Am I Being Random?
We’re going to be talking about patterns.
Look at the following three sequences of playing cards.
| Sequence 1 | Sequence 2 | Sequence 3 |
| 7 ♣ | J♠ | 8♠ |
| 10♡ | K♣ | A♡ |
| K♠ | 5♣ | A♢ |
| 3♢ | 2♡ | 7♡ |
| 6♣ | 9♠ | 3♣ |
| 9♡ | A♠ | 7♣ |
| Q♠ | 3♡ | 9♣ |
| 2♢ | 6♣ | 2♡ |
| 5♣ | 8♢ | Q♠ |
| … | … | … |
What can you tell us about each of the three columns? Start with the one on the left.
A few seconds spent looking at the first column and you will notice a black-white-black-white pattern repeating. On closer inspection you might see Club-Heart-Spade-Diamond repeated. Finally, if you are really paying attention, you’d see that the numbers increase by three each time: 7 to 10 to 13 (King) to 3 to 6 to 9 etc. We have here a simple pattern, and it gives us a stacked deck.
Stacked decks are very useful to the magician in many circumstances. For example, suppose you are asked to pick a card and the magician peaks at the one next to it then he immediately knows which is yours. Or if you take one out and put it back elsewhere he will know which is the one out of sequence, and that’s the one you picked. Those are two easy, beginner, tricks. More sophisticated effects use the fact that the magician knows the position of each card in the deck.
The particular stack in the first column goes by the name “Si Stebbins,” the stage name of William Coffrin. Although there is a pretty clear pattern here — the suit order is easily remembered by the mnemonic CHaSeD — believe us when we say that with suitable distractions the layperson is unlikely to spot this when the magician briefly waves the deck in front of them. But sometimes the magician needs a stack that can stand up to closer scrutiny…
The second column is also part of a stacked deck, this time the Aronson stack, invented by magician, mentalist and lawyer, Simon Aronson. The stack is designed to look random but also once you’ve memorized this stack there are many tricks that work simply because of the clever order of the cards.
The third column is genuinely random, in the sense that we shuffled a deck and wrote down the first nine cards.
Being able to see patterns is important.
However humans also tend to see patterns even when there’s no pattern to be seen. The tendency to see patterns in random data is known as apophenia. We see shapes of animals in clouds. Or images of Jesus in a slice of toast. In finance the technical analysts promote the idea of trendlines and patterns in stock-market graphs, even though the proper statistics tell us that such lines and patterns have no predictive power. In extreme cases apophenia can be an indicator of delusional thinking or schizophrenia.
The magician knows about apophenia and so his goal with a stacked deck is to have it look random to the casual observer (or even to someone who “burns” the cards, i.e. stares intently at them). But there’s a big difference between being random and looking random, given the human urge to see patterns.
Let’s move on from cards to coins, and look at another sequence. Toss a coin many times, write down “H” when it lands Heads up, and “T” if Tails up. Here’s an example:
HTTTTHTTTTHHTHHH…
That’s a nice random sequence, no?
No! One H, four Ts, one H, four Ts, two Hs, one T, three Hs,… = 1.414213… The first digits in the square root of two.
How about this one:
THTTTTTTH…
You must be onto us by now. That’s a lot of Ts in a row, must be the part of some pattern. No! We generated that in Excel using one of its random number generators and it was literally the first sequence we did. We see patterns when there aren’t any and miss patterns when there are.
Exercise: Try writing down a sequence of Hs and Ts and try to make it look random. You’ll probably be reluctant to put down six Hs or Ts in a row. It just wouldn’t look sufficiently random.