# Quick way to tell if a set of dice is NOT non-transitive

Is there a quick way to tell if a set of six-sided dice cannot be non-transitive? I've writing an algo and brute force is taking too long to find out. I had a look at http://math.ku.edu/~jschweig/dice.pdf but it has a precondition that numbers on a die's face shouldn't repeat on other faces of that die or any other die. I want to allow the numbers on a die's face to repeat. It also restricts the number of dice to three and I want to calculate for larger number of dice as well. Any help will be greatly appreciated!

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What is wrong with applying the definition? That requires, for each of 3 distinct pairs of dices: 36 comparisons yielding -1,0 or 1; and adding these 36 values. Then, 3 comparisons of these 3 sums, and a decision based on that. For a program, that's nothing. – fgrieu Apr 24 '13 at 18:21
That sounds interesting. So here, are you assuming that numbers on each face of a dice range between 1 and 6? – bytefire Apr 25 '13 at 6:16
That works regardless of values on the faces. Your profile mentions programming, so.. For $n$ dices with $f$ faces, you need 3 nested loops, the outer one performed $n$ times with index $d$, and the two inner ones each performed $f$ times with indexes $i$ and $j$, comparing the value of face $i$ of dice $d$ to value of face $j$ of dice $d+1\bmod n$, adding the outcome $-1$, $0$ or $1$ to a score $s$ (initialized to $0$ before entry in the middle loop). The advantage of dice $d$ over the next dice $d+1\bmod n$ is $s/f^2$. Any non-positive advantage implies the dice set is NOT non-transitive. – fgrieu Apr 25 '13 at 8:17