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Anzac Day's two-up controversy: Why heads and tails may not have equal chances

A maths professor did a study to work out whether tossing a coin really is a 50/50 chance.

Aussies are flocking to pubs and venues all across the country this Anzac Day to play the game that is only legal one day a year. Two-up is an annual tradition that sees two (sometimes three, depending on where you play) coins tossed in the air and everyone waits with bated breath to see if heads or tails wins.

Venues that host two-up will traditionally use Australian pennies along with a wooden kip that's used to launch the coins. Many like the game because it's seemingly random, with some people choosing to stick with one side for the whole day, while others will change with each round as they try to calculate a win based off probability.

But there is a small rule that could make one side win more than the other.

Coin toss for two-up next to insert of man with $5 above his head on Anzac Day.
Aussies around the country will be heading to pubs and venues to play two-up on Anzac Day. (Source: Getty)

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Stanford University Professor of mathematics and statistics (and former professional magician) Persi Diaconis wanted to see whether tossing a coin was really tied to a 50/50 chance.


He and his fellow researchers discovered the odds were actually closer to 51/49, and it tipped in favour of whichever side faced up when a coin was thrown into the air.

According to NSW Liquor & Gaming rules, a two-up spinner has to place the two pennies tails up on the kip.

However, in some games, the spinner has to place one coin heads up and the other tails up, which would mitigate that small bias.

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

The researchers declared 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 other factors that could impact the results of a coin flip, 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.

Two-up is only legal on April 25 every year and is meant to commemorate fallen soldiers by playing a game they played in trenches and on troopships.

The game varies very slightly depending on the venue, but NSW Liquor & Gaming states no one under the age of 18 is allowed to join in on the fun and the game is usually played in a large ring set up by the venue.

A spinner will be elected to toss the coins, which are placed on the wooden kip. The coins have to travel at least two metres into the air to be declared a proper throw.

If a coin rolls outside the ring, or touches a player or the roof, then that game is void and another toss is needed to declare a winner.

If the two coins land on head and tail, then that game is tied and the spinner will toss the coins again. Each round will continue until two heads or two tails are rolled inside the ring.

Some venues will allow you to bet on a head and tail winning. Other venues will insist on playing with three pennies so that a winner is declared each round.

People usually bet between $5 to $20 each round, but there are always a few eager punters who will offer up to $50 and $100 in some cases. They have to hold their money in the air and yell to players around them to see if someone has a similar bet.

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