[Barkeep49]

Reading over my old Spawn games I came across a piece of math that bothered me at the time and I don't think I commented on it (being GM and all) but I think is important to get out there since I think statistics/probability offers a lot of value in WW and that value often goes untapped.

First a basic probability refresher:
Let's say you're flipping a coin. 50% comes up heads, 50% it comes up tails. So far so good. Now let's say you're flipping a coin 2 times. There are 4 possibilities that could happen for your two tosses:

Heads Heads
Heads Tails
Tails Heads
Tails Tails

There is, therefore, a 1/4 chance that the coin will come up heads both flips or tails both flips. Mathematically this is expressed as .5^2 in other words you multiply the chance that one particular event will happen (50% for heads) for each flip you're performing (2 flips) to find out the chance that this string of events will occur. Flip a coin 3 times and the math becomes .5^3 or about 13% that you'd get either all heads or all tails for those 3 flips.

Still with me, I hope.

So in WW it's easy to figure out the odds that in any particular group of people that there would be 1 wolf or at least would be easy if we knew definitively how many wolves there were in a game. For instance, if there were 4 wolves in a 20 person game, or a .2 chance that any one person is a wolf) if you randomly select groups of the following sizes here are the odds that at least one of the people in that group would be a wolf:

1 person = 20%
2 people = 36%
3 people = 49%
4 people = 59%

Click the spoiler for more a detailed explanation of how the math works there.

Spoiler

Because there is the possibility of multiple wolves you actually have to figure out the odds that all the people are human and then subtract that from 100. So while there is a 20% chance that someone is a wolf, there's an 80% chance that someone is a human.

So examining 1 person there's an 80% chance there is a human and 20% chance they're a wolf.
Examining two people there's a 64% chance (.8^2) they're both human and 36% chance they're a wolf.
3 people 51% chance human (.8^3) and so on

So if you just randomly take any random group of 4 people in a game of 20 players with 4 wolves you've got pretty decent odds of finding a wolf.

Now let's say you're the seer and you scan one of those 4 people and you find out they're not a wolf (or you're one of the 4 randomly selected people). What are the odds that at least one of the other 3 are a wolf?

Well since you know 100% for sure one of the people is not a wolf you would then have a 4 in 19 chance for each of the other people. This means that there is now a 49% chance that at least one of the people in that group of 4 is a wolf.

The math is

Spoiler

(1-(4/19))^3
It's only done 3 times because there is a 0% chance that one of your 4 randomly selected people is a wolf so you need only examine the other 3. It is also why you can do 4/19 rather than 4/20

There's a lot of other ways statistical analysis can be applied to WW and I'm happy to go over those ways if anyone wants because again I think some basic understanding of stats/probability can help with wolf finding analysis.

BTW this is the post with the bad math that caused me to write this up.