Heads or Tails

Experimental and theoretical analysis of coin tossing has shown that the outcome is predictable, to some degree at least, if the initial conditions of the toss (position, velocity and angular momentum) are known. Coin tossing may be modeled as a problem in Lagrangian mechanics. The important aspects are the tumbling motion of the coin, the precession (wobbling) of its axis, and whether the coin bounces at the end of its trajectory.

The outcome of coin flipping has been studied by Persi Diaconis and his collaborators. They have demonstrated that a mechanical coin flipper which imparts the same initial conditions for every toss has a highly predictable outcome — the phase space is fairly regular.

Moreover, they have demonstrated both mathematically and experimentally that the underlying physics of coin tosses appears to have a slight bias for a caught coin to be caught the same way up as it was thrown, with a probability of around 0.51. Stage magicians and gamblers, with practice, are able to greatly increase this bias, whilst still making throws which are visually indistinguishable from normal throws.

Since the images on the two sides of actual coins are made of raised metal, the toss is likely to slightly favor one face or the other. This is particularly true if the coin is allowed to roll on one edge upon landing; coin spinning is much more likely to be biased than flipping, and conjurers trim the edges of coins so that when spun they usually land on a particular face.

Although it is extremely rare, it is possible that a coin will come to rest on its edge (estimated at roughly 1/6000 for a U.S. nickel).

After looking at the this year's coin, it looks like the head side of the coin may weigh a bit more.  Also, with the coin always being flipped with the heads side up this will also favor those going for heads.

So my bet for the coin flip this year is:

Heads   1000 to win 952.

The coin itself will be coming from Florida. A company call Highland Mint, which is based in Melbourne, Florida has been charged with making the coin. After the coin flip takes place the coin will head to the Pro Football Hall of Fame. Because the coin will be minted in Florida, and Florida is considerably more humid than Arizona, you will have to factor in the different air densities and the coordinating differences in friction into your coin flip decision-making process. And no, I 'm not serious.

We haven't yet heard who will actually toss the coin, though there is a decent chance that it will be a quarterback. Four times in the last six years a quarterback has made the toss - Roger Staubach, Y.A. Tittle, Tom Brady and Dan Marino. Brady obviously won't be tossing it this year, but his presence is a very good sign for the NFC representative. The Seahawks won the toss when Brady was the flipper, and the Patriots have lost the toss every time Brady has been in the Super Bowl. On that basis alone you might want to take an extra look at the Giants. The Giants are riding a hot streak - they won the toss last time they made the big game.

The coin flip alone has four props, the most popular of which is "heads or tails." Krackman bets tails every year. "Traditionally, the 'head' on the commemorative coins used by officials has been puffed up," he says. Which, Krackman reasons, makes the coin ever-so-slightly top-heavy. "If you flip those coins 100 times, you'll see they come up tails a little more often." About 55 percent of the time, when he tried it.