This die defines your luck in life, and is rolled by your god of choice at every important event: roll a (0) you fail miserably, (6) you succeed briliantly, (4) you pass, barely.
Would you rather have:
A: a 000666 die?
B: a 111555 die?
C: a 222444 die?
D: a 333333 die?
Option C “222444”.
I coded successes as positive values and failures as negative values. I arbitrarily used a doubling for each greater success/failure level and came up with the following value coding:
This results in the following expected values for the offered dice:
A: -2
B: -1
C: -1/2
D: -1
All dice are bad, option C is the least bad. And this kinda makes sense. For option A, you may have a fantastic success, but you are also just as likely to complete crash out. And a “crash out” should happen after very few rolls. Option B is a slightly less extreme version of this, but any gains from the 5 results should be more than wiped out by the 1 results. And those should be happening with similar frequency. Option C is again the same thing, but with a slower circling of the drain. 4 results let you recover some, but the 2 wipes out that 4’s benefits and more resulting in a slow decline. And option D is just straight out bad, every result is a failure.
It seems that the only good choice is not to play. ;-)
EDIT: I realized, I made a mistake in my original numbers, I forgot to divide by 6. And this is why coffee should come before math. The conclusions are still the same, but the numbers are different. I’ve corrected those.