Blitz 21 - Hope plus One ―kibou― [End]

[Ether]

I like how the first three pages of the dead PT are about how bleak everything is, and then we all just rose up as one and smashed the poor scumteam against the wall.

Those first three days were pretty miserable, though. I don't think I'm gonna post hydralogs for this one, they crossed the angst threshold at some point.

[Ether]

Yeah, we got pretty lucky with power role assignments. (Although Plotinus would probably have done better as vanilla; being a doctor threw them off. Not me, though. My incompetence went way past our role. Blitz games are hard.)

[Ether]

So I was waiting for Expedience to claim doctor, I admit. Ankamius and we were going to be tough for him to get through, but at least there was a time when we were lynchable. Ranger and Gorkington were never on the table.

And then I was going to hit him with NUMBERS. Assuming random kills and random protections among the vanillas, there'd be a 62.5% chance of one of us getting a protection in between Night 4 and Night 5, setting the game back to odds with an extra lynch and forcing a win anyway.

(There's a strategy that raises that to a 77.78% chance of forcing a win, by the way. But I'm going to leave that one as a puzzle. Good night!)

-Ether

Two weeks later:

SO ACTUALLY the real odds are 58.33% (7/12) and 72.22% (13/18). Sorry, I know I'm the only person who is bothered by this, but I couldn't let bad math stand. Carry on!

[Ether]

Spoiler: The math behind the 58.33%

Okay, so assume random kills and random protections, which is probably optimal anyway. The people who can be killed on Night 4 are:
{Antihero, Gorkington, Ranger, Wisdom}

There's a 3/8ths chance the town makes a protection successfully. That's a 1/4th chance Scatterplot protects the right person, minus the 1/16 chance Ankamius also tries to protect him or her. And then the reverse is also true for Ankamius.

(1/4 - 1/16) + (1/4 - 1/16)
= 3/16 + 3/16
= 3/8

(The mistake I made before was only subtracting 1/16 once. It's true that there's a 1/16 chance that any given person would be protected twice, but that chance affects both doctors.)

So that's Night 4. On to Night 5!

If the kill fails, town gets an extra lynch and can force a win. If it goes through, which happens 5/8ths of the time, assume a doctor gets lynched. Then there's 1 doctor left for Night 5 and 3 confirmed vanillas, so that's a 1/3 chance of a successful protection.

3/8 + (5/8 * 1/3)
= 9/24 + 5/24
= 7/12, or 58.33% chance of a forced town win

Spoiler: Hint

The town only needs to have three lynches if the scum can survive the first two.

Spoiler: Hint #2

If the town doesn't get any protections in, only one claimed doctor will be left standing at the end. Focus on how to make that player's life harder, because if they're town, you've already won anyway.

(I'll give a straight answer later!)

[Ether]

Well, for the sake of completeness:

Spoiler: Solution

Decide beforehand which doctor survives the two lynches, and make them claim their protection targets beforehand. If they're scum, the two real doctors now have a smaller pool to work with. If they're town, the odds of a successful protection drop to 33% for Night 4 and 0% for Night 5, but the last scum still gets lynched, so it's a moot point.