

Amazing Dice: Rediscovering surprise - shawndumas
http://protonsforbreakfast.wordpress.com/2013/01/08/amazing-dice-rediscovering-surprise/

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datr
A UK investment firm called Gloucester Research used these for a cool
recruitment puzzle:

> You've probably come here via the dice we handed out at one of our
> recruiting

> events. By now you've hopefully noticed what's special about the 4 dice
> you're

> looking at: "red beats green beats blue beats white beats red", each with
> 66.7%

> probability. They are known as Efron's dice, and you can find some more info
> on

> this Wikipedia page.

> Your mission, should you choose to accept it, is to generalise the
> situation.

> For example, can you improve on the 66.7%? What if the dice are replaced by

> arbitrary random variables? What is the best "mutual beating probability" if

>you have only three dice? Or more than four?

It's a fun challenge and I'd recommend giving it a go if you have an interest
in maths.

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shawndumas
<http://en.wikipedia.org/wiki/Nontransitive_dice>

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andrewingram
The set with 5 dice is also more insane (you can buy all this stuff from
<http://www.mathsgear.co.uk/>), you can create a circle of dice that beat each
other going clockwise. But if you then double up the dice (two red, two blue
etc), the order switches to anti-clockwise. There's also a second (star-
shaped) loop in case someone works out how the first loop works.

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CurtMonash
The singular of "dice" is not "dice". Sigh.

Otherwise -- cool subject. I know about non-transitive voting (it was fairly
relevant to what I did in academia for a while). But I hadn't heard much
before about the dice. ;)

~~~
pja
The prescriptivists lost a long, long time ago: language is defined by usage.

You can be "correct" according to some prescriptivist definition of the
english language, or you can be understood by the people who actually use the
language to communicate. Since nearly everyone uses "dice" for both the
singular and plural form, and most people will never even have heard "die"
being used in this context, dice is the correct form.

~~~
CurtMonash
I guess you're saying that the dice is cast. :)

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auctiontheory
Very, very cool - thanks for posting.

The math principle here is similar to the logic underlying gerrymandering.

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VikingCoder
A friend of mine and I sat down and defined what we believe to be the best set
of 4 non-transitive dice. Our set has some great properties, like the numbers
1-24 each occur one time, each die has the same sum on its faces as the
others, each die has the number 1, 2, 3, or 4 on it (so they're easy to
identify.)

We manufactured about 10 sets of them, if I remember correctly.

I've wondered if we should Kickstart it. I can't imagine there'd be much
interest.

EDIT: I found my old rendering of what they'd look like:

<http://i.imgur.com/5EANlKp.jpg>

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petsos
The photo doesn't much the description.

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wasted_phd
much ado about nothing: if f is a linear function and g a non-linear one, it
is not surprising at all that f(g) != g(f)

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speeder
As a game designer this just stunned me!

I guess I will research more into that, and maybe see if I can pull a game out
of it!

~~~
groby_b
Try playing existing adversarial games with them. Instead of a single dice,
each player gets a set of them and picks one of them before rolling, without
showing it.

Risk gets much more fun that way, for example - because suddenly, even the
individual battles are about imagining you can read the other players
intentions.

