""Go First" Dice" Topic

Hi, everyone. I figure many of you might be interested in an interesting set of dice I recently co-designed: "Go First" Dice. It is a set of 4 twelve-sided dice.

"Go First" Dice are a set of 4d12 dice that allow you to roll to see who goes first in a game. Big deal, right? EXCEPT:

1. These dice will never tie.
2. Regardless of whether all 4 are used or ANY subset of 2 or 3 dice are used (if fewer than four people are starting a game), the odds of rolling highest is always exactly fair.
3. The dice actually do more than just determine first player fairly, all permutations of possible rolls are fair for any subset as well… meaning that you can designate the person who rolled 2nd highest as Second Player, 3rd highest as Third Player, and 4th highest as Fourth Player.

More information are available at my website:

link

Cheers,

Eric Harshbarger

Very clever ! You might want to consider a patent.

How is it that these dice will NEVER tie? Granted the odds of 2 players rolling exactly the sime sides on 4 d12s is 12 to the 4th power – but that isn't never

Check the charts – the dice that are rolled are all different.

You'd think the die with the "1" would have an advantage but the results table clearly shows it doesn't.

I can see how that would work.

Sounds like a good design.

Clever, but what is the big problem with re-rolling a tie? Or using the Saga "most impressive facial hair" rule?

Looks like a solution in search of a problem…..

Daft idea. Far simpler for each player to draw a card from a standard pack of playing cards. Highest goes first. Simple.

It is not a simple problem with a simple solution. It is an incredible solution, to a difficult problem.

It also solves players down to 4 so ranks them.

(I do wonder if it is possible to create a set of dice that do the same for 8 players)

I like dome of the dice on the website – and I have one or two ideas that I would like to fit to dice mathematically – I might set him a geeky challenge.

It is not a simple problem with a simple solution. It is an incredible solution, to a difficult problem.

What randomizing the order of play for a number of players?
Dead simple!!

It also solves players down to 4 so ranks them.

(I do wonder if it is possible to create a set of dice that do the same for 8 players)

As I have said, dead easy with a pack of cards. A pack of cards can randomize the order of play for up to 52 players! Why use dice when cards are so much easier, simpler and cheaper (and probably quicker)?

Not only that, but if each player retains their drawn card then there is no confusion over who scored what on the dice and no need to remember the scores.

Dice are not the answer to everything in game design.

Dice are not the answer to everything in game design.

That is heresy

There are certainly simple(r) ways to determine order for playing a game (drawing cards, drawing straws, modulo arithmetic), but I thought some people on this board might appreciate the mathematics behind the dice.

Whether or not there is a similar set of such dice that works for more than 4 players is unknown at this point. I (we) have been trying to construct a larger set for some time no, but to no avail.

It is known that a five player set would require at least 30-sided dice, possibly 60-sided or more; and if you wanted 7 players, the number of faces on the dice would have to be divisible by 7; and there is not an "elegant" geometric shape that satisfies that condition.

This was a "problem" that quickly became more academic than practical, but remianed interesting (at least to me and a few friends) nonetheless.

Eric Harshbarger

Inari7… You got me with that one…

As I have said, dead easy with a pack of cards. A pack of cards can randomize the order of play for up to 52 players! Why use dice when cards are so much easier, simpler and cheaper (and probably quicker)?

Dice don't have to be shuffled first every time you use them. Pick up dice, drop, look, done.

It's not really a big deal either way, but this dice idea is clever and amusing to me. But then, I happen to be one of those people who just like dice, and think it's fascinating how they can be modified and altered in unusual ways to produce out-of-the-ordinary results.

P.S. Cards are not truly random; they merely have the appearance of it, as the "shuffle" is only random in the sense that humans rarely can produce a perfect 1 to 1 interlacing of two halves of the deck, or a perfect cut. If you could, the ordering of the cards would be mathematically predictable after every shuffle and cut! The act of shuffling also determines the placements of a card, so that the result of the first draw is actually not equal in probability to the result of the second draw, and so on. That's why counting cards works in Blackjack, and why casino owners get p'o'ed if you can do it.

With dice, however, the probability of each event never changes, regardless of how often you roll. There is no advantage to being the next to roll in a dice roll off, whereas there very well could be an advantage (or disadvantage) in being the next to draw from a deck.

Eah! Just draw cards from a deck of cards, 2 times as many cards as you have players. spread out on the table. You picking one each at the same time is as random as the world can get.

the "shuffle" is only random in the sense that humans rarely can produce a perfect 1 to 1 interlacing of two halves of the deck, or a perfect cut.

A perfect 1 to 1 interlacing of two halves of the deck would not be random!

The act of shuffling also determines the placements of a card, so that the result of the first draw is actually not equal in probability to the result of the second draw, and so on.

Exactly. You don't want it to be. If it was you would have the possibility of two players drawing the same card – which defeats the object.

A perfect interlacing of two halves of the deck would not be random

That was my point. The shuffle doesn't start from a random premise to begin with; the only thing that makes it random is the fact that humans probably won't achieve a perfect interlacing. Thus what you have with a deck of cards is not actually a randomized set of choices but a broken pattern of choices, some of which still remain in their initial pattern and some of which remain in subsequent patterns. It's not truly random at all, it merely appears to be because most people don't bother to (or can't) calculate the actual probabilities of the patterns that occur. So a deck of cards does not actually produce a "fair" distribution of probabilities that any individual will wind up going first. Remember this very important rule: Patterns, by definition, are not random.

If you use a four-person situation with four cards there are in fact only 24 possible patterns that can be produced, which is pitiably small. Furthermore, the odds of being first in the first draw are 25%. The odds of being first in the second draw are either 33% or 0. In the third draw 50% or 0, and in the last 100% or 0. Thus it isn't actually a "fair" draw in terms of equal probabilities for any given event.

The Go First dice, however, provide an exactly equal chance of being first for each participant while still producing exclusive results.
As in the card example, no two rollers will wind up with the same result— only one will be first, only one will be second, only one will be third, etc.— but the chance to wind up in any given position is always completely the same for all four rollers.

Four dice bouncing around on a tabletop, with 0 possibilities of exact results, yet equal probabilities of being any one of 4 ordinal results? It actually doesn't get more random than that!

Now, I don't know that this fact is all that significant in terms of gaming, but it is mathematically quite fascinating and remarkably ingenious.

Yeah, don't listen to the naysayers Eric – it's a very clever solution. Of course probability has always intrigued me. I'll be emailing you this weekend about an order !

The Go First Dice are old news … Eric

What have you got that is new? :)

This post is mostly a joke .. I just wanted to get in a link for those who wanted to see these amazingly innovative dice

Show me the math…