Red or Black?

Congratulations – you’ve got a new job! OK, so the pay isn’t great, but it’s not without its glamour. Your job is to inspect roulette machines in casinos, arcades and betting shops to check that they are fair.

Your boss gives you a reminder of the basics of the game: customers place bets on whether a ball spun around the roulette wheel will come to rest in a red or a black pocket (and/or on particular numbers). Provided they are well maintained, traditional wooden roulette wheels are always completely fair. Computerised electronic roulette machines, however, are a different story: There’s always the risk that some enterprising hacker could have tampered with the software …

This is where you come in. You have received a report of a casino where some of the electronic machines are showing suspicious behaviour. You choose four machines, have twenty ‘spins’ on each and note down the results. Two look fine, but two give you cause for concern. Which two machines should you investigate further?


Machine B and Machine D look suspicious, don’t they? Machine B has a streak of six blacks in a row, and ends with a string of eight reds, split up only by a single black, right in the middle. Machine D has a streak of five reds, and two streaks of four blacks. It’s almost as if the machine has been programmed to lull gamers into a false sense of security, then wham! Just when you were expecting black … it’s red!

Machine A and C look much more honest, don’t they? A good, healthy mix of reds and blacks, with no suspicious streaky behaviour.

So, if you said that you should investigate Machines B and D …

Photo credit: Conor Ogle (Wikimedia Commons)


… you’re completely wrong.

B and D were actually generated at random. A and C are lists that I put together by hand, to have the appearance of randomness.

Why do most people get this wrong? The answer is that the human brain seems to be hard-wired to look for predictable patterns: so much so that it spots them even when there are none. Genuinely random patterns look ‘streaky’. Unless there is anything to stop it, a random sequence will generally have a couple of streaks somewhere, just by chance. After all, a roulette wheel has no memory. So the fact that black has come up on the last three spins has no bearing on the likelihood of the next spin also coming up black. The lists that look random, but are not, were deliberately created to avoid having more than two reds or blacks on adjacent spins. While this is what makes them look random, it is actually the giveaway sign that they are not: it’s pretty unlikely that no streak of three or greater should appear somewhere, in a sequence of genuinely random spins.

The method that people use for guessing which machines look random is a particular type of heuristic. Heuristics are the mental short-cuts that we use to make judgements when we don’t have all the necessary information (or when we do, but don’t know how to use it). For example, if we have to guess which of two people is a librarian given only their physical appearance, we are more likely to choose the one wearing glasses. Here, we are using a representativeness heuristic. The person with glasses is more representative of our mental picture of a librarian. The same heuristic is what leads us to the wrong answer in the roulette machine problem. A string such as Red, Black, Black, Red, Black is a better match for our mental picture of what a random pattern looks like than Red, Red, Red, Red, Red, even though it is no more likely.

The same misconception turns up all over the place. For example, basketball fans and commentators often talk about players having a ‘hot hand’ streak where they just can’t miss. Actually, when a group of psychologists analysed the performance of several teams they found that – exactly as for the roulette wheel – apparent streaks were just a consequence of random variation in performance.

Interestingly, some people have claimed – though Apple have always denied – that the iPod/iPhone shuffle mode is not, in fact, completely random. The conspiracy-theory version of this claim (which I am by no means advocating) holds that Apple deliberately over-play popular songs in the hope that others will overhear, and subsequently purchase them. The research discussed here suggests a more interesting possibility: hypothetically a manufacturer of music players might avoid true randomness because, paradoxically, purchasers would complain – when a few songs by the same band inevitably came on one after another – that the playlist wasn’t random enough.

Finally, buses. You know when you wait half an hour for a bus and then three come along at once? Knowing what you now know, you might assume that this is just another illusion, and that a ‘streak’ of busses is actually no more common than you’d expect by chance alone. Actually, no; buses really do come in streaks. The reason is that, when a bus gets to a really busy stop, it has to wait ages for everyone to get on, giving the bus behind it a long time to catch up. The only solution is for buses to leave the stop after a predetermined boarding period, even if people are still trying to get on. Unsurprisingly, few bus companies have ever attempted this solution, presumably fearing that it would enrage customers.

So next time you’re waiting for a bus, why not pass the time by trying to spot examples of apparent ‘streaks’ caused by random behaviour? What about the queue itself: are there streaks of gender, hair colour, shoe type? If you look hard enough, you’re sure to find at least one.

You can complete more tests of your pattern-spotting and powers of deduction, as well as tests of your intelligence, personality, moral values, thinking style, impulsivity, capacity for logical reasoning, susceptibility to visual and mental illusions, musical taste and preferences in a romantic partner in Ben Ambridge’s forthcoming book: Psy-Q

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