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, Health, Money, and Love & Why We Don’t Enjoy Them (Eerdmans, 1990)