How do you design 2-sided dice that aren't flat?

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*chortle* He doesn’t know how to use the 2 seashells!


I think it works like this:
1 flat 1 round (2 possibilities) = 1
2 flat / 2 round (2 possibilities) = 2


A sphere with north and south flattened.
You’re welcome.


That’s basically a coin.


That was my first thought as well, but it’s not clear why that’s an improvement over a single shell.

That two-shell solution still only works if each shell has equal probability of landing on either side, and at that point why not just use one?

I’m trying to think of a way that two shells could ever be used so that it counter-acts any geometric imbalance, but I don’t see one.

Not any coins I have in my pocket. (Evilgrin)

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I think this one would work pretty well:

The die is cast by opening the lid.



my $result=int(rand(1));


Go outside and pick a blade of grass. Your opponent says Odd or Even. Measure the grass and round to the nearest milimeter.

Really, the term die is poorly defined :smile:


I’ve seen similar variations of that wooden 2 sided die, which is my favorite form factor of it beyond a coin.

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@SamSam, it turns out that “fixing a biased source” is a solved problem.

I went hunting and almost immediately found this paper – – Early on, he makes reference to much earlier knowledge.

“Von Neumann offers perhaps the earliest written reference to the problem of simulating unbiased coin flips using a biased coin. He describes the following trick from the folklore. Flip the biased coin twice. If it comes up HT, output an H. If it comes up TH, output a T. Otherwise start over.”

Since the two wood pieces are almost identical, we can accept for our purposes that they have the same probability. Then all that is needed is a way to mark one of them as “first” and one as “second”. This could be done with wood stain colours, where “light = first” and “dark = second”. You also need to decide which side is “1” and which side is “2”. Let’s make it “flat = 1” and “curved = 2”.

Now you throw the linked pair. If you get “light flat / dark curved”, you have “1”. If you get “light curved / dark flat” you have “2”. If you have anything else, you throw them again.

SamSam - big kudos for realizing that without some special process, you still need an unbiased shape to start with. I wonder if the person who created these even knows how to throw and read them.


“I don’t know how to use those”

Live and Learn


Jiaobei blocks is most cool. And I do love to live and learn.

However - from the description given, jaiobei do not give equal probabilities of “yes” and “no”.

Interestingly, the original question at Core77 was “How Would You Design a Two-Sided Die That Isn’t Flat?” – but nowhere did it say it has to be a fair two-sided die. We’re all just making that assumption. I myself think it is a very reasonable assumption, but it is not present in the original query.

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Those are similar to the wooden sticks used as dice in the ancient Egyptian game of Senet as well as for divination. Basically a cylinder sliced lengthwise. If it lands on the flat side it’s “down”, if it lands on the round side it’s “up.”

In ultimate frisbee, it’s common to have a captain from each team flip one frisbee, and have a 3rd person call “same” or “different” while they’re in the air.

It’s an improvement because “same” and “different” are easier than “flat side up”, “round side down”, etc.

Also, because if the contest is between 2 sides, each side can flip one shell (so long as they’re not tied together like the picture), thereby reducing perceived unfairness.


Small world, I have a patent pending with Markus. He is a very hoopy frood indeed. Very genuine and whip smart.


Take a regular six-sided die and choose any of a number of methods to equally map the existing values to either 1 or 2.


No one has said a word about the middle option out of the three, and that’s the best choice in my opinion. It still throws like a die, even looks like one, and the clever design makes it a conversation piece.

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