Fair and unbiased coins have a bias to land on the same side they started

[Pmalek]

A group of researchers carried out a test to investigate the randomness of fair coin flips.

They collected 350,757 coin flips, recorded the results, and concluded that when a person tosses a coin in the air, it has about a 51% probability of landing on the same side it started. This same-side bias varies and is different from person to person. Some have almost none or very little bias, while others display a more significant bias.

The researchers believe the bias comes from the rotations and wobbliness of the coin, which causes it to land on the same side more often than not.

They posted this data in support of their hypothesis:

Pr(same side) = 0.508, 95% credible interval (CI) [0.506, 0.509], BF same-side bias = 2364

Their research also confirmed that the coin is equally likely to land on both heads and tails if those were the starting positions (the side that was up). They didn't record a bias that one side is more likely to end on the same side than the other.

Pr(heads) = 0.500, 95% CI [0.498, 0.502], BF heads-tails bias = 0.183

 

They carried out the test with 48 people who used 46 different coins and denominations. The total number of coin flips was 350,757. The results show 178,078 landings on the same side.

The researchers did mention a concern they had. The people who participated in the test were aware of the main hypothesis they were testing. With that in mind, manipulations or attempts to manipulate the results to either prove or disapprove the theory are possible.


The source also mentions the scope of this same-side bias in a betting scenario.
If you bet $1 on the result of a coin toss to get $2 if you predict correctly or lose the $1 if you predict wrong, you would earn an average of $19 after 1000 coin flips. But knowing the starting position of the coin is essential.

Could these findings lower the security of seeds generated from coin tosses, considering that the starting positions of the coins aren't known to a third party?
I remember that o_e_l_e_o recommended using von Neumann's unbiased coin flipping algorithm in a similar discussion from a few weeks ago. One more reason to use this algorithm if coin tossing is your system of generating seeds. 
 

Sources used:
https://arxiv.org/pdf/2310.04153.pdf
https://arxiv.org/abs/2310.04153

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[digaran]

From quantum physic's perspective, all the coin flips are landing on both sides at the same time, but who really decides which one of the outcomes become our reality?

A simpler example, in fall seasons usually trees lose their leaves, is it really random when they drop one by one whilst there are infinite possibilities of when they drop down, land where and on which side exactly.? 

Just use a secure random generator, ignore tossing coins, and don't reuse addresses.

We control absolutely nothing, we are just given options to choose from.

[ABCbits]

Can't believe some people actually research this, where they provide detailed documentation including video of tossing coin and image of all coins used as tossing (i checked few random image and video).

The source also mentions the scope of this same-side bias in a betting scenario.
If you bet $1 on the result of a coin toss to get $2 if you predict correctly or lose the $1 if you predict wrong, you would earn an average of $19 after 1000 coin flips. But knowing the starting position of the coin is essential.

Although if you visit casino, you still at disadvantage due to house edge and other fees.

Could these findings lower the security of seeds generated from coin tosses, considering that the starting positions of the coins aren't known to a third party?

In terms of entropy, shouldn't the difference (between ~0.508 and ~0.492) is extremely small? CMIIW.

[o_e_l_e_o]

We discussed this paper already in another thread here: https://bitcointalk.org/index.php?topic=5395587.msg62997786#msg62997786

And as I said in that thread, I think a far more accurate take away from that paper is that everyone has their own intrinsic bias. 10 of the 48 participants showed a bias to the opposite side, not the same side, and there was one individual who showed an extreme 60/40 bias.

I remember that o_e_l_e_o recommended using von Neumann's unbiased coin flipping algorithm in a similar discussion from a few weeks ago.

This remains the gold standard, and simply start each flip from the same starting conditions (i.e. heads up) to completely eliminate any bias in your flipping technique.

[BlackHatCoiner]

The total number of coin flips was 350,757

Wow. I can't imagine the boredom. Must be killing.

In terms of entropy, shouldn't the difference (between ~0.508 and ~0.492) is extremely small? CMIIW.

It is extremely small. It has been demonstrated in this post and in here, that this particular difference results in a loss of 0.05 bits of entropy when tossed 256 times; even extremely biased dice can provide more than enough entropy if you toss them enough times.

[DaveF]

Would be interesting to see how something different then coins would behave. i.e. casino chips or metal washers where people are not used to 'heads or tails'

Actually washers would probably be better since they do have a hole in the middle, would that have any factor in it.

-Dave

[philipma1957]

lets pretend it is true.

how bout alternative spin starts.

A)  you must use heads on top to start flips for first ten tosses
B) you must use tails on top to start flips for second 10 tosses

so on and so forth pretty much ends that issue.  if that issue is true.

Other things need be done when you flip it it must go up and over your head as it is spinning. It must spin.

I would be willing to bet that if done with the same coins as the first test for 350,000 spins it would be more accurate.

[Pmalek]

Although if you visit casino, you still at disadvantage due to house edge and other fees.

It depends on which casino games you play. The report makes a comparison between the advantages you get with side-biased coin tosses versus the advantage the house has in roulette and blackjack. The advantage and house edge is greater for roulette where the casino would profit more long-term. But blackjack is known as the casino game with the lowest house edge.

They mention that a comparable bet would earn the casino $5 for blackjack, but for single-zero roulette that profit would increase to $27. As mentioned earlier, side-biased coins can potentially earn you $17. 

[NotATether]

Although if you visit casino, you still at disadvantage due to house edge and other fees.

It depends on which casino games you play. The report makes a comparison between the advantages you get with side-biased coin tosses versus the advantage the house has in roulette and blackjack. The advantage and house edge is greater for roulette where the casino would profit more long-term. But blackjack is known as the casino game with the lowest house edge.

Coin toss has nothing to do with casino's house edge and odds, because they are using computer entropy to generate the random numbers that in turn determine the results. It's not affected by any gravitational bias - although some people do point out that heat conditions around the CPU's random number generator(s) might have a slight impact - but that can be mitigated by also using a software RNG like OpenSSL's.

[DaveF]

Would be interesting to see how something different then coins would behave. i.e. casino chips or metal washers where people are not used to 'heads or tails'

Actually washers would probably be better since they do have a hole in the middle, would that have any factor in it.

-Dave

I'm not sure there would be any noticeable difference. But at least last page of research paper mention all kinds of coins used.

At a quick look they were all coins. I was just wondering if you picked some other thing that you could flip like a coin but was not a coin it would be a different result.

In the end it probably does not matter, just more of a though of how things that should not matter or we think would not matter actually do.
Like flipping a poker chip or washer vs. a coin. But for some reason using those things do change the outcome.

-Dave

[Pmalek]

Coin toss has nothing to do with casino's house edge and odds, because they are using computer entropy to generate the random numbers that in turn determine the results.

I know, but they mention that comparison for the readers to understand how big of an advantage such a side-biased coin toss gives you (on average) compared to some well-known casino games like blackjack and roulette. It didn't have to be in the report. I think saying that you could potentially profit $19 on average after 100 coin tosses if you know the starting position of each coin before it's tossed is enough.

[philipma1957]

Coin toss has nothing to do with casino's house edge and odds, because they are using computer entropy to generate the random numbers that in turn determine the results.

I know, but they mention that comparison for the readers to understand how big of an advantage such a side-biased coin toss gives you (on average) compared to some well-known casino games like blackjack and roulette. It didn't have to be in the report. I think saying that you could potentially profit $19 on average after 100 coin tosses if you know the starting position of each coin before it's tossed is enough.

But did they be sure to make the coin spin and that it must go upwards over the head of the tosser.

I can favor a half dollar or a silver dollar if I flip it to a soft surface such as grass. And I start it on heads or tails I can bias the toss by doing a gentle lower toss.

say my hand releases at waist high and it arcs up to chest high and fall to grass with a slower spin.

Much like tossing a dart at a bulls eye  you can do some control over the coins.

But If you have to make the coin toss go over your head and spin rapidly hitting a hard surface like a maple wood floor control is far more difficult.

The bias is very likely subconsciously done by the tosser.

If you tested this with blindfolding I wonder if it changes.

[NotFuzzyWarm]

In the interest of being thorough, it should be pointed out that most washers *will* have a built-in bias because most have a rounded top edge and a much sharper bottom edge because they are stamped out of ribbons of metal. For no bias the washer should be flat-ground.

As an aside - that also affects how they work: correct orientation is rounded side against the head of a bolt or against a nut or lock-washer, sharp edge against what is being bolted. The edge digs in to grip the material a bit reducing chance of rotation and also helps seal against corrosion.

As for bias caused by how a coin is flipped - take that out of the equation by spinning it on the edge and counting what side it stops on. The huge number of spins that usually happen should remove any conscious or unconscious 'flip' technique bias.

[philipma1957]

In the interest of being thorough, it should be pointed out that most washers *will* have a built-in bias because most have a rounded top edge and a much sharper bottom edge because they are stamped out of ribbons of metal. For no bias the washer should be flat-ground.

As an aside - that also affects how they work: correct orientation is rounded side against the head of a bolt or against a nut or lock-washer, sharp edge against what is being bolted. The edge digs in to grip the material a bit reducing chance of rotation and also helps seal against corrosion.

As for bias caused by how a coin is flipped - take that out of the equation by spinning it on the edge and counting what side it stops on. The huge number of spins that usually happen should remove any conscious or unconscious 'flip' technique bias.

Good way to say it.  The key is lots of rotation of the coin. Although a very disciplined and skilled athlete may be able to play with that.

But I suppose it is like bowling a bowling ball on a 300 foot alley vs a 60 foot alley.

Lots of people have a perfect game on a 60 foot ally. I would suspect no-one would be able to do it on a 300 foot alley.

[pooya87]

Didn't they just prove the exact opposite?
Theoretically an unbiased scenario would be if the coin had a 50% chance of landing on the same side. They proved there is 51% chance for that. Correct me if I'm wrong but I wouldn't call 1% in a rather small batch with a lot of other variables to be the bias. It looks more like the negligible error (ie. 50% ± 1%).

The total number of coin flips was 350,757

Wow. I can't imagine the boredom. Must be killing.

But it seems everyone who perform coin toss is included as author of the research, so it's motivation if they need to fill work/research experience on their CV/resume .

It is not worth it since at the end of the study your thumb would stop working

[Pmalek]

But did they be sure to make the coin spin and that it must go upwards over the head of the tosser.

There are videos of the coin toss experiments but I haven't watched any of them. I don't think they tossed the coins over their heads to land behind them, but if you are interested to check it, you can find the videos at https://osf.io/mfkp9/. Each video has to be downloaded. It seems the site doesn't support video streaming in-browser.

[apogio]

A group of researchers carried out a test to investigate the randomness of fair coin flips.

They collected 350,757 coin flips, recorded the results, and concluded that when a person tosses a coin in the air, it has about a 51% probability of landing on the same side it started. This same-side bias varies and is different from person to person. Some have almost none or very little bias, while others display a more significant bias.

Sources used:
https://arxiv.org/pdf/2310.04153.pdf
https://arxiv.org/abs/2310.04153

This is interesting.

I will read the paper, but I don't have enough time currently.  To be honest I am not surprised. However, can someone who has read the paper tell me why did the choose to do this research? I mean we all know from our school years that true coin toss will give 50% as long as the number flips tends to infinity.

So couldn't it be just a coincidence even though the flips where that many?

[NotFuzzyWarm]

tell me why did the choose to do this research?

Probably because someone getting a degree in statistics had to choose a subject for their thesis and odds are this was easiest...

[apogio]

Probably because someone getting a degree in statistics had to choose a subject for their thesis...

This is exactly what I hoped I wouldn't get as an answer 

Do you think this "thesis" proves anything? To me it doesn't!

[philipma1957]

Probably because someone getting a degree in statistics had to choose a subject for their thesis...

This is exactly what I hoped I wouldn't get as an answer 

Do you think this "thesis" proves anything? To me it doesn't!

hmm if he did the exact test again and got 51-49 again it is a lot more likely there is a bias.