Coin flips don’t appear to have 50/50 odds after all

Will Shanklin

Conventional wisdom about coin flips may have been turned on its head. A global team of researchers investigating the statistical and physical nuances of coin tosses worldwide concluded (via Phys.org) that a coin is 50.8% likely to land on the same side it started on, altering one of society’s most traditional assumptions about random decision-making that dates back at least to the Roman Empire.

The team appeared to validate a smaller-scale 2007 study by Stanford mathematician Persi Diaconis, which suggested a slight bias (about 51 percent) toward the side it started on. The authors of the new paper conducted 350,757 flips, using different coins from 46 global currencies to eliminate a heads-tail bias between coin designs. (They also used a variety of people to rule out individuals with biased flipping techniques corrupting the results.) Regardless of the coin type, the same-side outcome could be predicted at 0.508, which rounds up perfectly to Diaconis’ “about 51 percent” prediction from 16 years ago.

The researchers found no evidence of a heads-tail bias when excluding its starting position from the data. In other words, if you pay no attention to which side the coin is on pre-flip, the odds of the outcome are equally likely to be heads or tails.

PHI02:SPORT-NFL:PHILADELPHIA,PENNSYLVANIA,3DEC98 - NFL referee Bernie Kukar (C) flips the coin at the start of the December 3 NFL game between the Philadelphia Eagles and the St. Louis Rams. The NFL instituted new rules for the coin toss following a controversial call in the November 26 game between the Detroit Lions and the Pittsburgh Steelers. Back judge Bill Leavy looks on from behind, as Eagles fan Mike Jenelli (34) looks on.

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Reuters Photographer / reuters

Coin flippers in the study selected their starting position randomly (or according to an algorithm), flipped the coin, caught it in their hand and recorded the landing position. (If they flipped it over in their palm before revealing it, the opposite side it started on had 50.8% odds.) All participants videotaped and uploaded recordings of their flips to simplify collection and coding errors. “Our data therefore provide strong evidence that when some (but not all) people flip a fair coin, it tends to land on the same side it started,” the authors wrote.

The paper notes there was a high degree of variability between coin flippers. “Some people appear to have little or no same-side bias, whereas others do display a same-side bias, albeit to a varying degree.” But taken on the whole, it leads to those 50.8% odds favoring the starting side.

The findings could even lead to (slight) financial gains. The researchers say that if you bet $1 on 1,000 separate coin flips, always betting on the side it starts on (and catching the coin rather than letting it roll on a surface or flipping it over in your palm), you’d make a $19 profit. The authors note that this is better odds than a casino’s built-in advantage for six-deck blackjack against a high-level player. They suggest that anyone making a high-stakes decision based on a coin flip would be wise to conceal its starting position.

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