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

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*chortle* He doesnâ€™t know how to use the 2 seashells!

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

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A sphere with north and south flattened.
Youâ€™re welcome.

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Thatâ€™s basically a coin.

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That was my first thought as well, but itâ€™s not clear why thatâ€™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?

Iâ€™m trying to think of a way that two shells could ever be used so that it counter-acts any geometric imbalance, but I donâ€™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.

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

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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

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Iâ€™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 â€śfixing a biased sourceâ€ť is a solved problem.

I went hunting and almost immediately found this paper â€“ http://markus-jakobsson.com/papers/jakobsson-ieeeit00.pdf â€“ Early on, he makes reference to much earlier knowledge.

â€śVon 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.â€ť

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 â€śfirstâ€ť and one as â€śsecondâ€ť. This could be done with wood stain colours, where â€ślight = firstâ€ť and â€śdark = secondâ€ť. You also need to decide which side is â€ś1â€ť and which side is â€ś2â€ť. Letâ€™s make it â€śflat = 1â€ť and â€ścurved = 2â€ť.

Now you throw the linked pair. If you get â€ślight flat / dark curvedâ€ť, you have â€ś1â€ť. If you get â€ślight curved / dark flatâ€ť you have â€ś2â€ť. 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.

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â€śI donâ€™t know how to use thoseâ€ť

Live and Learn

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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 â€śyesâ€ť and â€śnoâ€ť.

Interestingly, the original question at Core77 was â€śHow Would You Design a Two-Sided Die That Isnâ€™t Flat?â€ť â€“ but nowhere did it say it has to be a fair two-sided die. Weâ€™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 itâ€™s â€śdownâ€ť, if it lands on the round side itâ€™s â€śup.â€ť

In ultimate frisbee, itâ€™s common to have a captain from each team flip one frisbee, and have a 3rd person call â€śsameâ€ť or â€śdifferentâ€ť while theyâ€™re in the air.

Itâ€™s an improvement because â€śsameâ€ť and â€śdifferentâ€ť are easier than â€śflat side upâ€ť, â€śround side downâ€ť, etc.

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

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

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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.

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No one has said a word about the middle option out of the three, and thatâ€™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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