Non-transitive Dice(singingbanana.com)
singingbanana.com
Non-transitive Dice
http://singingbanana.com/dice/article.htm
6 comments
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%...
JTs > 22 : http://twodimes.net/poker/?g=h&b=&d=&h=2h+2d%0D%...
22 > AKo : http://twodimes.net/poker/?g=h&b=&d=&h=2d+2h%0D%...
AKo > JTs : http://twodimes.net/poker/?g=h&b=&d=&h=Ah+Kd%0D%...
JTs > 22 : http://twodimes.net/poker/?g=h&b=&d=&h=2h+2d%0D%...
22 > AKo : http://twodimes.net/poker/?g=h&b=&d=&h=2d+2h%0D%...
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.
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.
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.
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:YwutCvF...
Looks like a great game for on subways/trains and such to scam people a bit. I'm impressed.
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.