In post 312, Cerberus v666 wrote: In post 310, Gamma Emerald wrote: In post 271, Cerberus v666 wrote:I'm pretty sure purely random out of
5/22
is almost guaranteed to wind up with a scum. Purely random with a smaller number of people selected *might* be optimal, but really, I think that's a silly line to take.
huh?
23 total....FA is one of them, so 22 remaining...she picks *5* OTHER players...so 5/22 can be selected at most.
Assuming Frozen is town (18 / 23):
We have 17 town, 5 scum remaining.
The probability that Frozen picks an all town team is thus: (17 / 22) * (16 / 21) * (15 / 20) * (14 / 19) * (13 / 18) ~ 23.5%
Then the probability that Frozen picks at least once scum randomly is ~(100% - 23.5%) = 76.5%
Assuming Frozen is scum (5 / 23):
We have 18 town, 4 scum remaining.
The probability that the rest of the people Frozen picks are all town: (18 / 22) * (17 / 21) * (16 / 20) * (15 / 19) * (14 / 18) ~ 32.5%
Then the probability that the other members Frozen picks possess at least one scum is ~(100% - 32.5%) = 67.5%
The probability that the 5 members Frozen chooses contain at least one scum if Frozen chooses completely random is thus (18 / 23) * 76.5% + (5 / 23) * 67.5% ~ 75%. That's what the math says about this.
I'm not convinced though that choosing from a smaller pool will increase the odds, simply because that pool may contain multiple scum.... or it may not.