Just wanted to share this little fact with the mathematically inclined. While you could have anticipated that, I was able to figure out exactly by how much I should lower the difficulty in the NWoD (where it defaults to compared to the OWoD (where it defaults to 6) in order to get a similar increase in the chance of success when this power is applied (in the oWoD, it is lowered by two, in the nWoD you get the same effect by lowering the difficulty by only one). I plotted this as a function of d and r for ten sided dice, and lo and behold, changing the difficulty makes a huge difference, whereas changing the reroll threshold is virtually useless.
Maptool dicebox exploding dice series#
You can verify that the argument is strictly less than one, which is required for the series to converge, and the (textbook) result is then N = c_1 * sum from k=0 to k=infinity over (c_1 * c_e)^k
So the end result is, the average number of successes on a roll as defined at the top, taking all possible rerolls into account is So a single explosion happens with probabilityĬ_1 (simple success) * c_e (explodes) * c_1 (success on re-roll).Ĭ_1 (simple success) * c_e (explodes) * c_1 (success on re-roll) * c_e (explodes again) * c_1 (success on second reroll) If the roll was a success, which happens with probability c_1, AND it is above the reroll threshold, which happens in the fraction c_e = (s-r+1)/(s-d+1) of successful cases (again by just counting the exploding successes out of all possible successes). The simple chance for a die to yield a single success isĬ_1 = (s-d+1)/s, just by counting the number of results that are a success. To solve this puzzle and adequately balance the power in the NWoD system, I did some math: What is the expected average number of successes on a s-sided die, given it is a success on a roll of the difficulty d or higher, and you can reroll it on r or higher? Note that 1 < d <= r <= s for sensible results. Sounds nicer, but how exactly does the benefit compare to the one in the old world of darkness? Online I found another suggestion: lower the number on which the dice explodes. So, translating the super power from before boils down to adjusting dice (which tons of other powers already do: booooring). In the new world of darkness however, the difficulty is pretty much fixed and to modify the difficulty of a roll you get or lose dice. For this reason, some super powers affect the difficulty of rolls, fair enough.
In the old world of darkness, the difficulty of rolls was usually adjusted by raising or lowering the difficulty of the roll (that is, the target number you need to roll for the die to be counted as a success). For my New World of Darkness conversion of Orpheus, I ran into the following problem:
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