# Coin Toss Machine

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In analyzing the discussions on coin tosses we have going, I came across a question that might have derailed the other threads, so I'll open it here. Persi Diaconis had Harvard engineers build him a coin-flipping machine for a series of studies. Apparently the device could be adjusted to flip either heads or tails repeatedly. I assumed the next natural test would be to see if the machine could be calibrated to flip a coin on its edge every time, but I couldn't find anything on that.

How easily/cheaply could a device be made that flips a coin onto its edge (virtually) every time?

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Surely, the machine can technically be calibrated to land the coin on the edge every time, but it's a question of very precise engineering, physics and mathematics.

I cannot answer your question about the price (I'm not sure anyone can since the machine has never been built to my knowledge), but I want to comment on the article.

It seems incredibly ignorant and unscientific to me. Take this quote for example:

About a decade ago, statistician Persi Diaconis started to wonder if the outcome of a coin flip really is just a matter of chance. He had Harvard University engineers build him a mechanical coin flipper. Diaconis, now at Stanford University, found that if a coin is launched exactly the same way, it lands exactly the same way.

How could it be any other other way? How could a sane person, let alone a respected statistician not understand that coin flips technically have nothing to do with chance?

How stupid do you have to be to not understand that if you launch the coin the same way, you would always get the same results? I cannot fathom the thought process here. Otherwise, the coin would surely violate several laws of physics and logic.

The randomness in a coin toss, it appears, is introduced by sloppy humans.

Very obviously. When we speak of probability, we use coins as a visual example. Obviously, mathematical (perfectly unbiased) coins differ from actual ones.

My question is why do you think they even did the experiment in the first place? What did they expect?

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Since the machine wasn't built to flip a coin on its side, it is probably not accurate enough. Engineers generally don't build things more accurate than required, because that is usually a lot more expensive. So I expect no amount of calibration would help.

An American nickel has a 1 in 6000 probability of landing on its side. You can definitely increase that probability a lot by calibrating the machine.

If I had to design a new machine for exactly that, I might try giving the coin a spin around its vertical axis.

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Hello, phi perhaps you should contact the man who built the inverted triple pendulum balancer in 1995.

It doesn't look too expensive (perhaps a double malt?)

Edited by studiot

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That is a control problem. The point of a coin flipper would be that you cannot control the coin after it leaves the machine.

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Very obviously. When we speak of probability, we use coins as a visual example. Obviously, mathematical (perfectly unbiased) coins differ from actual ones.

My question is why do you think they even did the experiment in the first place? What did they expect?

I don't know. Perhaps that's why the wanted to test it?

I mean. Since you know the outcome of the experiment before the out come of the experiment, why didn't you publish an article explaining and proving the theory, without actually proving it?

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That is a control problem. The point of a coin flipper would be that you cannot control the coin after it leaves the machine.

Also the orientation of the coin, if it was put blindly, would be a random element.

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Also the orientation of the coin, if it was put blindly, would be a random element.

Yes, while not important for the regular coin flipping, that would be important for flipping it on its side. I don't know what the tolerances on these coins are, but you probably want to use the same coin every time.

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I don't know. Perhaps that's why the wanted to test it?

I mean. Since you know the outcome of the experiment before the out come of the experiment, why didn't you publish an article explaining and proving the theory, without actually proving it?

To assume that the coin may land differently if tossed under the exact same conditions is to assume that a ball might bounce differently if thrown into a wall at the exact same angle with the same force.

It violates at least Newton's third law and common sense. I really don't see why the experiment was necessary.

It's exactly the same as testing whether an object would fall downwards when released from a building. It's reduntant.

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To assume that the coin may land differently if tossed under the exact same conditions is to assume that a ball might bounce differently if thrown into a wall at the exact same angle with the same force.

It violates at least Newton's third law and common sense. I really don't see why the experiment was necessary.

It's exactly the same as testing whether an object would fall downwards when released from a building. It's reduntant.

No it is not.

For all we knew, there could be tiny variables we just can't control, that would affect the coin toss. He wanted to test it.

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No, there aren't. If you toss it with the same exact motion, you absolutely cannot get different results. It would violate Newton's third law.

And it seems to me they were considering the problem from a technical perspective, not engineering, which is even worse.

It was a waste of time.

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We build test setups to prove things we already know all the time, to demonstrate them to others.

A machine demonstrating that coins can be made to flip in a predictable way is much more convincing than just saying that's how it is.

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We have undoubtedly tested the ways that balls and other objects bounce countless times, but fine. What makes me think that it wasn't just that is this quote:

About a decade ago, statistician Persi Diaconis started to wonder if the outcome of a coin flip really is just a matter of chance.

''Started to wonder'' implies that he didn't know this and genuinely wanted to find it out. This may be a fault of the article, and not the person, though.

The other quote displays the same ignorance as well:

The randomness in a coin toss, it appears, is introduced by sloppy humans.

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To be fair, the outcome does depend on slight variations of the input, so he might have thought it could be a chaotic system, or wanted to know how large the variations could be.

Also, the quotes you give are the words of some dude's blog. To really know what Diaconis' purpose really was, it would help to find quotes from the man himself.

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Also, the quotes you give are the words of some dude's blog. To really know what Diaconis' purpose really was, it would help to find quotes from the man himself.

Yes, this makes the most sense to me. A random dude gave his interpretation of the experiment and didn't actually get the point.

To be fair, the outcome does depend on slight variations of the input, so he might have thought it could be a chaotic system, or wanted to know how large the variations could be.

The quote leads us to believe that they were flipped under the same exact circumstances, which again, seems wrong to me. Again, your suggestion that they wanted to test out how large the deviation would need to be to affect the result seems the most likely explanation to me.

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I'm sorry I linked to the NPR story instead of another take on Diaconis' machine. I was more interested in the machine than in what the other threads were already talking about regarding chance.

Here is another machine inventor, Nitipak Samsen, who has made several machines attempting to get consistent flips on a coin. Still nobody with a machine that can do edges, and I haven't seen anyone with the money and curiosity to even try. Or they may realize there are too many variables that even a machine can't control.

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Still nobody with a machine that can do edges, and I haven't seen anyone with the money and curiosity to even try. Or they may realize there are too many variables that even a machine can't control.

The variables would be impossible to predict unless this contraption would be completely isolated from any variable changes so this would have to be in a vacum with precisly controlled temperature, humidity and probably the whole thing have to be ballanced to cope with earths movement. Even if done so, each edge toss would have to be done with a new coin which would have to be maschined to ridiculous precision. The same goes for the table on which the coin would land. Im no expert but if you went to ask Boston Dynamics or some other robotics company capable of such a project to they'd probably ask millions if even remotely possible.

Edited by koti

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To be fair, I don't see why anyone would spend money on such a machine. We know, by the laws of physics, that this is possible and that hypothetically it is possible to make a machine which will land a coin on its edge with a probability of 1. I don't see why anyone would spend millions on creating it. It just wouldn't prove anything and would be largely useless.

It would be like creating a machine which would fire a chair a kilometer in the distance on a precise target with error margins of an inch. It certainly is possible from a technical perspective, but why bother with that?

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This made me recall the hypothetical problem which I read in a Hawking book 20 years ago but Im sure it was presented earlier - if we knew the position and properties of every particle in the universe would we be able to predict the future? If Im not mistaken, essentially entropy tells us the answer is no. An edge coin toss maschine is by no means the same levell of complexity but still sounds complex enough for me to give up thinking about it. Then again, I'm a huge pessimist so I might be wrong

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I'm not exactly sure what you mean.

About the Hawking problem, the answer is no if we just knew their still position at a certain point in time. But if we know the exact velocity, the answer should be yes. I don't mean that we humans could calculate it, I mean an objective perfect machine should be able to do it, even if entropy is a part of it.

For example, if I have a box with bouncy balls in it, and I shake it forever in the same exact repeating pattern, a hypothetical perfect machine will be able to calculate the position of the marbles at any given point in the future. It justs adds in the velocity of the marble, the angle of deflection with the walls of the box and other marbles, then the angle of deflection once it hits again and it just keeps going forever. To say that entropy would make it impossible to calculate this would be to imply that marbles violate the laws of physics and move in unpredictable ways, which is impossible. Of course, if we're talking about a human calculating all of this, it would certainly be too advanced for us and entropy would make it ''unpredictable'' for sure. It depends if we're talking from a technical or practical perspective.

A coin would be much simpler because it's a single object which should always repeat the same pattern, given that the machine is constructed correctly. Saying that it would be impossible (from a technical perspective) to make a coin always land on an edge would be to say that Newton's third law is incorrect.

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Yes, I missed pointing out velocity along with position of the particles. I think youre right about the coin toss maschine that theorerically its doable under very controlled conditions as does the box of marbles experiment sound equally valid. As for the Hawking problem Im not sure at this point...wouldn't QM's probabilistic fussyness play a role here?

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wouldn't QM's probabilistic fussyness play a role here?

Well, OK, you got me there. I forgot to include QM. Without it, there is not doubt it is possible.

However, the answer is still not certain. It is a question whether randomness in QM is truly random or not. For example, I have a wooden box with two holes in it, one on the top and one on the side and I place 100 pieces of paper in it, numbered from 1 to 100 and I shake the box and scramble the pieces of paper. I have two people next to the box. One is looking through the hole on the side and one is drawing numbers from the top hole. The chances for the person on top for drawing any particular number are 1 in 100, whereas the chances for the person looking from the side are 1 in 1, because he can see which number is being picked.

The same goes for coins. For humans, any coin flip has a 50% chance of landing on either side, simply and only because our brains are not sophisticated enough to calculate and know the force and angle with which the coin is being flipped. If we place our hypothetical machine, it will immediately know the force of the flipping, the angle, velocity, spin etc. of the coin and will be able to predict the outcome with the probability of 1.

So randomness is simply a result of human ignorance and this is true for everything we know so far. I don't know why people assume that QM is different. Why do they not assume that we simply cannot predict the pattern with which quantom randomness is occuring, rather than it being truly random? Seeing it this way would comply with all the observations on probability we have thus far. These are just my thoughts on the qustion, I am far from an expert on QM.

My point in all this being, if QM has a pattern to its randomness like everything else does, it would mean that, technically, entropy of everything could be predicted.

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Im no expert on QM as well but AFAIK you either know the position or the velocity of a particle for certain, never both. So essentially nothing has the probability of 1 on the micro scale, everything is determined by the wave probability function. There are patterns in QM and I think they are well understood but still you never have the same 1:1 probability like we observe in the macro scale governed by Newton and GR.

As for the coin toss Im thinking that its all doable like we agreed on unless we start trying to controll the micro scale. I mean if we were to want to have an outcome of a coin toss on its edge every time in say 100 milion tosses then it seems to me we'd have to start worrying about controlling the conditions of this experiment on the particle level and that would get us into the wave probability function side of things.

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I mean if we were to want to have an outcome of a coin toss on its edge every time in say 100 milion tosses then it seems to me we'd have to start worrying about controlling the conditions of this experiment on the particle level and that would get us into the wave probability function side of things.

Well, ''with probability 1'' means an infinite number of times, not just 100 million. My knowledge of QM is feeble, but as far as I've heard, there's a given technical probability that if you were to bounce a ball into a wall, it could teleport to the other side of it. So if done an infinite number of times, it would go through the wall an infinite number of times.

If this is true (again, I can't tell myself), then you would be correct. The coin would eventually go through the table and not land on its edge.

But still, it is a question whether this is truly random. In theory, it could be possible to calculate (for a perfect machine) whether an object would go through a wall by the motion and velocity of the micro-particles causing this. So then again, it might lead to it being controlled and thus, a perfect coin flipping machine being built which would be able to land coins on their edges with a probability of 1.

Im no expert on QM as well but AFAIK you either know the position or the velocity of a particle for certain, never both. So essentially nothing has the probability of 1 on the micro scale, everything is determined by the wave probability function.

So it could very well be that we simply don't know this and are assigning it a wave-probability function because probability, the whole premise of it, is based on our ability to calculate these things. It would not be unreasonable to assume that because everything else concerning probability works that way; everything. Of course, it could be that I'm wrong.

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All this latest discussion about angels and pinheads was why I wanted to compare the statistics of coin tossing with that of die rolling in an earlier thread.

With coin tossing there is only one way (and therefore one probability) to report a given outcome.

With die rolling you can report

A number greater than 3

A five

An odd number

and so on.

Each of these are respectable outcomes with their own particular probabilities.

But some are also combinations of each other.

The lesson about probability from this is that you can lump together a whole raft of minor outcomes in one single outcome labelled 'misfires', or whatever you chose to label it, in the case of the coin tossing machine.

If you can show that this combined probability form all causes is less than some set value, you can ignore it.

This is the basis of a modern engineering design method known as limit state analysis.

As regards the probability of a baseball penetrating a brick wall you don't need to be able to calculate it exactly if you can show it is below some acceptable level.

But remember that modern electronics depends upon there being an acceptably high probability of the equivalent happening to the charges in the circuit.

Edited by studiot

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