r24 dice rings

Congratulations, your r24 is the most versatile of all the wonderful dice rings!  You don't have a dice ring?  You can get one through their kickstarter until Dec 22, 2012 here: http://www.kickstarter.com/projects/critsuccess/dice-rings  or look for their retail store after the campaign.

This uncanny utility is because the number 24 can be broken down into its prime factors: 2*2*2*3 = 24 and these factors can be recombined to lots of other useful numbers.  As a result, you can very easily use it to naturally simulate any die that is a combination of these factors.  These natural combinations are as a d2 / coin toss, a d3, a d4 (2*2), a d6 (2*3), a d8 (2*2*2), a d12 (2*2*3) and of course a d24.  To easily translate your spin for these "natural" combinations:

1) You need to keep a magic number in mind.  That number is the result of dividing 24 by the size of the die you're simulating.  So if you want a d2, that number is 12 (24/2 = 12).  If you want a d6, that magic number is 4.  d8?  3.

2) Spin your ring.

3) Divide the spin result by the magic number in your head, rounding up.  You don't need a perfect result, only the whole number portion and if there is any remainder, so you can round up.

Let's do some examples for a d6.  The magic number you're going to keep in your head is 4 (24/6).
  * you spin a 17.  17/4 is "about 4, with some remainder" so you've rolled a 5 on your d6!
  * you spin a 3.  3/4 is "0 with some remainder" so you've rolled a 1!
  * you spin a 24.  24/4 is "6, no remainder" so you've rolled a 6!

Your r24 can also serve as any other dice with fewer than 24 faces, if you remember two simple things: (1) your magic number is 24 divided by the size of the die, rounding DOWN; and (2) if you overshoot the highest number, you must reroll.  For a d10 or d20, these rerolls will amount to 1/6th (16.67%) of your results, which is pretty reasonable to get a d10 or d20 roll from your one ring! You could even do a d100 in a pinch, with two consecutive d10 spins!

Let's look at some examples for a d10.  Your magic number here is 24/10 = 2.  Remember to round down for the magic number, and up on the spin results.
  * you spin a 13.  13/2 is "about 6, with some remainder" so you've rolled a 7 on your d10!
  * you spin a 21.  21/2 is "about 10, with some remainder" which would round up to 11.  You must *reroll* this die; it fell off the table.
  * you spin a 18.  18/2 is "9, no remainder" so you've rolled a 9.

Final example, the d20.  Your magic number here is 24/20 = 1.  No division necessary.  Just remember the second rule, to reroll overshoots.
  * you spin a 13.  You've rolled a 13 on a d20.
  * you spin a 21.  Respin!  This will happen the same 16.67% of the time as a d10.  Respinning any 21, 22, 23, or 24 that show up.

To recap all the possibilities (* indicates common gaming dice):

   d1 = you win, every time!
*  d2 = magic number 12, no rerolls
   d3 = magic number 8, no rerolls
*  d4 = magic number 6, no rerolls
   d5 = magic number 4, 16.6% rerolls
*  d6 = magic number 4, no rerolls
   d7 = magic number 3, 12.5% rerolls
*  d8 = magic number 3, no rerolls
   d9 = magic number 2, 25.0% rerolls
* d10 = magic number 2, 16.7% rerolls
  d11 = magic number 2, 8.3% rerolls
* d12 = magic number 2, no rerolls
  d13 = no magic number, just 45.8% rerolls - the worst case scenario, how unlucky.
  d14 = no magic number, just 41.6% rerolls
  d15 = no magic number, just 37.5% rerolls
  d16 = no magic number, just 33.3% rerolls
  d17 = no magic number, just 29.2% rerolls
  d18 = no magic number, just 25.0% rerolls
  d19 = no magic number, just 20.8% rerolls
* d20 = no magic number, just 16.7% rerolls
  d21 = no magic number, just 12.5% rerolls
  d22 = no magic number, just  8.3% rerolls
  d23 = no magic number, just  4.2% rerolls
  d24 = just read the number!
*d100 = two consecutive d10, respinning each on 21-24 results (16.7%)
d1000 = ok, now you're just being silly