# Wanna Bet?

You flip the coin ten times, and ten times in a row it comes up heads.  How much do you want to bet that the next time you flip it comes up heads?  Or will it be tails?  If you are convinced that the next toss has a better than 50/50 chance of coming up heads (or tails) because of the previous ten flips, you are guilty of the "Gambler’s Fallacy" or "Monte Carlo Fallacy."

Don’t feel bad; you’re not alone.  A whole city is built on the Gambler’s Fallacy; it’s called Las Vegas.  In fact, there’s an entire country called Monoco that’s underwritten by this fallacy.  We’re suckers for a sure bet.

The Gambler’s Fallacy is a fallacy of cause (a retroductive fallacy of soundness in the major premise, in case you’re keeping track).  We think we see a pattern in independent events, and so we assume that the events are not independent after all, even though there is no demonstrable connection.  We are prone to explain things, especially things that are rare or highly improbable.  We look for patterns and then assume the pattern will continue into the future.  If a slot machine hasn’t paid off in a while, we’re inclined to say it’s "due."  Or we might conclude it’s a loser.  But in fact, if the machine is honest, it is pre-programmed to pay out at a certain level of probability.  It is no more or less likely to pay out on one pull of the lever than on the next.

Here are some common examples of the Gambler’s Fallacy:

"Lightening never strikes twice in the same place."
Actually, lightning strikes many times in the same place all the time, otherwise lightning rods would be useless.

"I just knew I was going to win the Lotto.  I’ve lost so many times, I knew I was due."
Every lotto ticket has exactly the same statistical chance of losing as any other.

"Bad things always happen in groups of three."
Actually bad things just happen; we tend to stop counting after three.

"If anything can wrong, it will."
You’ll recognize this as a variation on "Murphy’s Law," the pessimist’s creed.  Given that Capt. Edward A. Murphy worked for the government, you can understand his pessimism.  However, when you stop and think about it, you’ll realize that everything has a finite probability of going right or wrong.  We tend to notice the wrong more often than the right, hence we make a "law" out of things going wrong.

"I always feel safer flying after there has been an airplane crash.  What are the chances of another crash happening the same day?"
Answer:  The same as a day when a crash doesn’t happen.

"Luck" is kind of a dirty, four-letter word among religious types.  To wish someone "good luck" at a pastor’s conference will usually draw a constipated look, if not a quick corrective.  Luck used to be considered something holy before the gambler’s got a hold of it and turned it into a religion.  Holy Luck.  The Divine Hand hidden under randomness and chance.  Luther’s Deus Absconditus.  Einstein opined that God doesn’t play dice, but He sure doesn’t seem to mind a few rolls at the cosmic craps table.1

The OT book of Esther is about "holy luck."  A decent subtitle for the book would be:  It Just So Happened.  It just so happened that a sharp-looking Jewish gal catches the king’s eye when he’s looking for a queen.  It just so happens that the king has a case of insomnia one night and has his servants read some bedtime stories to him about a guy named Mordecai who saved the king’s neck from a court conspiracy.  It just so happens that Mordecai is being targeted by a guy named Haman who hates the Jews and wants to kill them.  And it just so happens that Haman winds up hanging from the gallows he built for Mordecai.  God is never once mentioned in the entire book of Esther.  Holy Luck!  At the festival of Purim, which commemorates the events of this book, the Jewish people play a little gambling game with a kind of dice thing called a pur.  Very appropriate.  The hand of God hides behind holy luck.

When the church needed to fill the vacancy in the Twelve left by Judas, they chose two qualified men, prayed, and drew straws.  Rocks, paper, scissors.  The lot fell on Matthias (Acts 1:26).  Lucky him!  That approach to filling pastoral vacancies never really caught on.  Now we have call committees.

You can’t predict the future by patterns of independent past events.  So if you’re having a run of good luck lately, rejoice and be exceedingly glad, not to mention thankful to the Giver of every good and perfect gift.  But I wouldn’t bet the farm on it.

1 On "holy luck," see Robert Farrar Capon, (Eerdmans, 1990)

## 7 thoughts on “Wanna Bet?”

1. Rick Ritchie

So what is “a retroductive fallacy of soundness in the major premise.” From Google I could find that a retroductive fallacy is a fallacy having to do with a cause. Meaning, we made a mistake in how we argued that something caused something else. But I still don’t know what the rest of the term means, even if the individual words make sense. (Does it just mean that there is an unsound major premise? Or that we think because the major premise is sound, the whole argument must be sound?)

I’m enjoying these Logic posts, and especially the examples and your responses to those.

2. revcwirla

I’m using Prof. Bruce Thompson’s taxonomy of fallacies. (http://www.cuyamaca.net/bruce.thompson/Fallacies/gamblers.asp) I like his classification system chiefly because it makes the most sense to me. For the sake of anyone listening in, I’ll break it down. Retroduction goes like this:

Rule: All A are B.
Result: C is B.
Case: Therefore, C is A.

In the gambler’s fallacy, the “rule” is faulty. We assume a connection between indepedent events. The only relationship is probability, which is not a cause of anything. The major premise is not sound due to a fallacy. Our observation of the result is sound, but we are lead to make the wrong conclusion.

3. Rick Ritchie

The fuller description from the linked site describes the fallacy as “a retroductive fallacy of soundness with a falsehood in the major premiss.” Your decription missed the words “wiht a falsehood.” My confusion came when I tried to figure out how soundness in the major premise could be a bad thing. (Except by being absent, or deluding someone into neglecting to ask questions of soundness about the rest of the argument.)

Fun stuff.

4. revcwirla

I really do liike Bruce Thompson’s approach to the fallacies. Most just list them or try to categorize them. He’s the only one that organizes them under the categories of deduction, induction, and retroduction.

Thanks for the clarification, Rick.

5. john pawlitz

So maybe this is way out of line here, but what do you think about Pascal’s wager? I always take him as half-joking when he suggests that people should bet on religion, but does it seriously apply, logically? I have a lot more respect for Pascal than to want to pin his reputation on this one “doctrine” but I know it’s pretty frequently criticized by the doctrinaire atheist.

6. john pawlitz

I suppose the issue is do you take luck to be something God controls, and therefore put even more trust in God than you do in odds. Scripture does not hesitate on this subject, even though we hesitate to interpret it, clearly indicating that God is behind the roll of a die. Is interesting to think of in light of Caesar’s comment “the die is cast” (that the roll of a die had not yet landed one way or another, but was thrown as civil war commenced).

It is impossible to suppose that odds will be consistent with our position, like every time we flip a coin we will always see heads and tails alternating in perfect order. But that doesn’t mean the odds are inconsistent (well, not necessarily-the coin could be misshapen), it only means our position as the flipper of the coin is not authoritative on account of odds. In other words, though the odds are not flawed in and of themselves, we cannot count on our own relation to them for consistency. In other words, the gambler’s fallacy could be restated as supposing that one’s own relation to the odd determines how the odd will function (in producing probabilitous [just made up a word there...] outcomes).

I think this was somewhere in the depths of Pascal’s mind, in his doctrine of the theistic/religious wager. I think he was appealing to one of the basest–if not the basest–form of the human consciousness, a mind wholly set on gaining things, as Cain was (although Pascal was certainly an ardent student of game theory). He’s saying bet on God, you materialistic minded fools, because the laws of probabilty expect that whatever you pay gives you infinite dividends, whereas what you have to pay is finite. But it is more of an anthropological judgment than theological, because it’s just saying: here’s how the human mind works, rather than bicker, I’ll try to use it.

Anyways, I suppose the only thing that really pertains is: do you think that was a fair assessment of the gambler’s fallacy: to say that we judge odds as being subject to our experience, when in reality they are consistent, but subject to God (or not consistent, if consistency implies relation to our experience). And I threw in the bit about Pascal because I was curious…about a week late as Friday is back agin, but better late than never, right? Or…will that be this week’s fallacy

7. revcwirla

Sorry for not responding sooner, John, but my e-mail notification feature doesn’t seem to be working these days. I just happened to see your comment, since I usually don’t open my own blogs except to ratchet the counter to keep my numbers up.

Re Pascal: His “wager” was not exactly one of his most shining moments in apologetics. Though not the gambler’s fallacy, it does suffer from artificially limiting one’s choices to two: atheism or theism. At best, I think Pascal was appealing to common sense. Choose the less risky of the two alternatives. We do it all the time when we can’t be sure about something. But, as ardent atheists have pointed out, theism, if it is false, is not without negative consequences.

Re whether “luck” is something God controls: Who can tell? To answer that question would be to uncover the Deus absconditus. For the most part, I tend to side with Capon’s “non-interventionist God” who doesn’t rig the dice, but turns every roll into a winner in the all-reconciling death of Jesus.

Re your last question, I would agree with the first part. The gambler’s fallacy arises out of our experience not statistics. That’s why people are more afraid to fly than to drive to the airport, though statistically it should be the other way around. Stricly speaking, the gambler’s fallacy is attempting to predict the future from past events where there is no causal connection.

Are these things are “subject to God”? Well, all things are subjected to Christ, we just don’t know how that plays out. He can do nothing and leave things be as they are, like the farmer with the weedy wheat field, and still be “in control.” The age old problem of theodicy is tied to this discussion. I find it best not to speculate on causality, but to move the discussion to the all-reconciling death of Jesus in which the worst of luck becomes good news.