This is an easy experiment that anyone with a computer can do. It takes 2-4 hours to complete. The basic premise is to revisit the work of Joseph Banks Rhine, the famous ESP researcher, and observe the very first example of what he called “the decline effect”.

You will need a spreadsheet program. The example provided here was created using Excel 2010, but earlier versions of Excel, or OpenOffice, or other products, will all work too.

Rhine tested thousands of subjects for psychic abilities using a ‘Zener deck,’ which is a specially designed deck containing 25 cards divided evenly among five symbols — a circle, a square, a star, a cross, and some wavy lines. A typical ESP experiment would have the subject trying to guess which symbol came up next in the deck. In some cases the card would remain face-down so that neither the subject nor the experimenter could see it before the guess. This way of doing the experiment was meant to test for two specific ‘psychic powers’: precognition or clairvoyance. One is the ability to see the future, that is, to know what the card will look like once it is turned up. The second is the ability to ’see’ the card face without turning it up. Obviously it is a little difficult even in principle to disentangle these two phenomena.

Another variant had the experimenter privately examine each card before asking the subject to guess, creating the possibility that the subject could read his mind and find the information that way instead. This creates a risk that the experimenter might give away information through body language. Rhine was criticized for poor experimental controls, but in fact even when the experimenter had no knowledge of what card was coming, the results were about the same.

Rhine’s subjects did about equally well regardless of which protocol was used. Whether they were clairvoyant, or psychic, or precognitive, was never entirely clear. They were able to guess the next card at rates well above chance — but only for a while. After a few hundred trials, typically the hit rate would decline, and the subject would be less and less successful. After a few thousand trials the subject might actually lapse into what Rhine called ‘psi-missing’, or success in guessing that was below the purely random rate of 1 in 5.

This type of experiment has been run by hundreds of investigators over the past 75 years, always with this same result. As recently as 2004, Jonathan Schooler tested 2,000 university students for psychic abilities using a variant of this method, and once again got ‘phenomenal’ psychic scores that invariably declined to nothing after a while.

Our premise is straightforward, and derived from the work of George Spencer-Brown in his 1957 book *Probability and Scientific Inference*. ESP does not actually exist. Instead, our ideas about probability are subtly wrong. We expect each trial to be independent of the last. We expect the odds of a successful guess to be 1 in 5 regardless of whether we run 10, 100, or 1,000 trials. What actually happens is that there is a small surplus of successful guesses at the start, followed by a slightly more substantial shortage of successes. Only after several thousand trials will the score recover and converge on the equilibrium rate of 1 in 5.

We can test for this decline by taking human beings ‘out of the loop,’ shuffling the Zener deck, and looking to see how often two adjacent cards match. We count this as a successful ‘guess’ in the same way that a human saying ’star’ would be whenever a star symbol came up. Obviously there is no ESP involved as the computer doing the shuffling has no ‘psyche’.

There are 25 cards, making 24 adjacent pairings. Any given card has 4 matches in the deck, for odds of 1 in 6. Overall, for each shuffle of the deck, we should see an average of four adjacent pairs.

The reader should now examine the example spreadsheet titled:

The deck is simulated by the numbers 1 through 5, each repeated 5 times in a column of the spreadsheet. Shuffling is simulated by assigning the RAND() variable to a cell adjacent to each simulated card, and sorting the cards according to the current values of RAND(). After each shuffle, an IF statement in a third column tests for whether two adjacent cards match, scoring a match as 1 and a non-match as 0. A SUM statement adds up all the hits, so we know what number to record.

To do this experiment, do NOT copy and paste the example. Open a blank spreadsheet in your chosen application, and using the formulas provided as a guide, construct your own deck to be randomized from scratch. Reshuffle the virtual deck at least 500 times. For best results, 1,000 trials are better. You should get results like those in the graph below:

The surplus tends to be brief, and small. Here it peaks at about 10 hits more than expected, after 150 trials. The shortage is deeper and longer-lasting. Here, after 500 trials, there are 1934 pairs, or a shortage of 66. This is about 1.5 standard deviations below mean expectation. It isn’t phenomenally unlikely. What is phenomenally unlikely is that the pattern looks like this nearly every time the experiment is done.