Opinion: Probabilities

POSTED: 04/20/12 2:37 PM

The I-Tjing, or the Book of Changes, is a classic Chinese text. Its philosophy is about balancing contrasts and about accepting the inevitable. The Chinese knew one thing for sure thousands of years ago: there are no coincidences; everything happens for a reason.

And coincidences were the central theme in a court case yesterday. A defendant happened to give somebody a ride. He happened to be in the vicinity where a burglary was committed. Somebody happened to leave a gun in his car. Somebody happened to leave a bag with stolen jewelry in his car. Somebody happened to borrow his crowbar and failed to return it. Later a crowbar was found at the scene of a burglary. All these coincidences happened to tally with phone conversations the defendant had with others who also happen to be suspects in these burglaries.

For the prosecution this was too much to swallow. The total of all these coincidences added up to only one thing: guilty as charged.

We suspect, but we don’t know for sure, that this particular defendant knows better as well. He just could not bring himself to admit in open court that he had made a series of serious mistakes by giving people rides to places where burglaries occurred. That he had a police radio at his disposal for several days that enabled him to keep an eye on the men in blue while his rides went about their business did not exactly add to the credibility of his denials.

So we think that when the judge pronounces her verdict in three weeks time, we have a pretty good idea in which direction that is going.

This does obviously not mean that the defendant is guilty at this moment. He is innocent until proven guilty. In our legal system, the judge has the last word about that. Criminal suspects are not tried in the media, though every now and then it is unavoidable that details come to light about a defendant or about a particular case that create the impression that a verdict is already written in stone before the judge has had his/her say.

That is not how it works, and we’re quite happy about that. This does not stop us from having an opinion about criminal cases but that’s where the buck stops. And most of us know that saying about opinions: everybody has one.

In the case at hand though, we have to admit that the number of so-called coincidences is overwhelming. If we stick to the belief that there are no coincidences we’d have to rephrase the previous sentence: there are a lot of circumstances suggesting that the defendant had something to do with the crimes he is accused of.

But there is still a difference between circumstantial evidence and guilt. The way the defendant claimed his innocence was rather convincing – though at the same time we thought his approach was borderline belligerent.

Poker players are familiar with odds calculations. If they hold pocket aces in a Texas Hold’em game and the paired board shows four cards of the same suit to a straight flush and there are still four players in the hand the player with the aces has a situation on his hands, especially if his ace does not make the nut straight flush. His chances to win this hand are marginal at best and, realistically speaking, non-existent.

Good players know this; they apply the law of probability to such a situation. What are the chances that one of the other three players had the ace to make the nut flush? What are the chances one of them has the straight flush card? What are the chances that a player made a full house or a set? While all these chances are by themselves slim, the combination of these possibilities puts the player with the aces in a very bad spot.

The same situation occurs when one good player is playing against eight very bad players. Poker analysts have compared this situation with a classic shootout whereby all eight opponents are holding a loaded gun, while they are all lousy shots. Their lone opponent runs an excellent chance to get hit by one or more bullets – as the analysts like to say, simply because there is so much lead flying around.

The probability that our defendant gave a friend a ride once, and that shortly afterwards a burglary occurred, is by itself slim. But it is plausible. Things happen. But what is the probability that such an event happens not once, but three or four times? That is the question the prosecutor asked herself, and she found an easy answer: that is it is not probable or plausible at all.
So while there does not seem to be a lot of firm evidence, the amount of circumstantial evidence seems to weigh against the defendant.

Are we right or wrong? In three weeks, we’ll know the answer.

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