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Old 01-11-2018, 12:13 PM
filmore filmore is offline
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How to create a random number generator for 1-6 with just natural supplies in the wilderness?

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?
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Old 01-11-2018, 12:23 PM
Lumpy Lumpy is offline
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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".

Last edited by Lumpy; 01-11-2018 at 12:24 PM.
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Old 01-11-2018, 12:25 PM
Chingon Chingon is offline
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Draw straws, using six of them. The generated number is the ordinal in which the short straw is picked.
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Old 01-11-2018, 12:27 PM
filmore filmore is offline
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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?
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Old 01-11-2018, 12:30 PM
filmore filmore is offline
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Draw straws, using six of them. The generated number is the ordinal in which the short straw is picked.
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?
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Old 01-11-2018, 12:36 PM
Pleonast Pleonast is offline
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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.
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Old 01-11-2018, 12:37 PM
Riemann Riemann is offline
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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.

Last edited by Riemann; 01-11-2018 at 12:40 PM.
  #8  
Old 01-11-2018, 12:37 PM
Peter Morris Peter Morris is offline
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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.
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Old 01-11-2018, 12:38 PM
TriPolar TriPolar is offline
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Some of the methods used for I Ching divination may work.

Maybe Buffon's Needle could be modified to produce numbers between 1 and 6 also.
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Old 01-11-2018, 12:42 PM
Pleonast Pleonast is offline
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Originally Posted by Riemann View Post
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. I'm sure that can be improved upon, but I think an easy to use binary device is the way to go.
Your method has 8 outcomes. How would you fairly convert that to 6?

Instead, take your seed method and instead of doing an even-odd test, take the number modulo 6.
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Old 01-11-2018, 12:44 PM
Chingon Chingon is offline
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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:

2 -> 1
3 -> 2
4 -> 3
6 -> 4
8 -> 5
12 -> 6
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  #12  
Old 01-11-2018, 12:47 PM
Riemann Riemann is offline
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Your method has 8 outcomes. How would you fairly convert that to 6?

Instead, take your seed method and instead of doing an even-odd test, take the number modulo 6.
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.

Last edited by Riemann; 01-11-2018 at 12:52 PM.
  #13  
Old 01-11-2018, 12:47 PM
CalMeacham CalMeacham is offline
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Originally Posted by Riemann View Post
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.
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.
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  #14  
Old 01-11-2018, 12:54 PM
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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.
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Old 01-11-2018, 12:54 PM
iamthewalrus(:3= iamthewalrus(:3= is offline
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Originally Posted by Chingon View Post
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:

2 -> 1
3 -> 2
4 -> 3
6 -> 4
8 -> 5
12 -> 6
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.
  #16  
Old 01-11-2018, 12:55 PM
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How about one person drawing a ghost leg and the other person choosing a starting point at random?
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Old 01-11-2018, 01:05 PM
Mr Shine Mr Shine is offline
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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.
  #18  
Old 01-11-2018, 01:07 PM
Riemann Riemann is offline
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How about one person drawing a ghost leg and the other person choosing a starting point at random?
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.
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Old 01-11-2018, 01:08 PM
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Simplest is to have a way to generate 50-50 bits; call them Head/Tail bits.
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If the answer is 7 or 8, ignore and rerun, obviously.
Don't ignore it completely. Treat 7 as Head and 8 as Tail ó now you need only two more bits for the next round, instead of three.

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Originally Posted by Riemann View Post
But I'm thinking there's probably a simpler physical way to generate binary outcomes that can be set up pretty fair.
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
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Old 01-11-2018, 01:10 PM
Willcross Willcross is offline
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You could draw the six wedge circle and instead of a pebble, you drop a beetle or any in the center and see which wedge it exits the circle from.
  #21  
Old 01-11-2018, 01:11 PM
Riemann Riemann is offline
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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.
  #22  
Old 01-11-2018, 01:13 PM
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You could draw the six wedge circle and instead of a pebble, you drop a beetle or any in the center and see which wedge it exits the circle from.
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.
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Old 01-11-2018, 01:15 PM
Max Torque Max Torque is offline
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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.
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Old 01-11-2018, 01:16 PM
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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.
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.

Last edited by Riemann; 01-11-2018 at 01:21 PM.
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Old 01-11-2018, 01:21 PM
iamthewalrus(:3= iamthewalrus(:3= is offline
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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.
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Old 01-11-2018, 01:24 PM
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May I just say, filmore, this is one of the most entertaining questions raised on this board since I've been here.
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Old 01-11-2018, 01:27 PM
Pleonast Pleonast is offline
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Originally Posted by septimus View Post
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
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.

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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.
You're incredibly wrong. That's going to approximate a normal distribution rather than a uniform distribution.
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Old 01-11-2018, 01:29 PM
Pasta Pasta is offline
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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.
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.

Last edited by Pasta; 01-11-2018 at 01:32 PM. Reason: I see the double-flip was already mentioned upthread...
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Old 01-11-2018, 01:30 PM
Riemann Riemann is offline
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That's going to approximate a normal distribution rather than a uniform distribution.
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.
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Old 01-11-2018, 01:32 PM
RaftPeople RaftPeople is offline
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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.
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.
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Old 01-11-2018, 01:36 PM
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A grid + pebble approach could us grid markings that run from 1 to any small integer (vs. just two types of grid values)...
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.

Last edited by Riemann; 01-11-2018 at 01:37 PM.
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Old 01-11-2018, 01:45 PM
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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.
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Old 01-11-2018, 01:48 PM
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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.
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Old 01-11-2018, 01:57 PM
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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.
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Old 01-11-2018, 03:05 PM
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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.
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.
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Old 01-11-2018, 03:13 PM
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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.
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Old 01-11-2018, 03:15 PM
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Any of the methods requiring tossing, dropping, etc. of objects is open to manipulation...
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?

Last edited by Riemann; 01-11-2018 at 03:16 PM.
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Old 01-11-2018, 03:42 PM
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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.
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Old 01-11-2018, 03:46 PM
Tim R. Mortiss Tim R. Mortiss is offline
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I'd make a die out of mud, left to dry in the sun. Possibly even "fire" it over a campfire, like pottery.
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Old 01-11-2018, 04:01 PM
Lucas Jackson Lucas Jackson is offline
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If you are on an island I assume you are playing in the sand. Just carve a die. Even itís a little off throwing it in sand will should balance out any imperfections.
  #41  
Old 01-11-2018, 04:09 PM
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Quote:
Quoth Chingon:

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:

2 -> 1
3 -> 2
4 -> 3
6 -> 4
8 -> 5
12 -> 6
Even if both players choose their number of fingers randomly, this still isn't fair. The other numbers all have two ways to come up, but a product of 4 (result of 3 in your mapping) can come up three ways: 1*4, 4*1, or 2*2.

You're also neglecting 16, but I guess that's just a re-roll.
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Old 01-11-2018, 04:14 PM
Blue Blistering Barnacle Blue Blistering Barnacle is online now
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I like the modulo 6 of sum of six finger signs mentioned upthread. Sounds quick and efficient. Some psch-out potential, though.

instead of fancy signs, they could put out 0 (fist) to 5 fingers.

You could even do both hands together, and get both dice at once.

Last edited by Blue Blistering Barnacle; 01-11-2018 at 04:17 PM.
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Old 01-11-2018, 05:35 PM
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Step 1) Murder your friend and eat his flesh.
Step 2) Whittle dice from his bones.
  #44  
Old 01-11-2018, 05:35 PM
Hari Seldon Hari Seldon is offline
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Originally Posted by Pasta View Post
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.
I like this solution the best. I propose a better variant. Throw a coin four times. Six times out of 16 you will get two heads and two tails. Assign each one of the six a number 1 to 6. Ignore the other 10 possibilities. So you get a number 37.5% of the time. I haven't figured it out, but I guess you will need more throws to get 3 binary digits than you will here to get a number between 1 and 6.
  #45  
Old 01-11-2018, 06:29 PM
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Even if both players choose their number of fingers randomly, this still isn't fair. The other numbers all have two ways to come up, but a product of 4 (result of 3 in your mapping) can come up three ways: 1*4, 4*1, or 2*2.

You're also neglecting 16, but I guess that's just a re-roll.
You missed the fact that he said re-roll if both players put out the same number of fingers. So it doesn't suffer from overcounting. But it does still suffer from a player being able to influence the outcome unilaterally.
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Old 01-11-2018, 07:50 PM
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Pick a decent-sized spruce branch, and count the needles, modulo 6. Hey, you was looking for a way to pass time!
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Old 01-11-2018, 07:56 PM
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Find six pebbles of similar, but clearly different sizes (representing 1-6). Player one buries them in the sand in a random no pattern area at the same depth about the size of a dinner plate with out player two looking and smooth's out the top of the sand. Player two would then poke a finger in the sand and with a swirling motion pulls out the first rock that gets exposed.

You may need a flat surface to place the rocks under the sand so that they are all the same depth.
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  #48  
Old 01-11-2018, 10:06 PM
Lucas Jackson Lucas Jackson is offline
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Quote:
Originally Posted by snfaulkner View Post
Step 1) Murder your friend and eat his flesh.
Step 2) Whittle dice from his bones.
Annnd... scene.
  #49  
Old 01-11-2018, 10:28 PM
Chronos Chronos is online now
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The first rock to get exposed would be more likely to be the largest one.
  #50  
Old 01-11-2018, 11:58 PM
glowacks glowacks is offline
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Have 6 distinct objects, and 6 numbered areas of sand. Have one person put one of the objects on each of the areas of sand while the other is looking away, then the former person moves into the sight of the latter but the latter remains without sight of the objects and names an object. The person positioning the objects would be unable to influence which object was on which area while in view of the person making the selection, and so could not change things once he knows what the other person is going to pick. The person without sight of the objects that picks one has no knowledge of where each of the objects are. Thus neither player can meaningfully physically influence the outcome, but might through psychologically outwitting the other person. That might be seen as a virtue to this system, not a drawback, adding to the game that one is playing. So not random, but just as good.
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