Fake or flip
Can you tell a real coin from a fake?
Each pair shows 32 tosses. One strip is a real coin. The other was made up to look like one. Tap the strip you think is real. After five pairs, a map of bombs.
Why the real coin looked fake
A real coin changes from heads to tails about half the time. People who fake a coin change it more often, about 6 times in 10, because a run of five heads feels wrong to them. Ruma Falk and Clifford Konold found this pull in study after study. So the fake strips here switch 6 times in 10, and the real ones switch 5 in 10.
That small gap makes a big difference to the streaks. In 32 real tosses, about 2 strips in 3 hold a run of 5 or more of the same side. The faked strips get there about 1 time in 3. The long streak was the clue, and it was the clue that looked least random.
The bomb map is a real story. In 1944, German flying bombs fell on London, and people were sure they fell in clusters, as if some streets were targets. After the war, R. D. Clarke, an actuary, cut 144 square kilometres of south London into 576 equal squares and counted the 537 hits. The counts matched pure chance almost exactly: 229 empty squares against 227 expected, and 7 squares with four hits against 7 expected. The clusters were what chance does on its own. The map in this game was made by a random number generator, and it clusters the same way.
The same game in a trading room
Bill Miller ran the Legg Mason Value Trust fund, and it beat the S&P 500 every year for 15 years, from 1991 to 2005. One estimate put the odds of that at 372,521 to 1. That number answers the wrong question. It asks about one fund chosen in advance. Leonard Mlodinow asked the right one: with thousands of funds running over 40 years, how likely is it that somebody, somewhere, gets a 15-year streak? His answer was about 3 in 4.
Streaks of winners, hot sectors and fund managers who seem to call every turn are coin strips with a story on top. A long run among thousands of runners is what chance gives. Clusters of winning trades in one month are bombs on south London.
Before you read a cause into a streak, ask: across everyone who was trying, how often would chance alone make one like it?
Sources
- R. D. Clarke, "An application of the Poisson distribution", Journal of the Institute of Actuaries 72 (1946), 481.
- Ruma Falk and Clifford Konold, "Making sense of randomness: implicit encoding as a basis for judgment", Psychological Review 104 (1997), 301–318.
- Leonard Mlodinow, The Drunkard's Walk: How Randomness Rules Our Lives (2008).