# The Probability Of A Head In A Coin Flip Is 1, Not 1/2

My dad and I built a coin flipping machine. Then made this video (you might have to click the link):

Link, because the embedding is not working.

(The double dashes are screwing things up. The damned interpreter is changing the double dashes in the YT link to an em-dash, and the embedding breaks. Tried PRE tags and that did not help. Ideas? Tried purging the cache and stopping it, too. No go. Could be my server.)

I am still new to this “video” thing, so I stupidly forgot to film the process of making the machine. I did, however, remember to take some pictures:

The idea, as the video explains, is to make a machine that flips a coin so that it always lands heads.

The base is scrap 2×4 we had lying around. Onto which is glued and screwed a spare clothespin with steel spring. The hope was the base would not move, and it doesn’t. Or at least not in any visible or important way.

The top part of the clothespin holds the quarter. It had a lot of lateral movement; basically the spring acted like a pivot point for sideways movement. To greatly reduce that, I pounded four nails into the board lined up with the clothespin as stops.

The forward stops fixed the amount of force the spring could give. To within limits. The wood of the pin had some give and flex, so that if you pushed too hard the amount of force could be increased.

The back stops were there to stop a great deal of the lateral movement of the pin. But as you’ll see in the video, it was not a good idea to put the quarter up against them, because that imparted a good deal of friction. Because of the cut grooves on the side of the quarter, this imparted friction was not predictable, and thus the coin would not always land heads.

Luckily, the clothespin had two lateral cuts made into it, which are designed to hold the spring. There are two because the sides of the wood could fit either side of the pin. So we lined up flips on one of the grooves.

The landing pad was tricky. A quarter hitting a hard surface, like a board, bounces, and in unpredictable ways. Something to soften the impact and allow the coin to lay flat was needed. Luckily, there was a styrofoam plate lying around, on which were once crackers loaded with pickled bologna (my dad’s favorite). Next time we’ll try pretzels.

Onto the plate I folded some shop rags. Took quite a few of them to make a landing zone soft enough to eliminate all bounce.

In the end the thing worked. There’s two sections showing it works in the video. The first test with my dad, at which it only worked so-so. Then another at the end after my explanation and after I made some tweaks. Worked great after that. You’ll see.

Still pretty ugly, though, but functional. A prototype only. A working—at least most of the time–prototype.

It works well enough to prove the contention that the probability of a coin flip showing a head is 1, or close to 1.

For this machine.

Because with this machine we have controlled most, but alas not yet all, of the causes of the result. Therefore the result is not random, which is to say it is predictable, because random means unpredictable. And this flip is predictable because we know the causes.

In a regular flip with your thumb there are the same forces, but they are uncontrolled, and delicate. There is friction on the thumbnail. The amount of upward force imparted to the coin is highly variable. The coin is not put in the same spot every time, which affects the amount of spin. The coin is caught at variable times and heights and on a surface (your hand) which changes from flip to flip.

The outcome is random, because it is unpredictable, and it is unpredictable because all the causes—those forces and material conditions—are not controlled.

Like I say in the video (and a million times elsewhere), nothing has a probability. All probability is conditional on the assumptions made. Here, the assumptions are fixed, or mostly so. On your thumb, they are not.

This doesn’t just work for coin flips, but for everything. Yes, even quantum mechanical objects, but we haven’t the time to go into that today.

Nothing has a probability. Probability doesn’t exist.

The video is choppy, ill-edited, and even confusing. Still getting the hang on it.

Subscribe or donate to support this site and its wholly independent host using credit card click here. Or use the paid subscription at Substack. Cash App: \$WilliamMBriggs. For Zelle, use my email: matt@wmbriggs.com, and please include yours so I know who to thank.

1. muhsin sk

The probability of winning a coin toss, assuming a fair coin, is 50%. Each flip is independent and has an equal chance of landing on heads (H) or tails (T), making the probability 1 out of 2, or 0.5, for landing heads.

2. Briggs

muhsin skk,

Yes, that’s the standard line. But it’s wrong. Just plain wrong, for all the reasons I give.

Interesting you use “fair”, which (as I explain in Uncertainty) is the premise that the probability is 1/2, from which you deduce the probability is 1/2. A circular argument.

3. McChuck

Quantum mechanical events have a probability because we have no means of measuring all the forces acting upon the subject, and those forces are myriad. Every effect has a cause, those causes are discrete and absolute, but they are also chaotic and unknowable.

In QM, as in war, everything is simple, but simple things are very difficult.

4. Briggs

McChuck,

I disagree. Probability is something we assign when we don’t know cause, as we don’t in QM.

5. Very cool !

The emdash problem is endemic.. and happens because MS windows fonts don’t follow pre-existing standards. The easiest way to beat it is to avoid characters like dash and single quote (apostrophe) because the variation isn’t entirely predictable – e.g. some wordpress apps work correctly, others don’t.

If you are uploading to someone else’s server you will usually have a “save as” option – so just delete the offending chars from that.

If you run your own server or are running on shared servers using Linux (e.g. dreamhost) you can use the link command to create aliases differing only in the dash (or other mismatching char) and the apache (nginx is trickier) server will pick the one the user’s software supports. e.g. ln -s real-name real_name will cause apache to return whichever the user’s browser understands.

6. Hagfish Bagpipe

Kidding aside, that was a nifty experiment that not only demonstrates your coin probability assertion, and that you are a Chip Off the Old Block, but also shows how Real Science may still be done regardless the pettifogging political poppycock of The Science™?.

7. Briggs

Hagfish, I do have a slide rule (as you know!).

8. Yancey Ward

There is a person born every minute who cannot ever be convinced by your device. Just ask P. T. Barnum.

9. Hagfish Bagpipe

And it slides into your lab coat’s pocket protector, just as Fermi’s did.

10. Hagfish Bagpipe
11. oops – turns out apache won’t normally do this (read x as y) anymore without scripting – my mistake.

excuse: I use nginx (alias lists) .. but should have checked. My mistake.

12. Cary D Cotterman

Hagfish: “N. DeGrasse Tyson”

I can’t help laughing when I see that name. M. Tyson has more credibility. Hell, Tyson Fish Sticks do.

13. Fascinating as always, Briggs.

You say:

“Like I say in the video (and a million times elsewhere), nothing has a probability. All probability is conditional on the assumptions made. Here, the assumptions are fixed, or mostly so. On your thumb, they are not.”

You are correct that “probability is conditional on the assumptions made”. However, when we discuss probability, it is almost invariably with the assumption that the assumptions are not fixed, like with your thumb.

Thus, when I say “a coin flip has a 50/50 probability of coming up heads”, the clear assumption is that we’re NOT talking about your most ingenious machine. We’re talking about what you call “on your thumb”. And with that unspoken but omnipresent assumption, yes, a coin flip DOES have a probability of coming up heads, and it’s not “1”.

Best regards to you and yours,

w.

14. Briggs

WE,

Better to say the probability of the coin flip depends on the premises assumed — like all probabilities. There are no exceptions. All probability is epistemological, and all depends on assumptions made.

15. there is a difference between knowing the “behavior” of previous data points and knowing nothing (other that previous data points exist).
want an example?: in my hobby I have tables for planetary conjunctions (part of transit measurements); when looking at just a few 100 years (of data points) then there are [calendar] weeks where Jupiter never was in a conjunction.
now, in order to predict by formular new data point/s for this effective gap one must know how the previous behavior did it; if you are not wrong with the “behavior” analysis you may find a “correct” prediction [but the uncertainty is != 0 & this is cause for more uncertainty if this data is again used].
Yet if your analysis is false (or does not exists except as aim or desire) then uncertainty can only grow for whatever new data you generate.

16. john b()

If a die is fair, is it D.I.E?

What are the chances?

17. Rudolph Harrier

Willis,

Then what ARE you talking about? Clearly the answer is not “every coin flip made in the entire world EXCEPT for the ones done by William Briggs’s machine” since there are other ways of flipping coins where (due to technique or the coin itself) one side is more likely to show up than the other.

If you say “well, we are only talking about fair coins, flipped in a fair way” then you are just appealing to a tautology, since in this context “fair” would mean “a coin that has a 50/50 chance of showing up heads.”

18. Hagfish Bagpipe

What does it mean that probabilities are not inherent but rather depend on knowledge of cause and assumptions made about causes? How does that effect the “real world”? It must be something significant for Briggs to… flip over it. So what is it? Lemme make a stab at it:

Probabilities are the art and science of understanding future events. Knowing what’s going to happen is bigly useful, hence the prognostication industry. If prognosticators believe the likelihood of a future event is an inherent number they will seek only to divine this magic number. If however the prognosticators are afflicted with Briggs Syndrome they will seek to understand, and isolate, cause — a more rigorous process fraught with uncertainty. Financial and political pressures, not to mention laziness, favor the sloppy process of magic inherent probabilities. But a more rigorous process that accounts for cause while acknowledging uncertainties will make better predictions while reducing the quantity of spurious prognostications drowning the world in nonsense.

How’d I do, Professor?

19. gareth

@ Willis Eschenbach, September 19, 2023 at 1:33 am

a coin flip DOES have a probability of coming up heads

I think the point is that neither a coin, nor a “coin flip” has “a probability of coming up heads”. Neither possesses the attribute of “a probability”. The “probability” is only a human assessment of likelihood of a coin or a “coin flip” (in general or in particular) “coming up heads” and is conditional on the assumptions made by the human observer.

I think I’ve got that right. If not please be explicit as to where I’m wrong.

20. gareth

@ Willis Eschenbach, September 19, 2023 at 1:33 am

a coin flip DOES have a probability of coming up heads

I think the point is that neither a coin, nor a “coin flip” has “a probability of coming up heads”. Neither possesses the attribute of “a probability”. The “probability” is only a human assessment of likelihood of a coin or a “coin flip” (in general or in particular) “coming up heads” and is conditional on the assumptions made by the human observer.

I think I’ve got that right. If not please be explicit as to where I’m wrong.

Re-posted – bloody html…

21. Steve

@Willis, you are reading too much into this. What Briggs is getting at is that in a cause and effect universe, “probability” is just a way to lump all the unknowns into a single entity. Regardless of the fact everyone knows you can’t add apples and oranges and get an answer in bananas. It’s “better” that than admit gaps in our knowledge.

The problem is not the implicitly presumed thumb, but rather our ignorance about all relevant initial conditions involved in that thumb/coin/gravity/wind current/temperature/barometric pressure/etc. instance. If we knew all those, and we had formulae of how they interact with each other, the thumb-based coin flip would be as deterministic as the clothespin machine.

Someone above used the term “chaotic”. I’m not sure whether that was a referent to chaos theory, where the phenomenon is too interconnected and complex to solve mathematically in any reasonable timeframe (42!) , or the more mundane use of “chaotic”, but the former is pretty close to the truth. There is an answer to the heads or tails question, and given a second instance with exactly the same conditions as the first, it will be the same answer, but we know not all the relevant values, nor the functions for how they interact. It’s not that the answer is unknowable, but rather that it is beyond our ability to understand and calculate.

Heck, apart from a few special cases, we can’t even handle a simple three-body problem.

22. – There is a formal error in the link to your video: the colon is missing after https. recte: https:// etc.
– Changing double hyphens to a single em dash is a feature of many word processing programs. In Word and LibreOffice for example, somewhere in settings/preferences you will find a selectable list of such translations where you can switch this behaviour off.

Otherwise, food for thought, as usual. Thanks.

23. Even as a child (I’m 66), I understood that with enough practice, one could “steer” a “fair” coin-toss to a desired outcome.

24. Trippy

You tried pre tags. Never mind my previous comment.