The Lotto “miracle”

lotto-2-ballsApparently some local Christian apologists believe that the New Zealand Lottery Commission performs a miracle each week with its Lotto draw. They claim that:

“Given the complete randomisation of 40 balls, falling into any sequence of six is 1:2,763,633,600.”

If they are correct, and given New Zealand’s population, we would  expect a winner only every 15 years or so. Despite this there is a winner most weeks. In September 1993  38 people won First Division! With these odds they might be justified in calling most of the winning miracles.

However, these poor souls got their maths wrong. They forgot to divide by 720. The real odds are 1:3, 838, 380. That sounds more like it, doesn’t it?

So, no miracles. But the mathematical error was really caused by their desire to describe the regular Lotto result as “extraordinary”:

“Consider the lottery reported last night on television as one such event. The chances of winning, or indeed any random sequence of numbers, is extraordinarily improbable, yet if it is true that extraordinary claims require extraordinary evidence, you should never believe it happened. Weighing the probability of the extraordinary event will swamp the reliability of the witnesses every time so that you should never believe it. Even if the programs reporting is 99.9% accurate.”

So, they claim, if we can accept the Lotto “miracle” on the hearsay evidence of a news report we don’t need extraordinary evidence to accept “God raised Jesus of Nazareth from the dead.”

Can’t see what Lotto has to do with it. The event itself is not extraordinary (nor is the selection of “any random sequence of numbers” which actually has a probability of 1) and while the actual numbers drawn are pleasantly extraordinary to the winner – they aren’t to the rest of us.

But what about the evidence? We know that there is a legal requirement for police observation of the draw as well as other checking of the equipment and procedure. The winners ticket is also thoroughly checked. We just wouldn’t be investing our hard-earned cash in Lotto if this checking didn’t occur. Seems like pretty extraordinary evidence to me.

These Christian apologists claim that because we accept the Lotto result we should accept the hearsay claims of biblical miracle with no real evidence.

Now, if they could just produce evidence of their miracles with similar thoroughness and robustness to that used in the Lotto draw we would have something to look into – wouldn’t we?

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24 responses to “The Lotto “miracle”

  1. Wow. What is it about fundamentalism that attracts stupid people?
    This isn’t just dumb, it’s way-down-deep-in-the-bottomless-pit-dumb.
    This is the kind of dumb that has to be worked on. Lovingly crafted for years until it’s ready for public astonishment. :(

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  2. Nicely said, Ken :-)

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  3. We know that only God can perform miracles, so if the Lotto win rate is miraculous, then God is involved in gambling! This is troubling, to say the least.

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  4. I have to be honest that I tend to think of the “ThinkingMatters” as the “Brain Dead Society”. “Welcome, we’ll try kill your brain, ours are already gone…” Unkind humour I know, but the sheer illogic of the people and the self-deceit is extra-ordinary. It’s eye-opening and informative in it’s own way, I just can’t say that’s a positive way.

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  5. the “ThinkingMatters” forum. Missed a word!

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  6. Revright – I assure you that no one else is seeing the Lotto results as miraculous (except perhaps some lucky winners). The win rate is what one would expect from the statistics. God’s off the hook.

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  7. Ken,

    You have distorted and misread what I have actually wrote. For one I never claimed the lottery was in any way a miracle. The analogy is that a miracle is, according to Hume, an extraordinarily improbable event and so we should never believe it – but another extraordinarily improbable event, the lottery draw, we have no trouble believing.

    Secondly, it is not someone winning the draw which is extraordinarily improbable, but the actual specific random sequence of 6 balls from 40. To get any random sequence the probability is 1 – I agree (after all they roll each week without fail), but the probability of a specific random sequence is 1:2,763,633,600, thus the analogy is correct to use. One factor why the actual chances of winning is less is because they do not require the correct order.

    Third, I don’t claim that you should accept the claims of the biblical miracles without evidence. I claim that the probability calculus instructs us to consider the occurrence of extraordinary events (i.e., biblical miracles, the lottery result’s sequence of numbers) without requiring extraordinary evidence, but taking into account the ordinary evidence, the background knowledge of the world, and the expectation that we should have the evidence we do have had said event not occurred.

    Those errors are three of your most egregious.

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  8. 7: It’s pointless anyway as your original arguments are self-justifying babble. Word games, like you’ve posted here won’t save you: your persistent egregious mistake is to try defend the indefensible. It’s is the entire “purpose” of ThinkingMatters, after all.

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  9. Actually, Stuart, I quoted what you had written. But of course your presentation was confused. So, its good that you now accept the probability of a draw is 1. Progress.

    But your quoting the probability of a specific six numbers is incorrect because you are referring to public perception of the draw – where the order that the numbers are drawn is not a factor (certainly not on my ticket). The actual and relevant probability is 1:3,838,380. This is how people judge how “extraordinary” the event is. I suspect you quote the inappropriate figure because you wanted to present the event as more “extraordinary” than it actually is.

    However, the real probability of the Lotto event is still 1 for the uninterested observer. There is absolutely no suggestion of violation of known information about how the world behaves, no need to violate accepted laws of nature. All we have done is removed six numbered balls from a total of 40. Yet you are putting this in the same class as a biblical “miracle.”

    I think the reasonable person will accept that the claim of turning water into wine (no matter how desirable) is going to require more supporting evidence (because it violates our understanding of laws of nature) than the hearsay fact of a lotto draw. The reasonable person would probably accept that evidence similar to that available for us to ascertain which specific six numbers came out of any specific Lotto draw would be a good start.

    When Rutherford converted nitrogen into oxygen we had what could have been considered an “extraordinary” event – in some people’s eyes equivalent to converting water into wine and violating the laws of nature as then understood. Now we accept this event because of the evidence provided, and its reproducibility – that’s the way in science. We don’t accept the biblical story of conversion of water into wine because the evidence is inadequate – basically hearsay and urban legend.

    What the hell is the “probability calculus” that “instructs us” to accept “biblical miracles” “without requiring extraordinary evidence.”? I don’t recall any “probability calculus” being required to win acceptance for Rutherford’s discovery (or for any specific Lotto draw either). Surely we just rely on good verifiable evidence.

    All this talk or “extraordinary” is a red herring. Why not just say good verifiable evidence.

    And the “probability calculus” are just vague words used in an attempt to make the argument appear “sciency.” If not – present us with the “probability calculus” formulae, the input values, the calculation and the result. Let us judge for ourselves how appropriate you claimed “probability calculus” is for these situations. That’s the way in science.

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  10. Stuart,

    I realise (well, I place a high prior on the fact…) you have picked up your Bayesian argument from William Lane Craig or someone similar but it seems to me to be a bizarre interpretation of Bayes Theorem.

    In its simplest form Bayes tells us that the probability we should place on an event having occurred given a piece of evidence [P(H|E)] is equal to the probability of observing that evidence if the hypothesis is true [P(E|H)] multiplied by the probability we would have assigned to the event before the evidence [P(H)] divided by the probability we would place on observing that evidence [P(E)]. That is P(H|E) = P(E|H)*P(H)/P(E).

    Now, surely an extraordinary claim is one which would think is very unlikely to be true? So, our prior, P(H), will be very low then and we will need a very low P(E) in order for P(E|H) to be likely? That is, we’d need extraordinary evidence to settle an extraordinary claim?

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  11. And applying David’s representation of the theorem to Lotto wouldn’t we say that the probability of observing the draw given that it occurred is 1; the probability we would have assigned that the event would occur is 1; and the probability of observing the evidence is 1. So the probability of the draw having occurred is 1. And that the actual numbers drawn are actually irrelevant to the event.

    So, Stuart, what about giving us some figures for turning water into wine that we can plug into the theorem? And we can accept that the actual wine variety (chardonnay, pinot gris, ec) is irrelevant to the event itself.

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  12. David W,

    I believe you have skewed the formula. See my original article here http://talk.thinkingmatters.org.nz/2009/bayesian-probability-theorem/. Or else John Earman, the agnostic philosopher and author of Hume’s Abject Failure.

    Ken,

    Your comment 9 commits another egregious error – you have expanded the definition of miracle of I have been working with to include a violation of the law of nature. Such an argument against miracles begs the question.

    I thought it was clear the probability calculus was Bayes’ Theorem.

    Certainly we look at the evidence. That should be clear from the P(H|E). But you see the theorem expresses that to calculate the probability of the hypothesis on given evidence we must also look at the background knowledge of the world apart from the specific evidence, and the probability that we would have the evidence had the event not occurred.

    So in the case of the resurrection (I’m not interested in water to wine – I don’t know how this could leave any evidence in history apart from the gospel narratives) the probability of that event is calculated by considering the evidence, the background knowledge of the world and the expectation we would have the evidence we do had Jesus not risen from the dead. Thus, to establish a favourable probability of the resurrection we may not need an overwhelming amount of evidence – we might only garner only a small amount of evidence if we would not expect that evidence if Jesus did not rise from the dead.

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  13. So – come on then, Stuart. Front up with the input data and do the calculation. Or is the formula only for decoration?

    Clearly your starting point is to “establish a favourable probability of the resurrection” and you want to do that without “an overwhelming amount of evidence” – or any evidence, perhaps.

    I personally don’t see any more evidence for this resurrection than the water into wine – only hearsay and urban myth. Now, there is some pretty reliable evidence for Rutherford’s transmutation (which appeared to violate the laws of nature – as most new discoveries do). And we don’t need shonky application of a theorem or “probability calculus” (or any irrelevant bafflegab about Lotto).

    If the theorem you quote is relevant then you will surely use it.

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  14. Stuart,

    No, that’s the formula in its simplest form (http://en.wikipedia.org/wiki/Bayes%27_theorem). The one you present is derived from that one, it’s just explicitly describing how P(E) is calculated.

    In fact, your later arguments are just reiterating the the need for extraordinary evidence:


    Thus, to establish a favourable probability of the resurrection we may not need an overwhelming amount of evidence [who said you did, it was never about amounts of evidence?] – we might only garner only a small amount of evidence if we would not expect that evidence

    Yes, exactly, you would need evidence that was extraordinarily unlikely! I think where you have gone wrong is not understanding what Earman and others are talking about. Hume (of the abject failure) argued that on a balance of probabilities you could never conclude that a miracle had occurred. That is not true in a Bayesian framework. However, the only way a miracle can be supported in a Bayesian framework is, as you say, with evidence that you think you would be very unlikely to occur without the miracle having happened. You would need extraordinary evidence. For me, 2000 year old accounts of empty tombs and bodily appearances don’t seem extraordinary.

    And Ken,

    Really what is the point of being able to turn water in to wine if you don’t care what variety you’re going to make! Imagine wasting that power on make Sauvignon blanc!

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  15. Ken,

    The formula is used in its refutation of Hume’s objection to miracles and the phrase (extraordinary events require extraordinary evidence) that remains in popular culture as a result of Hume – not as a proof for the resurrection. I thought this was clear! The resurrection is used as an example, but as I said before, the data for the inputs is inscrutable.

    Now I do think we have pretty good evidence for the historicity of the resurrection, but right now I’m not making that case. All I have been arguing for it this: the phrase “extraordinary events do not require extraordinary evidence” is, as commonsensical as it sounds, demonstrably false.

    David W,

    I suspect your statement of Bayes’ Theorem is from just under the title “Statement of Bayes’ theorem” on the wikipedia link you provided. If so, that is not the correct formula for my purpose (you have also stated it in a fashion that is ripe for misinterpretation – though I know its hard using only plain text). The form of the Bayesian formula (I think) you have used, as the wikipedia said, describes the way in which one’s beliefs about observing ‘A’ are updated by having observed ‘B’.

    For my purpose what we want is the second formula on that link under the title “Alternative forms of Bayes’ theorem.” – that is to establish the probability of a hypothesis (H) with respect to the evidence (E) – P(H|E)

    Yes, exactly, you would need evidence that was extraordinarily unlikely! I think where you have gone wrong is not understanding what Earman and others are talking about. Hume (of the abject failure) argued that on a balance of probabilities you could never conclude that a miracle had occurred. That is not true in a Bayesian framework. However, the only way a miracle can be supported in a Bayesian framework is, as you say, with evidence that you think you would be very unlikely to occur without the miracle having happened. You would need extraordinary evidence. For me, 2000 year old accounts of empty tombs and bodily appearances don’t seem extraordinary. [italics mine]

    Your jump to “You would need extraordinary evidence” in comment 14 mistakes the actual evidence we do have (E) with the expectation we would have the evidence had the said event not occurred P(not–H|E&B). So the accounts of the empty tomb and bodily appearances (thats not all the evidence there is by the way) may not be extraordinary, but it might be enough if we consider the probability we would have these accounts if the resurrection did not occur.

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  16. Ok, so this thread is verging on the level of ridiculousness displayed in the original one so lets be concise:


    For my purpose what we want is the second formula on that link under the title “Alternative forms of Bayes’ theorem.” – that is to establish the probability of a hypothesis (H) with respect to the evidence (E) – P(H|E)

    They’re the same formula, do yo see the first term in the shorter formula P(H|E)=. The only difference is yours is explicit in declaring the components of marginal probability P(E).
    both formulae describe the way in which one’s beliefs about observing ‘A’ are updated by having observed ‘B’:

    M: Hey David, I reckon this Jewish guy was bodily resurrected three days after his death
    D: Really? That seems unlikely
    M: well, I have these pamphlets that say his tomb was empty and he talked to the lost tribes of Israel in America
    D Hmm, i think it’s quite likely that tradition would have arisen in a world in which your Jewish man wasn’t resurrected so, no, you’ll need some more improbable evidence to win me over, and why do you guys always ride bikes?

    If you actually do the maths (it’s a bit of a pain to represent in plain text) you’ll find that in order to turn a prior of 0.1 (hardly extraordinary)to a posterior of 0.95 the term you are so keen on (the probability of finding the evidence if the hypothesis was not true) needs to be 0.0006. You really are at sea on this one.

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  17. I agree David. Stuart will try write off anyone that disagrees agrees with him with what amount to word games, it’s what he does. Word games, like he has posted here won’t save him, of course: he’s to try defend the indefensible but because he has a set “goal” he wants to be true at all costs (including honesty and correctness of any argument) he’s blind to the nonsense he writes.

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  18. David W – I agree with you about wine variety and quality being important. One thing I have learned with age is that there is such a thing as a bad wine.

    Stuart:

    “The formula is used in its refutation of Hume’s objection to miracles”.

    But you haven’t used it. It’s only there for decoration (to make your arguments look sciency). This doesn’t work by osmosis you know. Give us some input data (this is what it boils down to) and plug them into the formula.

    You claim that the requirement for evidence is “demonstrably false” – and have done absolutely nothing to support this. If anything you have been discrediting you argument.

    Stuart – you are quite welcome to believe in this resurrection thing, and you are welcome to argue for it and to provide evidence. You discredit these arguments, though, when you drag in irrelevancies (Lotto and the formula) because these are obvious diversions, poorly argued and falsely equated with the situation you really support “but right now” are not wanting to “make the case” for.

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  19. Ken,

    Im not making the case for the resurrection now (though I hope to soon), and not plugging in the probabilities for the data because I think those are inscrutable. All I’m saying is that extraordinary evidence is not required to establish the historicity of an extraordinary event, so using the phrase as a refutation of the resurrection is ill-considered and accordingly false – as demonstrated. Bayes’ Theorem supports this conclusion. The formula isn’t just decoration – that should be obvious enough – its the centre-piece of the article and subject-matter.

    I think David W believes he has refuted me, but in actual fact he agrees when he says “The only difference is yours is explicit in declaring the components of marginal probability P(E).

    To everyone else, the strawman of my article that Ken has presented above is a travesty of thinking, and further ridicule, rather than sincere engagement and actual refutation will only underscore the general ineptitude so often displayed here and by people unfamiliar simple philosophy.

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  20. @19 Any evidence at all would be a start Stuart. Also, have you ever heard of the phrase “on the balance of evidence”?

    As with the others, I fail to see what the probabilities of a single instance of a perfectly ordinary event (being a lotto draw) that is consistent with all known physical laws and observations has to do with speculations that have no consistency with same said laws and observations (resurrections of dead people, water to wine etc..) and thus has no information on which to calculate a probability for.

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  21. Ok Stuart, I’m not quite sure why but I’m going to do this once more, really clearly.

    An extraordinary claim will be one with a low p(H), so even when you presume p(E|H) to be one (ie if the event had happened we’d definitely have the evidence we do) and only an event with a 1/100 chance of happening the top half of your equation will be 0.01. Yes?

    So, if we are to move that prior to a posterior of 0.95 (the point where scientists start paying attention to what someone is saying) we need p(E) to be equal to 0.01/0.95 ~ 0.0105 right?

    So p(E)= 0.0105
    = p(E|H)p(H) + p(E|!H)p(!H)

    Yeah? We know the first half of that is 0.01 and p(!H) has to be 0.99 – p(!H)+p(H) has to equal one doesn’t it? Or is a miracle in fact a temporary suspension of set theory?

    0.015 = 0.01 + p(E|!H)*0.9
    0.0005 = p(E|!H)*0.9
    p(E|!H) = 0.00053

    So, to turn over something that we thought had a 1% chance of happening we need evidence that we think, with all our background knowledge, would have a .05% chance of happening! Moreover, it obvious that more extraordinary claims will need more extraordinary values for p(E|!H to keep up.

    Tell me where I am mistaken.

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  22. I take it Stuart is using ‘inscrutable’ (eg ‘the probabilities for the data… are inscrutable’) in the sense of “not readily investigated, interpreted, or understood”? How terribly convenient…

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  23. Stuart:

    “The formula isn’t just decoration – that should be obvious enough – its the centre-piece of the article and subject-matter. “

    And you have the cheek to talk about “ineptitude”!

    Where have you used the formula? You have not shown anything about its applicability to your claim! And as David W has pointed out if you did use the formula it would show the opposite of your claim.

    It would have been more honest and simpler just to have referred to Craig’s original argument rather than try the impossible task yourself.

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  24. ………here’s the deal :)

    The “GOvernments” are given to us by GOD.
    Right?

    If GOVERNMENTS (State, country, local, providence, city, town, village, street) have a lottery, and its open to play, as long as you can control yourself, and have it not become, what we call “an idol” – then it could be ok.

    If you have issues with gambling, well, hello? Dont do it

    Wayne

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