Everything You (Probably Never) Wanted To Know About Coin Flips

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Here’s a “didja know”: When a new state joins the union, a drawing of lots — or flip of the coin — determines which class the new senators will be in, with “class” basically meaning which year they are up for re-election. There’s three classes, and whichever two classes have the fewest senators are the classes in which the two new senators will join and …

And I’d say it’s even odds political betting markets will be legal in America by the time the 51st state is added to the union, and I’d put it at -10000 we will be betting on the coin flip to determine which senator from Puerto Rico or D.C. gets in class number one.

Yep, we’re silly like that, betting on random events like a coin flip, which, as of the time of this writing, is the most bet Super Bowl prop on DraftKings. Technically, “tails” has the most action, with “heads” coming in as the no. 2 most bet prop. And not only is it the most popular wager; tails and heads are also second and fourth in handle, respectively.

“It’s something to bet early, there it is, let’s bet it and see what happens,” said Johnny Avello, the director of DraftKings Sportsbook, trying to get into the minds of those who place the bet. “It’s one of those things. Sunday comes, I want my first bet on heads/tails, then I have another 25 props throughout the game to watch. Or maybe you want to bet the coin toss, put up $1,030 to win $1,000, you win your bet, you’re done for the day, see ya.”

History and science

Here’s what we know about the coin flip: The earliest we know for sure it was happening was in Roman times, when it was called navia aut caput (“ship or head”). From there, it’s gone on to big things, from deciding political races, to even bigger things, like determining who gets the ball first on Sundays. And it’s not just football: Cricket, tennis, Australian Rules football, and volleyball — among others — also use a coin toss.

It’s also used in French sword duels to determine who gets to parry with the sun at their back, which sure seems like a decided advantage.

And since we’ve already cured cancer and mapped the entire universe, some scientists have spent time trying to figure out just how random the seemingly random act of coin flipping actually is.

Results have been interesting.

A 2007 study conducted by Persi Diaconis, Susan Holmes, and Richard Montgomery at Stanford University found that a coin flip can, in fact, be rigged. In short: A coin will land the same way it started depending “on a single parameter, the angle between the normal to the coin and the angular momentum vector.” Basically, it’s physics, if you want it to be. Angle the coin just right, flip it at just the right angle, it will come up heads every time if it started on heads, tails every time if it started on tails. They built a machine to prove this. They referenced no fewer than 39 other scientific papers. Again, this is at Stanford.

So theoretically, a bent referee could, you know, theoretically — theoretically!!! — rig the toss.

Maybe we should be keeping stats on each ref’s coin toss results … 

You can handicap the ref that’s going to flip the coin, good luck,” Avello quipped.

The authors do note in the conclusion, however, that without this exacting tomfoolery, “for tossed coins, the classical assumptions of independence with probability 1/2 are pretty solid.”

Then there was the 2009 study by Matthew Clark and Brian D. Westerberg and published in the Canadian Medical Association Journal that looked at the Diaconis study and basically tried to duplicate the results, but without a machine doing the flipping. And guess what? They kinda did duplicate it. They had 13 people toss a coin 300 times, and they told the coin-tossers to try and have the coin come up heads each time. And guess what? All 13 managed to get heads more than tails, seven of them in a statistically significant manner.

A most popular wager

“We’ve been taking bets on this for, gosh, probably 20 years now,” Avello said. “We were doing it in Vegas for a while, and then we were told to stop by the gaming board, and we did, but then we started up again maybe two or three years later.”

Avello thinks one of the reasons for the popularity of the bets is because most sportsbooks offer “good” odds on the wager.

“The great part about it is you’re only laying $1.03 juice on either side, whereas under normal circumstances you’re laying -110,” he noted.

DraftKings, of course, isn’t alone in offering better-than-average odds. PointsBet is also coming in at -103.

The interest on the coin toss prop is not surprising, as it’s always been a popular prop bet,” said Patrick Eichner, the director of communications for PointsBet. “Even if you don’t know anything about the game, you can pick the result of a coin toss, which appeals to bettors who may want to have an interest in the Super Bowl but don’t follow the NFL at all.”

So far, the biggest wager PointsBet has taken on this year’s toss is a $2,500 bet on heads.

Avello has seen bigger.

“I’ve taken some big bets,” he said. “I’ve taken $10,000 on it, so there are guys who will bet this for a decent amount.”

The most +EV bet ever?

Of course, there’s more than just the coin toss itself. For instance, over at BetMGM, you can bet what will the call be for the toss (right now, 77% of the action at BetMGM is whoever calls it will call “heads”), which team will win the toss, and whether the coin toss winner will choose to receive the kickoff or defer to the second half.

One bet missing, however, is whether the coin will land on its side.

That’s right, its side. You know. The edge.

A 1993 study published in the Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics) — that’s Volume 48, Issue 4, October 1993, pp. 2547-2552 for those scoring at home — found a tossed nickel has a one-in-6,000 chance of landing on its side.

Science!

Anyway, 6,000/1. 

This study had not yet been found by the author of this article when Avello was asked about a “coin landing on its edge” prop.

“It’s never happened before, and then I know it won’t happen,” he said. “Well, probably never happen. I’d say 1 in 100,000, but I’d probably go higher than that.”

Well, that’s 100,000/1, compared to that science-y nickel at 6,000/1.

Now there’s a +EV bet if there ever was one. Law of averages and all you may have to wait until Super Bowl MMMDCCXXIV to cash the ticket, but still: +EV.



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