Prologue: Why Randomness Is (Not) Hard in Real Life
Disclaimer: I might have designed too many probability theory basics exam questions in my life; whether this left permanent damage is up to you to judge.
What I really like is finding mechanical apparatus that behave randomly: That's slightly surprisingly a bit of a challenge: Our reality is full of true randomness, and unless you restrict yourself to (often rather artificially-feeling) experiments where that is really not the case (like drawing colored marbles from an urn without putting them back, or cards from a deck), you can model extremely many phenomena as truly 50/50.
Small problem is that these really random effects tend to happen on a microscopic or very weak level – you need some amplification to see them! That's why the computer (or phone) based answers are excellent: These devices both include true random number sources1,2: because they're anyways based on electronic logic dealing with very small phenomena, it's inherently possible to measure these small random effects and translate them into values observable by software. (People like to say that "randomness on a deterministic machine like a computer is hard", but that's not really the case. Millions are spent keeping the random behaviour out of a computer processor, each time one is designed, because the effects that make your computer work are really only a bit stronger than what noise you can expect. And that noise is random.)
Building a Good Tosser
Good: Truly fair, truly uncorrelated, and most of all: fast and easy to use
Now, I think computers are cool; I really think that a neat little box with a small half-spherical dome on top where a small "coin" disk is spun on a horizontal axis by a motor, controlled by a 1€ microcontroller that takes a bit of truly random external input to compute nearly arbitrarily many random throws would be the nicest solution in terms of usability. Put a little momentary switch on the bottom of the box to trigger the "toss" with a satisfying *smack* on the top.
It will be quite hard to beat that in terms of fairness and uncorrelatedness, in addition of the ease-of-use³.
Building a 🤌 Beautiful Randomification Device
But the hardcore usability and probability side ignored, what mechanical ways are there to amplify a small random effect in a way that stays really random.
Two devices that already exist come to mind:
Just like the actual coin toss, this isn't actually random: toss a coin twice in exactly the same way, it will land the same way. There's a deterministic input/output relationship. The thing is that humans just aren't great tossers, so that basically never happens in amateurs (whether someone could train to throw a coin reliably, I guess they could! Have you seen olympic archers?).
The main thing why "throwing a coin" seems fair is that the movement it makes for the methods we usually use when throwing seems chaotic, i.e., tiny changes in input conditions lead to very drastic changes in output.
Here's a picture of one possible implementation of a magnetic pendulum:
Source: Chalk Dust Magazine, Authors James Christian and Holly Middleton-Spencer, Link
You can build one with an even number of magnets, as well. It's very hard to predict from the initial position at which magnet the pendulum will end up; I found the simulation on this website very beautiful.
Now, this is Fancy (capital F) and overkill, because in the form that you usually see it it's used to demonstrate what happens when you chain a lot of identical, but independent, random decisions:
Source User Matemateca (IME USP); CC-BY SA 4.0
The loads of balls are dropped through the narrow channel on top, each of them hits various pegs on the way down, and each time takes a random left or right. See the device in action here.
Of course, instead of throwing hundreds of balls at once, you could throw one down the chute (that ends up being a game quite similar to Pachinko), and base your head/tails decision on whether it comes out left or right.
Because you don't care to see the beautiful Gaussian distribution, just the half it comes out in, you could omit the outer pegs on the lower rows, where a deflection can no longer change the side the ball comes out.
Technically, of course, you would need but a single peg and a very precise chute for your ball, but keeping tolerances and sizes in check, at least a few pegs which stand a fair chance of cancelling bias is probably a good idea; also, more clang = more fun.
¹ on x86 (i.e., your laptop/desktop):
² on ARM application processors (i.e., in your phone, your TV or your smart camera), you typically find peripherals that offer true physical random numbers at some address in memory space
³ I might be crazy enough that if someone funded me for that product development, I might be willing to undertake that engineering effort.