief is a choice.  See The Internet Encyclopedia of Philosophy,

[9] KJV, Matthew 20:14

[10] And in the same morbid vein, he wrote: “All great amusements are dangerous to the Christian life; but among all those which the world has invented there is none more to be feared than the theatre.”  (Pensees, 11)

[11] J. Lataste, “Blaise Pascal.”  The Catholic Encyclopedia, Volume XI.

[12] Or, more precisely, for the greater good of society, which in turn benefits all members.

[13] Mesnard, 81-82.

[14] Pensees, 222.

[15] Not, that is, until the advent of biotechnology.