I recently saw something cool about choosing which player should go first in a game. A lot of people roll dice, though ties can happen. One dice enthusiast came up with a set of four dice that can be used to determine who goes first among two players, with the awesome properties that:
* The dice only need to be rolled once (no ties), and
* Each die has an equal chance of being the highest among the four.
do this, the dice cannot have any ties. Four twelve-sided dice are
used, so the numbers 1 - 48 must be on them. The more complicated part
is how to arrange the numbers so that each player has a 1/4 probability
of winning the roll.
Is there a way to generalize this? If you have n players, what size
dice do you need? (How many sides?) If you have access to up to
20-sided dice, how many players does this support? For four players,
are 12-sided dice the smallest you need?
It seems like this must all be proven somewhere.
Another awesome thing I saw was this gaming shed
someone built, mostly to house all their board games, but also with a
place to play them. That forum post shows all the steps to create the
building. Very cool! I am extremely jealous! Someday perhaps I'll
have the funds to copy this exact thing.
There are many other things I desire, but these two are definitely worth sharing.
A Domino-Covering Problem
2 weeks ago