Imagine you and a friend are lost in the wilderness or on a deserted island and you want to play a game like backgammon to pass the time. It’s simple to make the game board and pieces from primitive materials. You can draw the board in the dirt and use dark/light stones for the pieces. But how would you come up with dice or something which could work like dice? That is, some method to produce a random number from 1 to 6. Even if you could make a cube from wood or rock to be a die, it would almost certainly not be evenly weighted and typically land on a certain side.
Basically, just using things like body parts, rocks, sticks, dirt, etc., what method can you use to make a random number generator for the numbers 1 through 6?
Using an improvised compass (a string and stick will do), draw a circle in the dirt and divide it into six wedges. Place sticks at the borders to separate the wedges, and a stone at the center of the circle. Drop a pebble on the center stone and whichever wedge it bounces into is the “roll”.
Interesting idea, but the shape of the center stone will tend to deflect the pebble in a certain direction. Is there another way to utilize the 6-wedge circle?
That would work great, but probably just a few times. The savvy player will start to recognize the sticks and pick them in a specific order. Could the sticks be dumped on the ground and their pattern be used to calculate a number? Or something where a savvy player wouldn’t be able to manipulate the outcome?
Using two gourds, open one and take out it’s seeds. Dry them, then divide into six groups with equal numbers. Tag each group differently somehow: staining or scratching or writing, etc.
The other gourd must be hollowed out intact and dried. A narrow neck is preferred. Once it’s dried, put the dried seeds into it.
To generate a random number, shake the gourd until exactly one seed comes out. Whichever group it’s a member of determines the random number. Always replace seeds before shaking again.
Rather than trying to construct something with 6 outcomes, it will be much easier to construct a fair device with just two outcomes, and run it 3 times. Take a bunch of seeds, shake a random handful out. Odd or even. Repeat 3 times for 8 outcomes. I’m sure that can be improved upon, but I think an easy to use binary device is the way to go.
Take six pebbles of approximately the same size. Scratch the numbers 1-6 on them. Shake them in your hands, then open just enough so that one pebble falls out.
On the count of three, each player puts out a number of fingers (between 1 and 4). If both players pick the same number you try again until they differ. Multiply the two numbers together and map them in the following way:
If the answer is 7 or 8, ignore and rerun, obviously.
A single run mod 6 requires a much larger number number of seeds to be approximately fair, because there’s a problem of bias toward lower numbers. Binary with 3 iterations is better, I think.
But I’m thinking there’s probably a simpler physical way to generate binary outcomes that can be set up pretty fair. Tossing a pebble and having it land on an evenly measured grid of squares, perhaps, analogous to a checkerboard with alternate black/white squares. Unlike a coin toss, that’s independent of the shape of the pebble. And a grid with fairly small squares rather than just “one side of a line or the other” removes bias to tend to throw it up slightly to one side or the other.
Agreed. If you find three thin flat rocks (you can sometimes find these at the seashore, or somewhere where there’s rock like slate that comes in sheets) that can land either side up with equal probability, just mark one side on each and flip them. There are eight possibilities, but you ignore those two – if they come up, flip all three again.
Actually, it’s easiest to just use a six-sided die. These were originally manufactured from bone (I have an antique Mah Jong set with such bone dice). In fact, they used to use “knucklebones” made from the talus bones of animals. If the die slightly favors one side, you can either try paring it down until you get uniformity, or you can live with the unequal probability – it’ll equally inconvenience both of you.
ETA: if you imagine a chess board, it’s analogous to tossing a little pebble onto it and the outcome is whether it lands on a black or white square. Pretty much impossible to cheat if you scale it right and mark out the grid evenly.
This isn’t random unless both players are choosing randomly.
A player who puts one finger in knows that the result will never be higher than 3. A player who puts 4 fingers in knows that the result will only be 3, 5, or 6, etc.
each player has 6 pebbles noticeably different from each other, it’s agreed beforehand what each pebble is worth from 0-5. Each player chooses one of their pebbles, if the total is 0 then it’s a 6 otherwise take either the value or value-6 to get a value between 1-6. No matter what your opponent does you have a choice of 6 pebbles each corresponding to 1-6 but you don’t know which is which until you see your opponent’s. This would eliminate any chance of cheating/accusations of cheating as well.
For this task, I’m not sure that’s significantly superior to Person A just writing down the numbers 1 through 6 in pseudo-random order in 6 spots, covering each spot up with a rock, and Person B chooses one rock to lift up and reveal a number.
If you wanted to improve that method, you could do it with two (or more) iterations: each person writes down the numbers 1-6 in pseudo-random order in 6 locations and covers them up with 6 rocks. Person A chooses one of Person B’s rocks, and the outcome of that refers back to which of Person A’s rocks is uncovered.
Simplest is to have a way to generate 50-50 bits; call them Head/Tail bits.
Don’t ignore it completely. Treat 7 as Head and 8 as Tail — now you need only two more bits for the next round, instead of three.
One way is to start with a coin-like object: something that can be flipped to land on one of two sides, even though it might be 60-40, say, instead of 50-50.
Flip that quasi-coin TWICE:
H,T –> Head
T,H –> Tail
H,H –> Try again
T,T –> Try again