10 . Heads or Tails?

Careful: It’s not 50-50

The phrase “coin toss” is a classic synonym for randomness. But since the 18th century, mathematicians have _________ that even fair coins tend to land on one side slightly more often than the other. Proving this tiny bias, _________, would require hundreds of thousands of carefully recorded coin flips, making laboratory tests a logistical (后勤的，组织协调的) _________.

František Bartoš, currently a Ph.D. candidate studying the research methods of psychology at the University of Amsterdam, became interested in this _________ four years ago. He couldn’t _________ enough volunteers to investigate it at first. But after he began his Ph.D. studies, he tried again, recruiting 47 volunteers from six countries. Multiple weekends of coin flipping later, including one 12-hour marathon _________, the team performed 350,757 tosses, breaking the previous record of 40,000.

With one side initially upward, the flipped coin landed with the same side facing _________ as before the toss 50.8 percent of the time. The large number of throws allows _________ to conclude that the nearly 1 percent bias isn’t a fluke (侥幸). “We can be quite sure there is a bias in coin flips after this data set,” Bartoš says.

The leading theory explaining the _________ advantage comes from a 2007 physics study by Stanford University statisticians, whose calculations predicted a same-side bias of 51 percent. From the moment a coin is launched into the air, its entire track — including whether it lands on heads or tails — can be calculated by the laws of __________. The researchers determined that airborne coins don’t turn around their symmetrical axis (对称轴); __________, they tend to move off-center, which causes them to spend a little more time high in the air with their initial “up” side on top.

For day-to-day decisions, coin tosses are as good as random because a 1 percent bias isn’t __________ with just a few coin flips, says statistician Ameli, who wasn’t involved in the new research. Still, the study’s conclusions should eliminate any lasting doubt regarding the coin flip’s slight bias. “This is great experiment-based evidence __________ the bias,” she says.

It isn’t difficult to prevent this bias from influencing your coin-toss matches; simply __________ the coin’s starting position before flipping it should do the trick. But if your friends are __________ the tiny bias, you may as well benefit from your slight advantage. After all, 51 percent odds beat a casino’s house advantage. “If you asked me to bet on a coin,” Bartoš says, “why wouldn’t I give myself a 1 percent bias?”