Why two-up may not be as random as it seems

If you’re planning on playing two-up this ANZAC Day you might want to sway towards picking tails over heads.

While the classic coin-flip game might seem like a 50/50 shot, studies in the US have found that the head side of a coin is slightly heavier, thanks to the symbol being larger.

On the assumption that this also rings true for classic Australian pennies (which two-up games typically use), then heads are more likely to land face-down, with tails coming out as the winner.

• Also read: ANZAC Day public holiday: Will you get penalty rates?

• Also read: Anzac Day trading hours: Woolworths, Coles, Kmart, Bunnings and more

• Also read: Push for two extra public holidays: ‘A no-brainer’

Stanford University Professor of mathematics and statistics (and former professional magician) Persi Diaconis found that, even with regular coins, the chances were not as even as one might think.

Diaconis and his fellow researchers discovered the odds were closer to 51/49, in favour of whichever side faces up when a coin is thrown into the air.

“I don't care how vigorously you throw it, you can't toss a coin fairly," Diaconis said.

Their experiment found that the bias is rather small though, saying it would take around 10,000 coin tosses before a casual observer would notice that the side of the coin facing up before it was thrown was often the side that won the toss.

There are actually other factors that could impact the results, including how dirty the coins are. If more dirt or grime had built up on one side of a coin than the other, it would also land that side down slightly more often.

Why do we use Australian pennies?

Two-up, while illegal every other day of the year, was introduced by settlers who were looking to make a fortune in the Australian gold rush in the 1800s.

“When two-up reached the Australian shores, the game became a popular pastime on the goldfields of Kalgoorlie and Broken Hill and continued its run of success throughout the early 1900s as well,” the Royal Australian Mint said.

“In World War I, Australian and New Zealand soldiers played the game in trenches and on troopships, thus leading to the strong association with Anzac Day.”

The tradition of using two Australian pennies - as well as using a wooden kip to toss the coins - has stuck from when the game was originally introduced.

Follow Yahoo Finance on Facebook, LinkedIn, Instagram and Twitter, and subscribe to our free daily newsletter.