How gamblers fool themselves

Jan 16, 2006 2:22 AM

Gamblers can fool themselves. Even smart gamblers can fool themselves. Part of the reason is of course that gamblers must be optimistic in some sense otherwise their activities are senseless. You really have to believe that you are going to win in the short run or the long run. This optimistic attitude leads many gamblers to interpret the evidence in front of them in a way that affirms their expectations of a positive outcome.

You can see this phenomenon at work with both successful and unsuccessful gamblers. In the hearts of many gamblers (though not all) exists a system, or at least a collection of superstitions that instruct their behaviors.

A keno player might, for example, select for play only numbers that contain a 7, such as 7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78 and 79.

The truth is that this collection of 17 numbers will produce (if we assume that the selection process is anything like random) an average of 4.25 hits per draw over time.

The gambler might even test his theory that these numbers will produce more than 4.25 hits per game, by studying draws over a hundred games or a thousand games or even more.

If this system does not produce more than 4.25 hits per game of course the gambler won’t win. Suppose this test of the system produces over a thousand games an average of 6 hits per game for this selection of numbers.

Six hits out of 17 numbers is just about what is required to win consistently at keno. An easy way to understand this is to just assume that you are playing 17 "kings," or one spot per game. This will pay back to the gambler \$18 per game for every \$17 wagered at standard keno pay rates.

It is also easy to see that the required break even number of hits for 17 numbers is 5.67 per game. After affirming this system through watching a thousand draws, and seeing 6 hits per game, the gambler starts playing. He or she will either win or lose.

If the gambler wins, he or she will attribute his or her success to the system. And why not? It all seems very mathematical, very scientific! And if the gambler loses, the failure of the system will be attributed to a run of bad luck.

But what is really going on? What is going on is that random processes produce runs of events that persist over long periods of time, much longer than you might imagine. It is true (again assuming a random draw) that over time the average hits on the 17 numbers will trend closer and closer to 4.25.

That means over a thousand games you would expect 4,250 hits. But our test produced 6,000 hits, a surplus to the good of 1,750 hits.

Look what can happen though, when a million draws are considered. In a million draws, we would expect 4,250,000 hits. Our test might produce 5,000,000 winning hits, a whopping 750,000 winning hits over expectation. The point is that in relative terms the 5,000,000 hits are closer to the 4.25 that we expect, though in absolute terms we have far more winning hits than in the shorter test. It is also true that 5,000,000 hits are not enough to win.

In this case our gambler will be faced with the situation that his system is "working" but he is still going broke. Life isn’t fair.

That’s it for this week. Good luck! I’ll see you in line.