Making Book on God

A reader of Marginal Revolution posed a theological thought experiment this week, and a friend challenged me to answer.  Here’s the pitch:

In this thought experiment you are a contestant on a gameshow. The host of the gameshow (let’s call him Alex) has a notecard that says whether or not god exists and to what extent he is involved in the affairs of mankind. You start with $1,000,000 that you must allocate across five possible categories:

  1. Scriptural literalism. Bet into this category if you believe that one of the religious texts is precisely accurate.
  2. God is omnipresent. Bet into this category if you believe that god is everywhere and intimately involved in our lives.
  3. God as a guide. Bet into this category if you believe that god is only there for the major turning points in life and/or when we reach out in prayer.
  4. God as a watchmaker. Bet into this category if you believe that god set the universe in motion but is no longer around.
  5. Atheism. Bet into this category if you believe that god does not exist.

You can distribute the money however you like (e.g. all $1,000,000 in one category or $200,000 in each). After you’ve allocated your $1,000,000 Alex flips over the notecard and reveals which of the five categories is correct. You keep any money that you’ve allocated into the correct category.

There are a couple problems with this set-up, which is why I didn’t send my friend a bet distribution.  The nit-pickiest is that I would be really quite happy with $200,000, so I would be betting somewhere between my true expected probability distribution and a simple even split.  But the bigger problem is that I don’t think these five buckets are clearly defined enough that I’d feel comfortable betting at all (unless I really trusted the bookie).

Starting with the first category “Scriptural Literalism,” I’m a little chary of how the bookmaker is defining “precisely accurate.”  I’d put pretty much no money down on the proposition that the earth is 6000 years old or that the stars are painted on the inside of a celestial globe, which is what I think this category is meant to encapsulate.  However, some holy books (or subsections) are meant to be read as parables or allegories and they might be accurate in that sense.  There must be a better way to frame this section.

Categories 2-4 are too vague and probably need to be coupled with a definition of ‘God.’  Otherwise, a undefined First Cause definitely satisfies 4, but so does a computer science grad student if we’re all living in a simulation that has not been modified since start conditions.  Category 2 is so vague that I have no idea what satisfies it.


If you guys can come up with a better way to to divvy up the sample space, I’ll place my bets, and I’ll put together a google form so that the readership can weigh in, too.

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  • Ben L

    Of course, all effort expended to define different ways non-existent things can not-exist seems a little silly to me.

  • Slow Learner

    I think I would merge the first two categories, and define them along the lines:

    There is a divine being, who intervenes actively and repeatedly in the workings of the universe.

    because category 1 seems too absurdly narrow to get much betting.
    That does cause some knock-on problems with category three, so I guess I would alter that to:

    There is a divine being who intervenes in the universe, but only at significant turning points – not, typically, to find car keys, hold parking spaces etc for the faithful, except where these take a “For Want of a Nail” significance.

    For category four, I would go with:

    There is a divine being who set the universe in motion, but has not intervened since.

    If that definition includes a CompSci researcher running a simulation, so be it; I would consider living in a simulation as one example of a deistic, but not theistic universe.

    And finally I’d leave option five’s definition alone.

    As to how I would bet, I’d put say $780,000 into atheism, $200,000 into deism, partly because of unresolved First Cause questions, and partly because of the possibility of a simulated universe, $19,999 into occasionally interventionist theism, and the remaining $1 into actively interventionist theism, just because giving it nothing out of $1 million seems rude.

  • Ray

    As a side note, I don’t really see how you would run this game in an atheistic or deistic universe. You’d be relying on human fact checkers, like they do in real game shows. So if we live in either of these universes, you really would be better off placing your bets based on the host’s criteria for choosing judges.

    Seems to me, the only way the host could do this fairly without giving away the answer:

    Options 1 through 3, the host gives you no money, but promises God will reward you when you get home if you’re right and performs whatever religious rituals you think are required. If you get the money in non-miraculous fashion, lawyers will take it away. For option 3, if you don’t get the money, the Catholic church has made a legally binding promise to disband, just to make the miracle necessary for a major turning point.

    Option 4, You get half the money upfront, but God will punish or reward you in the afterlife with the same marginal utility plus interest. (Strictly speaking, this only works if Deistic God wants you to believe in him, but it at least puts an incentive there.)

    Option 5, you get all the money upfront. God will punish you by the same amount plus interest if you’re wrong.

    In this scenario, I’d put all the money but $1 on 5. I’d put the rest on 3. Hello, $999999, goodbye pope.

    • Jay

      I think it sort of defeats the point of the hypothetical to ask “how does the game master know the answer?” The point is just to say “if somehow you had to bet, what would you do?” It’s an exercise in revealing actual, quantitative probabilities (and risk preferences, I suppose), not in how you would test the existence of God.

      But if you really need something, then suppose the answer is determined by Omega, the Bayesian super-intelligence that assembles all information to generate maximally likely predictions about the universe. Assume further that Omega has been observed to be almost perfectly accurate in all prior tests, meaning that where Omega announced a 70% confidence level, it was right about 70% of the time, 90% right where it announced 90% confidence, and has not yet been observed to be wrong where it hit greater than a 99.999% confidence level. Assume also that Omega tells you “I predict that exactly one of these options is true, with ~100% certainty — the chance that I’m wrong, accounting as best I can for my own fallibility in making estimates, is 1 out of 1E10.” And after you lay out your money, Omega will announce the result.

      One problem with this formulation is that basically assures you that option 5 is correct. If there really was some kind of super-powerful mental entity running around out there doing stuff, it’s sort of inconceivable that Omega could be so sure that any of the first four (but no the others) were correct. It seems like only total atheism could generate a result that certain. But then again, I’m already pretty certain that option 5 is correct, so this doesn’t bother me that much.

      • Ray

        I’m not sure this works. Who built omega, do I trust them? I am certain that I am not qualified to examine the source code of a system capable of doing theoretical physics better than Richard Feynman.

        Honestly, I think the only way to make trickery less likely than options 1-4 from my perspective would be a really impressive miracle, or examining the card to see if it said (5.) I’m not even convinced the last option would work. I’ve seen too many 3-card monty scams.

        The point being, this scenario in no way makes me feel like I have skin in the game, which is supposedly the point (Or at least not for any reasons relating to how likely I think it is for a God to exist.) You might as well just ask for a subjective probability estimate. Or you could just notice that the original Pascal’s wager doesn’t even remotely scare me, despite much larger payoffs.

  • Nit picks aside, I think this is a good way to get people to stop thinking in black and white terms about the existence of god. How would you think someone like Richard Dawkins or the Pope would place their bets?

  • Jay

    I think when we’re talking about “God,” we probably all agree that we’re not talking about the Dark Lords of the Matrix, who are presumably still made up of old-fashioned quarks (or whatever fundamental entities exist in their universe). At a bare minimum, what any theist means by “God” probably at least includes “an ontologically basic mental entity with extraordinary power to translate its purpose into reality.” Note that I am likely excluding here Spinoza’s or Einstein’s conception of “God,” as well as many varieties of pantheism which might purport to say that “God is everything,” or whatever pantheists say they believe. But when we’re talking about betting on “whether God exists,” I think we pretty much have to be talking about whether some kind of super-powerful, fundamentally mental entity that exists out there somewhere. Neither Dark Lords of the Matrix nor super-powerful aliens make the cut.

    With that clarification, I’d probably put something like $10,000 on option 4 and the balance on option 5, although I want to make a few caveats. First, I think deism has much less than a 1% probability of being true, so my bet there is much more of a hedge due to diminishing marginal utility than a direct representation of my beliefs. If I were already a billionaire, it might be something like $100. Second, no, I don’t think the first three options have a literally 0% chance of being true, but I do find them so unlikely that none are even worth a dollar.

    And third, for whatever it’s worth, there are other sorts of religiosity not covered by these options — for instance, some kind of supernatural pluralism. If option 6 were something like: “Polytheism: Multiple ontologically basic mental entities exist and have some impact on the universe, whether or not any of them ‘created’ it,” then I might throw about $5,000 there as well. As a reductionist, I obviously think the existence of any supernatural entity is quite unlikely, if not an outright confusion in terms. But something like polytheism strikes me as way more plausible than any of the standard monotheistic understandings of “God.”

    • Jay

      One last point. If we’re counting a simulated universe under option 4, as Slow Learner did, then that would change things a lot — I’d maybe put something like $300,000 there, as I take this as a serious (although rather unapproachable) possibility. See

      But in my mind, asking if we’re in a simulation is simply asking a different sort of question than if God exists, just like it’s different from asking if there are super-powerful aliens out there that early civilizations would have called “gods.” After all, if some rebel computer nerd one day created a fully simulated universe in his basement, I don’t we’d start thinking of him as a deity. He’d just be some guy who created a simulated universe. And whether or not “God exists” seems like the sort of question that should have an objective answer independent of what level of reality you look at it from.

  • The problem I see is that the case is set up such that you’re not necessarily trying to find out the truth, just make some money. In that case, the smart person would just split it equally among the five choices and guarantee themselves $200K no matter what. To make it focused on the search for truth, you’d need to add a penalty for guessing wrong. (There’s hell, I suppose, but that’s only a penalty if option 1 is true; it would have to be something that applies no matter what.)

    • Jay

      This is a rather bizarre statement. Smart people trying to make money always take probability into account when betting on different outcomes. That’s kind of the whole point of finance and, well, economic decision-making in general. Sure, the more risk averse you are the more you’ll spread out your money, but there’s no feasible decision theory that has you betting the same on each one, unless you really thought they were all as likely. Or are you really telling me that if you had $1,000,000 to spread across the summed result of rolling two dice, you’d bet equal amounts on each number?

      • Slan21

        Taking probability into account doesn’t mean necessarily maximizing the expected benefits (see st petersbourg’s paradox). If you really need 200,000$ for a special plan, and anything more wouldn’t be useful, then you’d rather just split it whatever your epistemic probabilities are.

  • The first category doesn’t belong with the others, which are about God, whereas it’s about a sacred text. I also have problems with the second category, which doesn’t express how God is allegedly involved in the universe. One could imagine a God as a cosmic engineer, involved physically with every action, reaction, and event. Or as a lover who is present throughout the joys and disasters of life, but who is no more in control than the rest of us.

  • @b

    Try apportioning your confidence across each line of the Nicene Creed.

    1. the physical universe was created not by something, but someone
    2. that creator being was embodied as a homo sapien baby between 10BC – 10AD
    3. a mind survives the death of its brain
    4. prophets spoke the thoughts of that mind
    5. the bible contains those words
    6. church teachings are more righteous than the current academic concensus