Which is More Likely? October 27, 2007

Which is More Likely?

Being dealt the first hand of 13 cards or the second?

Bridge Hands

As onegoodmove writes:

There are 635,013,559,600 possible hands and the chances of being dealt the first hand is just as likely as the second though a common intuition is that the second is far more likely. This I believe is because the second has a more likely distribution of the cards, but we are talking about individual hands not distributions. I think it is the same wrong intuition that people use when presented with the fine-tuning argument for the existence of a designer god, the argument is that the laws and constants of physics are fine tuned and if they were different we wouldn’t exist. To which I answer okay, and what’s your point. Well there must be a designer to have just this set of laws and constants they respond, but like the two bridge hands above it is more likely that it is random.

The faulty analysis comes from the arrogant idea that we are somehow special and that leads us to believe that we can’t be here just by chance, or that it is somehow more likely that there is a designer.

[tags]atheist, atheism, probability, statistics[/tags]

"The way republican politics are going these days, that means the winner is worse than ..."

It’s Moving Day for the Friendly ..."
"It would have been more convincing if he used then rather than than."

It’s Moving Day for the Friendly ..."

Browse Our Archives

What Are Your Thoughts?leave a comment
  • I wouldn’t argue with some of this, about the cards.

    But wouldn’t “the second has a seemingly more likely distribution of the cards” be more accurate. If we recognized a pattern in the second it might seem as unlikely to us as the one we do recognize. Thus the poor fools who buy ten lotto tickets.

    It’s a bad analogy for evolution, though. The number of different vectors that went into evolution is far larger than that for shuffling cards. And those vectors aren’t discrete, they interact and, as we are finding out, the ways that those and other vectors just being discovered are far more complex than is widely believed. The likelihood of the outcome we have today is one in a much greater number than any one hand of cards being dealt. There is no way to know if that one out of n is due to intention or random chance, though. It isn’t science to assume that it is intentional, though there isn’t anything wrong with believing either way outside of science since it is an unanswerable question.

    You do realize, Hemant, that card dealing IS an act of intention, as was the design of the pack. It could be that there was intentionality of some kind, at some level in evolution, but that isn’t a question science can answer. The fact that whatever happened, happend through evolution IS the best scientific analysis of the evidence, though. That much is known.

  • I disagree with this refutation of fine-tuning arguments.

    Within the analogy of cards, let’s just say that we knew there is a .01% chance that someone is cheating (the cheater is analogous to an intelligent designer). And let’s say that if someone is cheating, we know there is a .01% chance that the first hand (ace through king of spades) would be dealt.

    The chance of getting ace through king of spades when there is no cheating is about 1 in 635,013,559,600, and the chance of getting that hand when there is cheating is about 1 in 1,000,000. Therefore, if you saw that hand, there’s about a 1 in 635,013 chance that no cheating is going on. This is known as Baye’s theorem. The chance that someone is cheating is so high because a cheater is more likely to choose the first hand over the second one.

    I’m sorry, I think the basic reasoning behind the fine-tuning argument is valid, and that a more sophisticated refutation is required. You might, for example, argue that our situation is actually more like the second hand of cards, or that the anthropic principle causes a selection bias that renders the reasoning invalid.

    That said, I think most people who make the fine-tuning argument don’t understand the details either.

  • Aj

    Within the analogy of cards, let’s just say that we knew there is a .01% chance that someone is cheating (the cheater is analogous to an intelligent designer). And let’s say that if someone is cheating, we know there is a .01% chance that the first hand (ace through king of spades) would be dealt.

    Doesn’t the premise contain the conclusion?

  • I agree that this analysis is flawed.

    The actual probabilities of getting each hand are:

    Probability of hand 1 = (probability of a designer)x(probability he provides hand 1)+(probability of no designer)x(probability of randomly getting hand 1)

    Probability of hand 2 = (probability of a designer)x(probability he provides hand 2)+(probability of no designer)x(probability of randomly getting hand 2)

    The probability of a designer plus the probability of no designer add up to 1. To arrive at the answer that the probability of both hands are equal, One Good Move has assumed that the probability of a designer=0 and the probability of no designer=1. You can’t prove anything about God starting from the assertion that God doesn’t exist. That’s not a proof; that’s an unproved assertion.

    Now, if there’s a nonzero probability God exists then a lot of discussion could ensue on what sort of hand God is more likely to provide. However, we cannot assume randomness in his choice of hand so the argument of One Good Move that both hands are equally likely is invalidated.

  • Stephen

    Context is very important when discussing probability arguments. To a bridge player deciding what to bid, the first hand is AKQJ10xxxxxxxx, while the second is Qxxx / Ax / KQxx / xxx

    In the context of a bridge game it is entirely reasonable to say that the second hand is more likely.

  • Stephen, maybe it would be better to say that a hand defined as being similar to the second hand would be more likely.

    In a really random deal every particular pattern would have the same chance of coming up, that is the objective definition. That two hands might seem to be similar isn’t objective. Analyzing the similarities of these two hands might reveal an enormous number of differences, including what can be considered to be patterns. It’s in the immediate perception that a particular hand has an easily identified pattern that its “likelihood” of coming up in any one deal is judged “unlikely”. It wouldn’t make any sense to bet that any one of them would come up if it was a random deal but it is more likely that a hand without a pattern you will recognize immediately will come up at any given time. That is due to our inability to quickly distinguish what we might take as patterns, not on the likelihood of them arising by chance.

    I seem to recall reading an abstract of a paper that said it took seven shuffles to approach true randomness in a deal. But I’m too lazy to look it up right now. Um. Seven. The most magical number….. I wonder……

  • Thinking about it more, the card game is entirely inadequate as an analogy for evolution. In playing cards any hand that happens to come up can be played, all of the evidence is that this isn’t true of how evolution happened. Every possible combination wouldn’t have worked the same way, many of them wouldn’t have evolved at all. You can see this on a micro-level with those organisms and, perhaps, species which didn’t work out. Some chance “deals” wouldn’t have gotten that far.

    I’m beginning to think that something as complex as evolution doesn’t have an honest analogy.

  • Aj,
    Yes, the premise contains the conclusion. That’s the mark of a valid deductive argument, is it not? But, yes, a good objection to the argument is that we don’t actually have the numbers, or that the numbers are not nearly so big.

    I think the cards aren’t supposed to be an analogy for evolution (and yes, that would be a horrible analogy), but for the fine-tuning of physical constants. You know, things like the masses of elementary particles.

  • miller, I don’t like the card deal as an analogy for the fine-tuning of physical constants for for the same reasons.

    As someone who used to tune pianos as a side line, tuning consists of one intentional act after another. And, little known to most, a finely tuned piano isn’t “in tune” but he octaves are “stretched” to be ever so slightly out of tune, even the octaves. Equaltemperment isn’t “in tune” either but a slight alteration of the just intervals so they will all be about equally acceptable, though “out of tune”. “Fine-tuning” isn’t a good analogy for these things either.

    The creation of the universe, evolution of life, these are sui generis. Analogies don’t work and will always lead away from the truth. Whatever that might be.

  • There’s no point arguing with christians. They’ll never get it.

  • The Worst of Perth, if that’s meant for me, I don’t happen to be a Christian. Or a member of any other religion.

  • I’m not Christian either, fyi. I just like math.

error: Content is protected !!