Coin flips don't always have 50/50 odds, study confirms

[Shawn Knight]

The big picture: Coin tosses have been used for centuries as a fair and unbiased way of deciding between two options, and some important decisions have been based on the flip of a coin. The game of chance was used to determine which of the Wright brothers would attempt powered flight first in 1903, and it 1959, a coin toss decided who would get the last seat on Buddy Holly's ill-fated plane.

Assuming fairness across the board, there's a 50 / 50 chance of the flipped coin landing on heads or tails, right? Well, it is not that straightforward.

Researchers from across Europe recently conducted a study involving 350,757 coin flips using 48 people and 46 different coins of varying denominations from around the world to weed out any physical design bias. The team found that more often than not (50.8 percent of the time), a coin landed on the same side it started.

Data revealed a considerable between-people variation in the degree of same-side bias. When the initial side-up is randomly determined, however, the coin was indeed equally as likely to land on heads or tails.

The study validates a previous model of human coin tossing developed by Diaconis, Holmes, and Montgomery (DHM) from 2007. According to the DHM model, the coin has a higher chance of landing on the same side it started because it spends more time in the air with the initial side facing up.

The same-side bias probably won't have much of an impact on impromptu coin flips but in certain scenarios, it could factor into the outcome in a meaningful way. In a betting scenario where you bet one dollar on the outcome of a coin toss in which you know the coin's starting position, and repeated the bet 1,000 times, you would earn $19 on average.

The next time you find yourself in a coin-flip situation and want to make it as fair as possible, be sure that the starting position of the coin is concealed from all participants.

Image credit: Coca Kola Lips, Andy Henderson

Permalink to story.

https://www.techspot.com/news/100485-coin-flips-dont-always-have-5050-odds-study.html

 

[waclark]

I'm not buying it. This is a bit of pseudo-science in my opinion. First 350K tosses, while sounding like a lot, really isn't when compared to infinite tosses. Second, not all tosses were equal. If different people using different coins did the tossing, then the results are biased based on the way that person tosses the coin and the type of coin used. In reality, if the coins are all the same and not biased to land on one side (weighted for example) and tossed exactly the same way every time, then there is an equal chance of heads or tails. That doesn't mean you can't have a run of heads or tails over a set of tosses. It just means there is equal chance, not necessarily equal outcome.

 

[Prrredictable]

Hm. What about if you flip the coin a foot into the air with precision versus 10 feet or 20 feet into the air each time?

 

[BakaRed77]

This is tech news?

 

[godrilla]

I'm not buying it. This is a bit of pseudo-science in my opinion. First 350K tosses, while sounding like a lot, really isn't when compared to infinite tosses. Second, not all tosses were equal. If different people using different coins did the tossing, then the results are biased based on the way that person tosses the coin and the type of coin used. In reality, if the coins are all the same and not biased to land on one side (weighted for example) and tossed exactly the same way every time, then there is an equal chance of heads or tails. That doesn't mean you can't have a run of heads or tails over a set of tosses. It just means there is equal chance, not necessarily equal outcome.

I wonder if the more you get to Infinity the closer you get to 50%.

 

[Prrredictable]

I wonder if the more you get to Infinity the closer you get to 50%.

We should have an International Coin Flipping Institute with a soul purpose of flipping a single coin incessantly for all time to see the variations in the percentages. It may even be possible to notice significant changes based on the position of the poles as the Earth navigates its orbit. I'm sold. I volunteer for the first 10 years.

 

[Lew Zealand]

I'm not buying it. This is a bit of pseudo-science in my opinion. First 350K tosses, while sounding like a lot, really isn't when compared to infinite tosses. Second, not all tosses were equal. If different people using different coins did the tossing, then the results are biased based on the way that person tosses the coin and the type of coin used.

That was their point. Coin tosses were not equal as different people will toss differently, and overall they were slightly biased to the upside face of the coin when tossed. Infinite tosses is irrelevant as that doesn't exist, instead they're looking for real life biases with the variations of how people do the toss.

In reality, if the coins are all the same and not biased to land on one side (weighted for example) and tossed exactly the same way every time, then there is an equal chance of heads or tails.

If tossed exactly the same way, they would land exactly the same way each time, so 100% heads or 100% tails. Obviously this will never happen in reality but that's a pitfall of logical explanations instead of doing the real world tests.

That doesn't mean you can't have a run of heads or tails over a set of tosses. It just means there is equal chance, not necessarily equal outcome.

100%, there will eventually be a trend towards the real numbers and the argument from the 350K tests is that a slight same-side bias is this trend in coin flips.

Until someone wastes their time repeating generates better data, their observation and arguments seem reasonable.

 

[p51d007]

I GUARANTEE you that if you drop a slice of bread, that has peanut butter, jelly or butter on it, it WILL 100% of the time, fall with the jelly, peanut butter or butter side down.
And, if you have a dog, they will get to it before you do.

 

[Prrredictable]

I GUARANTEE you that if you drop a slice of bread, that has peanut butter, jelly or butter on it, it WILL 100% of the time, fall with the jelly, peanut butter or butter side down.
And, if you have a dog, they will get to it before you do.

Source?

 

[waclark]

That was their point. Coin tosses were not equal as different people will toss differently, and overall they were slightly biased to the upside face of the coin when tossed. Infinite tosses is irrelevant as that doesn't exist, instead they're looking for real life biases with the variations of how people do the toss.



If tossed exactly the same way, they would land exactly the same way each time, so 100% heads or 100% tails. Obviously this will never happen in reality but that's a pitfall of logical explanations instead of doing the real world tests.



100%, there will eventually be a trend towards the real numbers and the argument from the 350K tests is that a slight same-side bias is this trend in coin flips.

Until someone wastes their time repeating generates better data, their observation and arguments seem reasonable.

I think my point is that another 350K tosses could result in a completely different outcome. Therefore, a coin has an equal "chance" to land heads or tails but may or may not do so depending on a ton of factors. Humans cannot possibly be 100% consistent on every toss and even if you had a machine do the toss, so you could control it, the outcome will vary unless you can control every aspect including the environment. But there is the random factor of what surface it lands on. A grassy or carpeted surface will have less bounce whereas a hard surface my cause the coin to bounce up, flip around, roll around and more.

 

[Prrredictable]

I think my point is that another 350K tosses could result in a completely different outcome. Therefore, a coin has an equal "chance" to land heads or tails but may or may not do so depending on a ton of factors. Humans cannot possibly be 100% consistent on every toss and even if you had a machine do the toss, so you could control it, the outcome will vary unless you can control every aspect including the environment. But there is the random factor of what surface it lands on. A grassy or carpeted surface will have less bounce whereas a hard surface my cause the coin to bounce up, flip around, roll around and more.

Well, sure. Any act repeated could have a different outcome. This study is determining a probability of the outcome.

 

[waclark]

We should have an International Coin Flipping Institute with a soul purpose of flipping a single coin incessantly for all time to see the variations in the percentages. It may even be possible to notice significant changes based on the position of the poles as the Earth navigates its orbit. I'm sold. I volunteer for the first 10 years.

Let's apply for a government grant. We will sell the idea based on football coin toss outcomes and the potential unfair advantage one might have if the coin doesn't have an equal chance of heads or tails. We will extend the grant so we can develop an absolutely fair tossing-coin. Billions of dollars are at stake here!

 

[wiyosaya]

The only thing that is truly random may be a device based on atomic decay, although, Carl Sagan, supposedly, thought it was worth investigating that people can influence such a device, too.

 

[Kam7r]

This is the kind of studies who make humanity go further

 

[kiwigraeme]

I think my point is that another 350K tosses could result in a completely different outcome. Therefore, a coin has an equal "chance" to land heads or tails but may or may not do so depending on a ton of factors. Humans cannot possibly be 100% consistent on every toss and even if you had a machine do the toss, so you could control it, the outcome will vary unless you can control every aspect including the environment. But there is the random factor of what surface it lands on. A grassy or carpeted surface will have less bounce whereas a hard surface my cause the coin to bounce up, flip around, roll around and more.

Did you click the link and read the study - many voting polls may have n= 1000 with a reasonable certainty of say %3 = here N= 350 0000 from study "A preregistered Bayesian informed binomial hypothesis test2
indicates extreme evidence in favor of the same-side bias
predicted by the D-H-M model, BFsame-side bias = 1.71 × 10 power of 17"

I don't like your odds

 

[kiwigraeme]

Three things to do if your favor

"heads I win tails you lose"
I have use that twice in stressful real life situations - where you know other person is not concentrating right
One doing a drive-away: a Pontiac Firebird - a taxi driver must have fell asleep - ran the light and crashed into the side of us Dupont Circle - Washington DC - who phones the owner

2nd one telling some guy he can't join our apartment again next year ( Uni break ) by phone call


Second - toss it and catch it covered on back of hand - heads side normally smooth - then either lift top hand or palm in top hand and turn that hand over to show - easier than a mexican card turnover - which is quite easy

Third - practice the throw and catch and you will increase it dramatically - ie consistent spin and height

do it properly - flip high - call in air - let it land on ground

 

[RudyBob]

It's 50-50 HAR HAR

 

[amghwk]

Why waste time doing a research like this? Some people have too much time.

You don't need to do research on the obvious.

If thinking logically, a coin with two sides will either fall on one side or the other.

Even if a strong wind blows, the chance of it landing on the same side again is still 50-50.

Unless the coin has more engravings, and subsequently, more weight on one side, then that might influence the fall to one of the same sides again and again.

 

[raydpratt007]

There was an news item within the last year or so where someone researched the results of dice throws (without efforts at "dice control"), and the conclusion was that the numbers initially on top of the dice were more likely to show up as the final numbers than other numbers. (As a practicing "dice setter" in the casino game of Craps, I was annoyed that the researcher did not look into the results of dice control methods.) So, the study about coin tosses in the above article was similar in concluding the the side of the coin first up when flipped has an edge in showing up as the final side. I looked for that study about dice and did not find it through Google, but I found another research paper that did consider dice control methods and concluded that the dice randomize after the first hit on the table even if they first hit with controlled synchronization. (see, https://digitalscholarship.unlv.edu/grrj/vol24/iss1/1/ and download for free.) Anyone who spins sticks or or other balanced straight objects in the air and catches them knows that leaving your hand where it was was when the object left will catch the object at the same angle it left (horizontally). Thus, coin tossing can be subject to the same physics and can probably be improved with practice. Dice setting? The study is sobering, but I still have ideas about improving my skill (if any).

 

[MaestroIT]

Clickbait title for article and study:
One opens to read, thinking it is like 20-80% or 40-60%, when it is just less than 1% off (50.8/49.2).

not a difference

 

[waclark]

Well, sure. Any act repeated could have a different outcome. This study is determining a probability of the outcome.

To me the study is only documenting the outcome for 350K tosses. What if the next 350 come out completely differently? How does that impact the study and it's conclusions? And of course, what if it were different people tossing the coin. Can we guarantee that the outcome would be exactly the same?

The point is, a coin can land one of two ways (excluding it landing on its edge). For any toss, there is the possibility that it can land heads or tails. There are no other options. How many tosses do you need to prove this concept? 10, 20, 350K, 1,000,000?

 

[waclark]

Did you click the link and read the study - many voting polls may have n= 1000 with a reasonable certainty of say %3 = here N= 350 0000 from study "A preregistered Bayesian informed binomial hypothesis test2
indicates extreme evidence in favor of the same-side bias
predicted by the D-H-M model, BFsame-side bias = 1.71 × 10 power of 17"

I don't like your odds

If by voting polls you mean surveys of people on how they will vote, this is entirely different. The odds are always the same. See my comment above, Any toss can result in heads or tails. That is it. So therefore, there is a 50/50 chance. Just because there was a bias in 350K tosses doesn't mean that the odds have changed. Another 350K tosses could result in a completely different result and that is the point. The test has many variables, most notably that humans were tossing coins and there is not way they can consistently toss a coin time after time. But every toss always has an equal chance of landing heads or tails. I'll take those odds all day long.

 

[Lew Zealand]

If by voting polls you mean surveys of people on how they will vote, this is entirely different. The odds are always the same. See my comment above, Any toss can result in heads or tails. That is it. So therefore, there is a 50/50 chance.

That's a hypothesis and a reasonable one. But with no data. Just because there are 2 outcomes doesn't mean those outcomes are necessarily equal. The point of the test was to see if there are biases induced by people flipping a coin that aren't immediately apparent. Because in the end it's people who are flipping coins IRL.

The answer is: Yes, a small bias.

However this paper hasn't been peer-reviewed yet so it'll be interesting to see if there are any methodological errors than anyone can pick out. It's pre-registered so they can't manipulate the tests after the fact to fit their hypothesis, which is good.

Just because there was a bias in 350K tosses doesn't mean that the odds have changed.Another 350K tosses could result in a completely different result and that is the point.

Another hypothesis. With no data. Statistical calcs exist to see what the chances are of a 50.8-49.2 deviation from 50-50 over 350K tosses (if you're hypothesizing completely random), that would give an indication of whether another 350K would go 49.2-50.8 the other way to even up the odds.

The test has many variables, most notably that humans were tossing coins and there is not way they can consistently toss a coin time after time. But every toss always has an equal chance of landing heads or tails.

Same as above, another hypothesis with no data. The people who did this test have the data.

Data >> no data every time.

 

[waclark]

That's a hypothesis and a reasonable one. But with no data. Just because there are 2 outcomes doesn't mean those outcomes are necessarily equal. The point of the test was to see if there are biases induced by people flipping a coin that aren't immediately apparent. Because in the end it's people who are flipping coins IRL.

The answer is: Yes, a small bias.

However this paper hasn't been peer-reviewed yet so it'll be interesting to see if there are any methodological errors than anyone can pick out.



Another hypothesis. With no data. Statistical calcs exist to see what the chances are of a 50.8-49.2 deviation from 50-50 over 350K tosses (if you're hypothesizing completely random), that would give an indication of whether another 350K would go 49.2-50.8 the other way to even up the odds.



Same as above, another hypothesis with no data. The people who did this test have the data.

Data >> no data every time.

Again, you're measuring outcomes, not probability. I have all the data I need. A coin has 2 sides, excluding edge landings, a coin can only be heads or tails, therefore, there is a 50/50 chance of either landing. That is universally true, no matter how many times you toss the coin.

Now a test of 350K tosses, with a limited number of people (48) isn't going to prove anything. It only proves that a coin tossed by those 48 people, will land one way, slightly more often than not, over a limited number of tosses. And, by the way, they didn't toss the same coin over and over, so you really have an even more limited data set. One wonders if certain coins had a higher bias than others. Were they new coins, was there something in the coin design that would bias it to fall a certain way, were they clean, were they worn unevenly to cause landing a certain way, etc etc. It doesn't change the fact that every toss has an equal chance of landing either heads or tails.

So bad data << no data.

 

[Lew Zealand]

Again, you're measuring outcomes, not probability. I have all the data I need. A coin has 2 sides, excluding edge landings, a coin can only be heads or tails, therefore, there is a 50/50 chance of either landing. That is universally true, no matter how many times you toss the coin.

Now a test of 350K tosses, with a limited number of people (48) isn't going to prove anything. It only proves that a coin tossed by those 48 people, will land one way, slightly more often than not, over a limited number of tosses. And, by the way, they didn't toss the same coin over and over, so you really have an even more limited data set. One wonders if certain coins had a higher bias than others. Were they new coins, was there something in the coin design that would bias it to fall a certain way, were they clean, were they worn unevenly to cause landing a certain way, etc etc. It doesn't change the fact that every toss has an equal chance of landing either heads or tails.

So bad data << no data.

You end with an assumption/hypothesis of bad data, again with no proof.

You can read the abstract of the paper to answer some of your questions instead of just dismissing things with prejudice. The differences were not with the coins, but with the people flipping them: some people were close to random, others not so much. Just because you can flip a coin close to random (which some do) doesn't mean that everyone is doing so. That is the point. Bias exists in coin flips and unless you take measures to remove that bias, then you will get a biased result.

That's the point of doing a real world test instead of only a mental exercise or making what seem to be reasonable assumptions. Use that as the basis for the hypothesis and then you test it.