Friday, 23 March 2012

Lots of eyes, lots of muscles

Inevitably, there comes a time when, convinced that there's something there to find, the whole party all search the same place to make sure that somebody picks up something that everyone else has missed, or all try to open the same stuck door, or pick the same lock, or find the same traps, or whatever. Apart from the fact that it takes up valuable time, and thus increases the chance of being mutilated by some treasure-less wandering monster, it can certainly help swell the party's coffers.

Assuming there really is anything to be found, that is.

Of course you can always throw a die for each individual searcher (I like to use a different coloured d6 for each character so I know who has and hasn't succeeded, just in case they want to keep the news to themselves or something, the sneaky bastards).

However, if you want to skip over all that and get the show on the road, you can always convert all those individual rolls into one combined d100 roll.

The formula for finding the probability from a whole bunch of d6 (or any other die type) is this:

1 - [(chance of NOT showing the desired pips) to the power of (the total number of dice)]


Assuming that you might just want to know the numbers and not have to do a whole lot of tedious maths to find out, here are some I prepared earlier:

Number of d6 Chance of at least one 6 showing on a handful of d6:
1 - [(5/6)^N]
Chance of at least one 1 OR 2 showing on a handful of d6:
1 - [(2/3)^N]
1d6 16.7% 33.3%
2d6 30.6% 55.6%
3d6 42.1% 70.4%
4d6 51.8% 80.2%
5d6 59.8% 86.8%
6d6 66.5% 91.2%
7d6 72.1% 94.1%
8d6 76.7% 96.0%
9d6 80.6% 97.4%
10d6 83.9% 98.2%
11d6 86.5% 98.8%
12d6 88.7% 99.2%
13d6 90.6% 99.4%
14d6 92.2% 99.6%
15d6 93.5% 99.7%
16d6 94.6% 99.8%
17d6 95.4% 99.89%
18d6 96.2% 99.93%
19d6 96.9% 99.95%
20d6 97.4% 99.96%