That Coin Toss Isn’t Actually 50/50

October 25, 2023 by Donald Papp 19 Comments

A coin flip is considered by many to be the perfect 50/50 random event, even though — being an event subject to Newtonian physics — the results are in fact anything but random. But that’s okay, because what we really want when we flip a coin is an unpredictable but fair outcome. But what if that’s not actually what happens?

There’s new research claiming that coin tosses demonstrate a slight but measurable bias toward landing on the same side they started. At least, this is true of coin flips done in a particular (but common) way. Coins flipped with the thumb and caught in the hand land with the same side facing up 50.8 percent of the time.

The new research builds on earlier work proposing that because of human anatomy, when a human flips a coin with their thumb, the motion introduces a slight off-axis tilt that biases the results. Some people do it less (biasing the results less) and some do it more, but while the impact is small it is measurable. As long as the coin is caught in the hand, anyway. Allowing the coin to fall on surfaces introduces outside variables.

Therefore, one can gain a slight advantage in coin flips by looking at which side is facing up, and calling that same side. Remember that the flipping method used must be that of flipping the coin with the thumb, and catching it with the hand. The type of coin does not matter.

Does this mean a coin flip isn’t fair? Not really. Just allow the coin to fall on a surface instead of catching it in the hand, or simply conceal which side is “up” when the coin is called. It’s one more thing that invites us all to ask just how random is random, anyway?

Flipping A Coin 10,000 Times With A Dedicated Machine

July 21, 2020 by Lewin Day 32 Comments

Flipping a coin is often the initial example used to help teach probability and statistics to maths students. Often, there is talk of how, given a fair coin, the probability of landing heads or tails should approach 0.5. Of course, if you want to test this, it pays to have a machine do the hard work for you. [Andrew Consroe] has the rig to do just that.

The build consists largely of 3D printed parts. A large cylindrical shroud is used to keep the coin within the flipping area. A spring-loaded dowel is actuated by a stepper motor spinning a cam, which flips the coin. Once the coin has landed, it is photographed with a webcam. An image processing pipeline then determines whether the coin landed heads or tails. A black spot is used on one side of the coin to aid analysis, as the poor-quality webcam images weren’t good enough to recognise the coin in its standard form. Once the flip has been analysed, a sliding aperture is used to push the coin back towards the flipper for the next cycle.

The machine completes a flip approximately every two seconds, meaning 10,000 flips would take approximately 2.5 days. Unfortunately, due to noise and occasional coin escapes, [Andrew] hasn’t yet been able to achieve his goal. He aims to increase speed significantly before making an all-out attempt.

Coin flips can make for decent random numbers, but if you need better ones, perhaps NIST can help you out. Video after the break.

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