[munk-a]

Possibly, though if we want to be pedantic "weighting" has shifted from merely meaning "increased in weight" to meaning "biased through manipulation" - colloquially you can describe a situation as "weighted against someone" if you think that person may be unfairly disadvantaged - like in a multi-talent contest a continued draw of activities that favor one party using a hidden method that is suspected to be directed to the end of favoring that party.

You absolutely can manufacture unfair coins either using a two surfaced approach (like a weak magnetic field acting on a magnetized coin) but even a one surfaced approach is possible if you make use of carvings on the surface of the coin to get a favorable result from air resistence - lastly you can even achieve it through density, if one side of a coin is significantly more dense then the other then it will tend to land face down - you can play with this a bit by trying to flip a weighted cylinder and observing the landing pattern - I might suggest taking a coin roll (like you get in a bank) and gluing some coins into one end of it - then try and flip it in the air so it lands coin-side up.

It is, however, very hard to bias a coin significantly without skewing the dimensions or having clear alterations visible on the coin.

[jackpirate]

To add to your point: I ran some experiments a while back with curved coins. The coins have to be absurdly shaped before the shape affects the outcomes:

https://izbicki.me/blog/how-to-create-an-unfair-coin-and-pro...

[Retric]

Falling below the noise floor is different from proving no correlation. Negative results for a given experiment simply mean it’s below an the experiments ability to detect.

Aka, you need to pick a threshold for bias that’s interesting before designing the experiment. A casino might care a great deal about say 0.5% bias which would take a lot of trials to detect.

[mythz]

I respect the level of free time taken to run and publish this experiment!

Interesting results, I thought they'd be more skewed.

[thedirt0115]

The parent comment that a coin of lead and balsa wouldn't be biased, but to clarify, the linked research paper states it can't be biased unless allowed to bounce/spin. Maybe your weighted cylinder flipping is not biased if you throw+grab instead of letting it land?

[paulmd]

> Possibly, though if we want to be pedantic "weighting" has shifted from merely meaning "increased in weight" to meaning "biased through manipulation"

Not sure what your point is here. Yes, that is the meaning that is being discussed. You understood it yourself. Grandparent understood it as well. What value do you feel bringing up this point brings to the debate?

> like a weak magnetic field acting on a magnetized coin

Probably not. The field will act through the other face of the coin as well. The coin is pulled towards the magnetic surface, but it doesn't alter the revolution of the coin. If the field is sufficiently weak to not pass through the coin then it wouldn't have any impact on the other side either.

The exception would possibly be mu metal or something else that prevents the magentic field from acting on one face entirely, in combination with a strong magnetic field, and I'm still going to lean towards "probably wouldn't work". It would still intermittently pull the entire coin towards the surface, it's not clear that it would counter the rotation of the coin itself.

> even a one surfaced approach is possible if you make use of carvings on the surface of the coin to get a favorable result from air resistence

No, because air resistance is acting on both sides of the coin at once. The air resistance is a constant A+B, not A,B,A,B.

> lastly you can even achieve it through density

No, this is the entire point of the article. The coin doesn't revolve around its geometric center, it revolves around its center of gravity. By changing the density of one side (balsa wood and lead, as I said) you change the center of gravity but the coin itself has the same rate of revolution.

[catblast]

> Grandparent understood it as well.

Considering you were the grandparent, I guess that should be somewhat reassuring.

FWIW, I interpreted your use as rigid in the same manner as the GP (of this post).

As far as I’m concerned a electronic bistable generator that is biased through manipulation is effectively a “weighted coin”.. those exist.. and are counter to your claim unless you restrict “weighted coin” to the completely literal.

[paulmd]

> Considering you were the grandparent

God no, GP here means the contextual grandparent of the topic, as it always does. GP means the person I responded to. Why in the world would I respond to myself just because "GP"?

If you haven't read the rules, you need to be giving the most gracious reading of the comment chain here. Pretty obvious what the implication was. Try reading again.

> As far as I’m concerned a electronic bistable generator that is biased through manipulation is effectively a “weighted coin”

Oh cool you're trying to impose a change of topic from the ability to literally bias a coin when a normal person flips it randomly, into telling me to defeat... all attempts of people manipulating all RNGs ever?

Super weird angle for a discussion about flipping coins. Not really interesting.