

Non-transitive Dice - amichail
http://singingbanana.com/dice/article.htm

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amalcon
This does a great job of demonstrating some of the curious effects of
premature rounding. The non-transitivity is only possible because after
generating a pair of random numbers, the outcome is rounded to one of two
values ("Win for Player A" or "Win for Player B"). If there was a notion of
"Player A won by two", then the dice could be ranked by expected value.

This is one reason why (for example) counting the number of studies that
confirm vs. reject a hypothesis is not going to give the best indication of
its validity. It's also why we don't track changes in market indices by
counting how many items increased against how many decreased.

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mattrjacobs
For any poker players out there, this is analogous to the Texas holdem preflop
matchups JTs, 22, AKo.

AKo > JTs :
[http://twodimes.net/poker/?g=h&b=&d=&h=Ah+Kd%0D%...](http://twodimes.net/poker/?g=h&b=&d=&h=Ah+Kd%0D%0AJs+Ts)

JTs > 22 :
[http://twodimes.net/poker/?g=h&b=&d=&h=2h+2d%0D%...](http://twodimes.net/poker/?g=h&b=&d=&h=2h+2d%0D%0AJs+Ts)

22 > AKo :
[http://twodimes.net/poker/?g=h&b=&d=&h=2d+2h%0D%...](http://twodimes.net/poker/?g=h&b=&d=&h=2d+2h%0D%0AAd+Kh)

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jat850
To elaborate on your point a bit, for the non-poker players (I am one, so I
understand your analogy, but non-poker players might not quite, at least in
this presentation):

Typically, when playing a game of poker, one considers a pocket pair (22, 33,
44, etc.) in a game of Texas Hold'em, vs. two "overcards" (2 hole cards bigger
than the pocket pair) to be considered, for quick calculation purposes, a coin
toss. However, the pocket pair in a given situation vs. two overcards of a
different suit, is a slight favourite overall.

So this problem typically presented - I believe it was originally stipulated
by Daniel Negreanu, a professional player, but I could be wrong - is, a
knowledgeable poker player challenges a poker player with less knowledge to a
speculative bet.

The knowledgeable poker player offers the opponent to choose a hand from the
following: AKo, JTs, or 22. Then the player on the up-and-up chooses second -
and given their knowledge of the slight advantage in a given situation,
chooses the hand with the higher odds.

However slight they may be, of course, the expected value always allows the
player choosing second to edge out the person who chose first.

Because they are so similar in odds, an average or below average player may
not realize the slight advantage 22 has over AKo, while JTs has the slight
advantage over 22. AKo over JTs is of course a larger advantage than the other
two situations - almost a 60/40 advantage.

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roryokane
There’s a Flash game about non-transitive dice at
<http://ded.increpare.com/~locus/OfDice/>, called Platonic Archetypes of Dice
(found via <http://www.metafilter.com/88574/Nontransitive-dice>). In the game
you start off with a normal die and battle NPCs in the manner described in the
article. After you defeat them, you get their die to battle the other NPCs
with. It’s actually a long, boring, tedious game, and you would only want to
play it to perhaps get a grip on the idea of non-transitive dice. If you do
play it, I recommend stopping playing after winning about three matches,
before getting sucked in trying to finish a timewasting, boring game.

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spyrosk
I'm getting a 509 bandwith limit exceeded so here's google's cached version,
without the images.

[http://webcache.googleusercontent.com/search?q=cache:YwutCvF...](http://webcache.googleusercontent.com/search?q=cache:YwutCvF5DbAJ:singingbanana.com/dice/article.htm+http://singingbanana.com/dice/article.htm&cd=1&hl=en&ct=clnk)

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tibbon
Looks like a great game for on subways/trains and such to scam people a bit.
I'm impressed.

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korch
This looks like a really good way to conceptually grasp how the probability
parts of quantum mechanics work!

~~~
powrtoch
This is not obvious to me, can you elaborate?

