Of course, if one of the two players has memorized the first million digits of pi and the other has not, the one who has not could just ask for the nth digit.
Do you think that insects just wander around aimlessly? I guess that’s the way human activity probably looks to our hyperintelligent insectoid alien overlords. Why not just blindfold a human, put him in the middle of the wedge circle, take off the blindfold and see which way he goes.
First thing that came to my mind (and someone tell me why I’m incredibly wrong, which no doubt I am):
Get six leaves that are lighter colored on one side than the other. Go somewhere that they won’t blow away or get mixed up with other leaves. Toss them in the air. Count the number that land lighter-side up.
Yes that’s smart.
But I think my method of tossing a pebble onto a checkerboard grid is probably easier to set up fair than trying to find the perfect pebble that will function as a fair coin, and once it’s set up it’s easy to run. Your method of overcoming an unfair coin-pebble is clever but adds a lot of iterations.
Still, I guess if you find a candidate fair coin-flip pebble, it’s easy enough to test if it’s approximately fair by just tossing it a bunch of times.
Expanding on the fingers idea, since it’s the simplest and quickest.
Pick 6 different hand-shapes and assign them numbers: 0. Rock, 1. paper, 2. scissors, 3. heavy-metal horns, 4. thumb-forefinger circle “ok”, 5. thumbs up.
Each player throws one, add the numbers together and mod 6.
No supplies needed, no multiple iterations, no bias.
It does have the limitation that humans aren’t particularly good at randomization, so clever players can nudge the outcome by observing the other player. (“Good old rock. Nothing beats rock”). On the other hand, it also trivially expands to more people. The more people you have, the harder it is to game.
May I just say, filmore, this is one of the most entertaining questions raised on this board since I’ve been here.
Yes, and this is mathematically equivalent to a fair coin toss. This is how hardware real random number generators (that is, not pseudo-RNGs) are implemented. The only drawback is the farther from fair your real coin is, the more tosses you have to make to get a fair toss.
You’re incredibly wrong. 
That’s going to approximate a normal distribution rather than a uniform distribution.
If the goal is to just get a bit from a coin, it needn’t be a fair coin. Flip twice. Reject HH and TT. If TH, bit=0. If HT, bit=1.
Any bit-by-bit generation, though, strikes me as too inefficient for really playing games unless it was a one-off event. A grid + pebble approach could use grid markings that run from 1 to any small integer (vs. just two types of grid values), and a container full of marked seeds or pebbles drawn with replacement also saves the multi-bit processing.
Sure, but you can just use the binary outcome and do it three times. I’m sure we all love the idea of spending our years on a desert island raking leaves up and throwing them in the air over and over again.
I think this is the winner to get closest to truly random. The problem with other methods listed is the requirement for evenly spaced/correctly drawn type of thing.
Even or odd would be just about impossible to influence if the items are small enough and numerous enough.
Yes, it kind of depends on resources. If you have a large flattish area of slickrock that you can scratch measured lines on, it would be easy to draw a large enough grid with small enough squares that you mark squares 1-6 and just do one iteration. It would require that much more care to make the areas equal, though. But with a fine enough grid, and rules about how you have to toss the pebble, it would be impossible to deliberately bias the outcome.
My biggest worry with this technique is how often arguments would break out over which square the pebble is actually sitting in.
Well, if there’s no consensus on which square it’s in, obviously you just pull a quarter out of your pocket and call heads or tails.
It seems like there’s an underlying joke here. Like, how do you tell if two nerds are lost in the woods?
Any of the methods requiring tossing, dropping, etc. of objects is open to manipulation because as mentioned in the OP it’s difficult to make a fair die even if you could make a reasonable cube. If you made a wooden cube you could toss it repeatedly, sanding down any side that ends up on the bottom repeatedly. The cube is troublesome though because adjusting one side could affect the adjacent sides and you may run out of cube before tossing seems to give you random results.
A spinning device might be the solution. Just find some fairly symetrical balanced object and a hard flat rock and do it like spin the bottle.
Most leaves I’ve seen are at least a little bowl-shaped, which would seem to bias them to generally land with with the same side down.
Sometimes the leaves in my garden fall up. Usually when I’m trying to rake them.
Too dismissive. You’re lumping the good methods with the bad. Could you toss a tiny pebble onto a chessboard from a couple of feet away and manipulate whether it landed on a black or white square?
How long am I on the island? With enough practice, yes (at least enough to skew the numbers). Probably no harder than hitting bulls-eye with a dart.
I’d make a die out of mud, left to dry in the sun. Possibly even “fire” it over a campfire, like pottery.
If you are on an island I assume you are playing in the sand. Just carve a die. Even it’s a little off throwing it in sand will should balance out any imperfections.