# Non-Transitive Dice

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Pt314
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Joined: 12/31/1969

Hello everyone, I haven't been here for a while, due to the fact that ever since I finished finals I haven't had much access to the internet.

Anyway I am still working on my card/board game and hopefully I should be able to fix enough stuff so I can upload it here for all of you to try out.

Anyway I have been thinking about non-transitive dice, and wondering if I can use them for interesting game ideas.

An example of non-transivity is Rock-Paper-Scissors, just because A > B & B > C does not imply that A > C.

Non-transitive dice are dice where die A has an advantage on die B, which has an advantage on die C, which has an advantage on die D, which has an advantage on die A. I have a set of four non-transitive dice where every die has another that has a 2/3 probability of rolling higher.

Heres a site that describes them, it also has lots of other neat stuff too.

http://www.jimloy.com/puzz/nontran.htm

Nazhuret
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Joined: 12/31/1969
Non-Transitive Dice

thank you for that link... it is very very interesting...

definately sparks some ideas....

FastLearner
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Joined: 12/31/1969
Non-Transitive Dice

Such a cool idea, thanks!

Fos
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Joined: 12/31/1969
Non-Transitive Dice

Perhaps I'm not thinking in the right direction...

For the non-transitive dice on the website, D has a 66% to beat C, C has a 66% to beat B, B has a 66% to beat A, A has a 66% to beat D, A has a 50% chance to beat C, and B has a 50% chance to beat D.

What I don't get is that these are all very simple ratios that can be aquired by a single die role, not requiring keeping track of 4 different dice. It seems like there would be easier mechanics that could get you the same results without all the bits required for non-transitive die...

One of the easiest applications I can envision with this is 4 players each getting a die, having advantages for rolling against the player to their left, and having an equal chance of rolling against the player across from them. Unfortunately, this seems to limit the game to 4 and only 4 players (not that much of a problem... lots of card games do that).

However, another way to accomplish this same mechanic is to simply say, "A successful roll against a player on your left requires 3 or greater on a D6, a successful roll against a player on your right requires 5 or greater, and a successful role for the player across from you requires 4 or greater." That system could be expanded to have a 50% chance for all players not to your immediate left or right, and would still have that interesting level of strategy.

EDIT:though now that I've thought about it some more...

a bidding system for the different dice would be pretty damn cool. It would still limit the game to 4 and only 4 players (the dice really only work as a set, and larger numbers of dice would need a completely different set to work together), but bidding (or any mechanic, really) to have a higher chance of rolling successfully against a specific player while putting yourself in jeapordy from another player might be fun. Problems: first player who picks his die would always be at a disadvantage, as would the last player, and the bidding mechanic (or any decision-making mechanic) would have to account for the unusual attractiveness in positioning.

However, you could also abstract out the non-transitive idea to the point where picking dice (or markers or whatever) only gives you slight strategic advantages and disadvantages against other players, and then you could even randomize the process. This might be a fun twist to a tactical game if it were paired up with a fitting theme.

Anonymous
Non-Transitive Dice

One option is haveing the (in/non)transitive relationship between the units in the game.

A medieval/fantasy example of this is:
Spearmen beat Cavalry (length of spear - gets first strike)
Archers beat Spearmen (can atack at longer range)
Cavalry beat Archers (move fast & better armored)

You then use normal dice to decide the outcome of the attacks.

This way you get the nontransitive relationship without the need of special dice.

From my understanding of the nontransitive theory is that it works better with an odd number of choices (you can do it with even numbers but there will be a slight dominance of one or more choices). So Scissors/Paper/Stone has 3 choices (same as my eaxmaple), but you can make them with 5, 7, 9, ...
(Hmm, a 9 way relationship with dice :D 8O ).

jwarrend
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Joined: 08/03/2008
Non-Transitive Dice

I was thinking along the same lines as Brykovian, but from my thinking, the dice are what create these relationships. So, one of the dice represents the spearmen, one represents the cavalry, etc. These dice give two big advantages over RPS or standard die rolling -- (a) uncertain outcome and (b) no ties!

Pretty cool, thanks for sharing. Definitely an interesting idea.

Also, I may be crazy, but doesn't the C die beat the A die more than 50% of the time? That might not be a bad thing...having a "most powerful" die could probably be modeled thematically as well...

-Jeff

Fos
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Joined: 12/31/1969
Non-Transitive Dice

jwarrend wrote:
Also, I may be crazy, but doesn't the C die beat the A die more than 50% of the time? That might not be a bad thing...having a "most powerful" die could probably be modeled thematically as well...

Yeah, I think you're right, but it's around 55% of the time. 1/3 of the time A loses no matter what, and 1/3 of 2/3 of the time A loses to C with a roll of 4 to 6. So it's a little more powerful, but not by much.

Anonymous
Non-Transitive Dice

Quote:
Quote: jwarrend
having a "most powerful" die

Having a "most powerful" die, breaks the idea of a nontransitive system. This will create a dominant strategy (ie grab the "most powerful" die first).

The idea was to create a circular system where there will alwase be one that can beat another.

jwarrend
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Joined: 08/03/2008
Non-Transitive Dice

Nautilus wrote:
Quote:
Quote: jwarrend
having a "most powerful" die

Having a "most powerful" die, breaks the idea of a nontransitive system. This will create a dominant strategy (ie grab the "most powerful" die first).

Not necessarily; in the context you articulated, where the dice correspond to different piece types, the "most powerful" die could also be more expensive, for example. The system above may not be properly "non transitive", but it could still work in a game.

-Jeff

Pt314
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Joined: 12/31/1969
Non-Transitive Dice

Just because one die can beat its oppisite counterpart 4/9ths of the time doesn't make it the most powerful. Its still a nontransitive system. It may not be a perfectly symetric system, but you could make one. In fact I have a set of nontransitive dice somewhere that is perfectly symetric, I just assumed they were idenical to those on the website before checking.