The carefully arranged numbers 1-48 on the four d12s guarantee the following properties when used to see who will go first (each player will take one of the dice and they will roll against one another):
- First, there will never be a tie.
- Second, and here was the tricky part in designing the dice, regardless of what subset of dice are rolled against one another, each player will always have an equal chance of rolling the high number (and thus being the “starting player”). Put another way, two, three, or four players may each take one of the dice, roll it, and each will always have a 1/2, 1/3, or 1/4 chance, respectively, of having the highest result.
- Finally, not only can the set (or any subset) be used to determine First Player, but the rolled numbers may also be used to determine all starting positions (the 2nd highest number can be the Second Player, the 3rd highest the Third Player…) The chances of all permutations of any given subset of dice are equal, so there would never be the chance of a particular subset favoring some ordering of the players.
“Go First” dice were used at the start of the TableTop “Sheriff of Nottingham” playthrough.
From the US dice maker Eric Harshbarger – have a look at the other specialist dice he makes.
If you have a game with more than 4 players, you could pre-qualify people for the dice-roll, by getting everyone to flip a coin and everyone who flips heads, goes through to the roll-off.